Applied Mathematics
[ APMA ] Program
William W. Roberts, Jr.
Director
School of Engineering and Applied Science
University of Virginia
Charlottesville, Virginia 22903, U.S.A.
wwr@virginia.edu
(434) 924 6216
Presentation at VCCS – UVA Engineering Coordination Meeting,
June 12, 2009
„
The Applied Mathematics Program coordinates
and administers applied mathematics instruction
through its APMA courses to undergraduate
and graduate students in all departments of
SEAS.
„
SEAS students constituted 2983 official APMA
course registrants during 2008-09 and completed
71 sections of APMA courses during 2008-09,
including seven APMA courses taught in the
2008 Summer Session
(Course Offering
Directory APMA enrollment figures).
„
The mathematical tools and expertise developed
through APMA courses are essential to the
professional development of the future engineer
and applied scientist.
„
The APMA applied mathematics instruction
forms the core of the analytical-mathematical
component of an engineering education and
lays the foundation for accelerated ongoing
professional development.
„
Extensive efforts have been made toward
continual improvement of the APMA Program
during 2008-09 and over the past five-year
period 2004-09.
„
Data for evaluating and assessing these
APMA improvements are available from several
sources.
„
Summary Tables of Topics and Subtopics in
APMA Courses (at the 100, 200, and 300
level).
Information Exchange, today?
„
Comprehensive Mathematics Instruction for
SEAS students in APMA Courses?
APMA Program improvement, contributing to levels of excellence
Standardized APMA Course Summary Tables of Topics and Subtopics [CSTTS] and
standardized APMA Beginning Of Course Memos [BOCs] and End Of Course Memos
[EOCs] have been enhanced over the past five-year period 2004-09 and now constitute
consistent, definitive criteria for assessing how well SEAS students learn the mathematics
covered and how well the students are able to demonstrate that knowledge, topic by topic
and subtopic by subtopic, by the times of the final examinations in all APMA courses.
CSTTSs for APMA Courses are included in the following pages.
Stewart’s Calculus 6th Ed
APMA 1090 (Section _ ) – Single Variable Calculus I
Section
2
2.1
2.2
2.3
2.4
2.5
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.7
4.9
4.10
5
5.1
5.2
5.3
5.4
5.5
6
6.1
6.2
6.3
6.4
6.5
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Proficiency
Rating
Limits
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
The Precise Definition of a Limit
Continuity
Derivatives
Derivatives and Rates of Change
The Derivative as a Function
Differentiation Formulas
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Rates of Changes in the Natural and Social Sciences
Related Rates
Linear Approximations and Differentials
Applications of Differentiation
Maximum and Minimum Values
The Mean Value Theorem
How Derivatives Affect the Shape of a Graph
Limits at Infinity; Horizontal Asymptotes
Summary of Curve Sketching
Optimization Problems
Newton’s Method
Antiderivatives
Integrals
Areas and Distances
The Definite Integral
The Fundamental Theorem of Calculus
Indefinite Integrals and the Net Change Theorem
The Substitution Rule
Applications of Integration
Areas Between Curves
Volumes
Volumes by Cylindrical Shells
Work
Average Value of a Function
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 1110 (Section _ ) – Single Variable Calculus II
Section
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
8
8.1
8.2
8.3
8.4
8.5
8.7
8.8
9
9.1
9.2
9.3
9.3
6.4
11
11.1
11.2
11.3
11.4
11.5
11.6
12
12.1
12.2
12.3
12.4
12.5
12.6
12.7
12.8
12.9
12.10
12.11
Problem
On Final
Exam
Topic
Stewart’s Calculus 6th Ed
Wgt
%
Average
%
Proficiency
Rating
Inverse Functions
Inverse Functions
Natural Logarithmic Function
Natural Exponential Function
General Logarithmic and Exponential Functions
Exponential Growth and Decay
Inverse Trigonometric Functions
Hyperbolic Functions
Indeterminate Forms and L’Hospital’s Rule
Techniques of Integration
Integration by Substitution
Integration by Parts
Trigonometric Integrals
Trigonometric Substitution
Integration of Rational Functions by Partial Fractions
Strategy for Integration
Approximate Integration
Improper Integrals
Further Applications of Integration
Arc Length
Area of a Surface of Revolution
Applications to Physics & Engineering – Hydro Force
Applications to Physics & Engineering – Moments
Applications to Physics & Engineering – Work
Parametric Equations & Polar Equations
Curves Defined by Parametric Equations
Calculus with Parametric Curves
Polar Coordinates
Areas & Lengths in Polar Coordinates
Conic Sections
Conic Sections in Polar Coordinates
Infinite Sequences & Series
Sequences
Series – Geometric Series and Divergence Test
Integral Test & p-Series
Comparison Test
Alternating Series
Absolute Convergence and the Ratio & Root Tests
Strategy for Testing Series
Power Series
Representation of Functions as Power Series
Taylor and Maclaurin Series
Applications of Taylor Polynomials
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 2120 (Section _ ) – Multivariable Calculus
Section
13
13.1
13.2
13.3
13.4
13.5
13.6
14
14.1
14.2
14.3
14.4
15
15.1
15.2
15.3
15.4
15.5
15.6
15.7
15.8
16
16.1
16.2
16.3
16.4
16.5
16.6
16.7
16.8
16.9
17
17.1
17.2
17.3
17.4
17.5
17.6
17.7
17.8
17.9
Stewart’s Calculus 6th Ed.
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Proficiency
Rating
Vectors and the Geometry of Space
3-D Coordinate System
Vectors
Dot Product
Cross Product
Equations of Lines and Planes
Cylinders & Quadric Surfaces
Vector Functions
Vector Functions & Space Curves
Derivatives & Integrals of Vector Functions
Arc Length & Curvature
Motion in Space: Velocity & Acceleration
Partial Derivatives
Functions of Several Variables
Limits & Continuity
Partial Derivatives
Tangent Planes & Linear Approximations
Chain Rule
Directional Derivatives & Gradients
Max & Min Values
Lagrange Multipliers
Multiple Integrals
Double Integrals over Rectangles
Iterated Integrals
Double Integrals over General Regions
Double Integrals over polar Coordinates
Applications of Double Integrals
Triple Integrals
Triple Integrals in Cylindrical Coord.
Triple Integrals in Spherical Coord.
Change of Variables in Multiple Integrals
Vector Calculus
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green’s Theorem
Curl and Divergence
Parametric Surfaces and Their Areas
Surface Integrals
Stokes’ Theorem
The Divergence Theorem
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 2130 (Section _ ) – Ord. Diff. Eqn.s Boyce & DiPrima’s Elem Diff Eqn.s & BVPs 8th Ed
Problem
On Final
Exam
Section
Topic
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.9
8
8.1
8.2
8.3
3&4
4.1
3.1, 4.2
3.2
3.3
3.4
3.5
3.6, 4.3
3.7, 4.4
3.8
3.9
5
5.5
6
6.1
6.2
6.3
6.4
6.5
6.6
7
7.1
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
First Order Differential Equations
Linear Equations
Separable Equations
Modeling with First Order Equations
Differences between Linear and Nonlinear Equations
Autonomous Equations
Exact Equations
Numerical Approximations: Euler’s Method
Miscellaneous Problems: First Order Equations
Numerical Methods
The Euler or Tangent Line Method
Improvements on the Euler Method
The Runge-Kutta Method
Higher Order Linear Equations
General Theory of nth Order Linear Equations
Homogeneous Equations with Constant Coefficients
Fundamental Solutions of Linear Homogeneous Equations
Linear Independence and the Wronskian
Complex Roots of the Characteristic Equation
Repeated Roots; Reduction of Order
Method of Undetermined Coefficients
Variation of Parameters
Mechanical and Electrical Vibrations
Forced Vibrations
Series Solutions of Second Order Linear Equations
Euler Equations
The Laplace Transform
Definition of the Laplace Transform
Solution of the Initial Value Problem
Step Functions
Diff. Equations with Discontinuous Forcing Functions
Impulse Functions
The Convolution Integral
Systems of First Order Linear Equations
Introduction
Review of Matrices
Systems of Linear Algebraic Equations
Basic Theory of Systems of First Order Linear Equations
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Fundamental Matrices
Repeated Eigenvalues
Nonhomogeneous Linear Systems
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Wgt
%
Average
%
/
/
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA 3080 (Section _ ) – Linear Algebra William’s Linear Algebra w. Appl.s 7th Ed
Problem
On Final
Exam
Section
Topic
1
1.1
1.2, 1.3
1.4
1.5
1.6
2
2.1
Linear Equations and Vectors
Matrices and Systems of Linear Equations
Gauss-Jordan Elimination, The Vector Space Rn
Basis and Dimension
Dot Product, Norm, Angle and Distance
Curve Fittings, Electrical Networks, …
Matrices and Linear Transformations
Addition, Scalar Multiplication, and Multiplication of
Matrices
Properties of Matrix Operations
Symmetric Matrices, The Inverse of a Matrix, …
Matrix Transformations, Rotations, …
Linear Transformations, Graphics
Markov Chains, Population Movements, …
Determinants and Eigenvectors
Introduction to & Properties of Determinants
Determinants, Matrix Inverses, and Systems of Linear
Equations
Eigenvalues and Eigenvectors
Google, Demography, Weather Prediction
General Vector Spaces
General Vector Spaces and Subspaces
Linear Combinations
Linear Dependence and Independence
Properties of Bases, Rank
Orthonormal Vectors and Projections
Kernel, Range, Rank/Nullity Theorem
One-to-One Transformations and Inverses
Transformations & Systems of Linear Eqn.s
Coordinate Representations
Coordinate Vectors
2.2
2.3, 2.4
2.5
2.6
2.8
3
3.1, 3.2
3.3
3.4
3.5
4
4.1
4.2
4.3
4.4, 4.5
4.6
4.7
4.8
4.9
5
5.1
5.2
Matrix Representations of Linear Transf.s
5.3
Diagonalization of Matrices
5.4
Quadratic Forms, Difference Equations, Normal
Modes
Inner Product Spaces
Inner Product Spaces
6
6.1
6.3
6.4
7
7.1, 7.2
7.3
7.4
Wgt
%
Average
%
Proficiency
Rating
Approximation of Functions, Coding Theory
Least Squares Curves
Numerical Methods
Gaussian Elimination, LU Decomposition
Practical Difficulties in Solving Systems
Iterative Methods for Solving Systems of Linear
Equations
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 3100 (Section _ ) – Probability Yates-Goodman’s Prob. & Stochastic Processes 2nd Ed
Section
1
1.1, 1.2, 1.3, 1.4
1.5, 1.6
1.7, 1.8
1.9, 1.10
2
2.1, 2.2
2.3
2.4, 2.5
2.6
2.7
2.8
2.9
3
3.1, 3.2
3.3
3.4
3.5
3.7
3.8
4
4.1, 4.2, 4.3
4.4, 4.5
4.6, 4.7
4.8, 4.9
4.10
5
5.1, 5.2
5.3, 5.4
6
6.1, 6.2
6.6, 6.7
7
7.1
7.2
7.3, 7.4
8
8.1, 8.2
8.3
9
9.1
9.2
9.3
10
10.5
10.6
Problem
On Final
Exam
Topic
Experiments, Models, and Probabilities
Set Theory, Probability Axioms
Conditional Probability, Independence
Sequential Experiments, Tree Diagrams, Counting Methods
Independent Trials, Reliability Problems
Discrete Random Variables
Definitions, Probability Mass Function (PMF)
Families of Discrete Random Variables (RVs)
Cumulative Distribution Function (CDF), Averages
Functions of a RV
Expected Value of a Derived RV
Variance and Standard Deviation
Conditional Probability Mass Function
Continuous Random Variables
CDF, Probability Density Function (PDF)
Expected Values
Families of Continuous RVs
Gaussian RVs
Probability Models of Derived RVs
Conditioning a Continuous RV
Pairs of Random Variables
Joint CDF, Joint PMF, Marginal PMF
Joint PDF, Marginal PDF
Functions of Two RV’s, Expected Values
Conditioning by an Event, Conditioning by a Random Variable
Independent RVs
Random Vectors
Prob. Models of N Random Variables, Vector Notation
Marginal Probability Functions, Independence
Sums of Random Variables
Expected Values of Sums, PDF of the Sum of Two RVs
Central Limit Theorem (CLT), Applications of CLT
Parameter Estimation Using the Sample Mean
Sample Mean: Expected Value and Variance
Deviation of a Random Variable from the Expected Value
Point Estimates of Model Parameters, Confidence Intervals
Hypothesis Testing
Significance Testing, Binary Hypothesis Testing
Multiple Hypothesis Test
Estimation of a Random Variable
Optimum Estimation Given Another Random Variable
Linear Estimation of X given Y
MAP and ML Estimation
Stochastic Processes
The Poisson Process
Properties of the Poisson Process
Final Exam Average
Number of Students Who Passed Final Exam/ Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Wgt
%
Average
%
/
/
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA 3110 (Section _ ) – Appl. Stat.s & Prob.
Section
1.1, 1.2
1.3
2.1
2.2
2.3
2.4
2.5
3.1
3.2
3.3
4.1
4.2
4.3
4.5
4.7
4.9
4.11
4.12
5.1
5.2
5.3
5.4
5.5
5.6
5.7
6.1
6.2
6.3
6.4
6.5
6.6
6.10
6.11
6.12, 6.13
7.1
7.2
7.3
9.1
9.4
10.1
10.2
Problem
On Final
Exam
Topic
Sampling and Descriptive Statistics
Sampling, Summary Statistics
Graphical Summaries
Probability
Basic Ideas
Counting Methods
Conditional Probability and Independence
Random Variables
Linear Functions of Random Variables
Propagation of Errors
Measurement Error
Linear Combinations of Measurements
Uncertainties for Functions of One Measurement
Commonly Used Distributions
Bernoulli
Binomial
Poisson
Normal
Exponential
Some Principles of Point Estimation
Central Limit Theorem
Simulation
Confidence Intervals
Large Sample – Mean
Proportions
Small Sample – Mean
Difference Between Two Means
Difference Between Two Proportions
Small Samples – Difference Between Two Means
Paired Data
Hypothesis Testing
Large Sample – Mean
Drawing Conclusions from Results
Proportion
Small Sample – Mean
Large Sample – Difference Between Two Means
Difference Between Two Proportions
Chi-Square Test
F test for Equality of Variance
Fixed Level Testing, Power
Correlation and Simple Linear Regression
Correlation
Least-Squares Line
Uncertainties in Least Squares Coefficient
Factorial Experiments
One-Factor Experiments
Randomized Complete Block Design
Statistical Quality Control
Basic Ideas
Control Charts for Variables
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Navidi’s Stat.s for Engr.s & Scientists 2nd Ed
Good (75 – 89 %)
Wgt
%
Average
%
Proficiency
Rating
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 3120 (Section _ ) – Statistics Devore’s Prob. & Statistics for Engr & Sci 7th Ed
Section
CH 6
6.1
6.2
CH 7
7.1
7.2
7.3
7.4
CH 8
8.1
8.2
8.3
8.4
8.5
Ch 9
9.1
9.2
9.3
9.4
9.5
CH 10
10.1
10.2
10.3
CH 12
12.1
12.2
12.3
12.4
12.5
CH 15
15.1
15.2
15.3
15.4
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Point Estimation
Some general concepts of Point Estimation
Methods of Point Estimation
Statistical Intervals Based on a Single Sample
Basic Properties of Confidence Intervals
Large-Sample Confidence Intervals
Confidence Intervals on a Normal Population
Confidence Intervals for Variances and Stds
Tests of Hypotheses Based on a Single Sample
Hypotheses and Test Procedures
Tests about Population Mean
Tests about Population Proportion
P-Values
Some Comments on Selecting a Test
Inferences Based on Two Samples
Two sample z-Tests and Confidence Intervals
Two sample t-Test and Confidence Intervals
Analysis of Paired Data
Inferences concerning a Difference between Population
Proportions
Inferences concerning two Population Variances
Analysis of Variance
Single-Factor ANOVA
Multiple Comparisons in ANOVA
More on Single-Factor ANOVA
Simple Linear Regression and Correlation
Simple Linear Regression Model
Estimating Model Parameters
Inferences about the Slope Parameters
Inferences about the Prediction of Future Y Values
Correlation
Distribution-Free Procedures
Wilcoxon Signed-Rank Test
Wilcoxon Rank-Sum Test
Distribution-Free Confidence Intervals
Distribution-Free ANOVA
Final Exam Average
Number of Students who Passed Final Exam/Course
Number of Students who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA 3140 (Sec 1) - Partial Diff. Eqn.s Haberman’s Appl. PDEs .. 4th Ed
Section
1
1.1, 1.2
1.3
1.4
1.5
2
2.1, 2.2
2.3
2.4
2.5
3
3.1, 3.2
3.3
3.4
3.5
4
4.1, 4.2
4.3
4.4
4.5
5
5.1, 5.2, 5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
6
6.1, 6.2
6.3
7
7.1, 7.2
7.3
7.4
7.5
7.6
7.7, 7.8
7.9
7.10
8
8.1, 8.2
8.3
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Proficiency
Rating
Heat Equation
Derivation of the Conduction of Heat in a 1D Rod
Boundary Conditions
Equilibrium Temperature Distribution
Derivation of the Heat Equation in 2D and 3D
Method of Separation of Variables
Linearity
Heat Equation with Zero Temperatures at Finite Ends
Heat Equation: Other Boundary Value Problems
Laplace’s Equation: Solutions and Properties
Fourier Series
Statement of Convergence Theorem
Fourier Cosine and Sine Series
Term-by-Term Differentiation of Fourier Series
Term-by-Term Integration of Fourier Series
Wave Equation: Vibrating Strings and Membranes
Derivation of a Vertically Vibrating String
Boundary Conditions
Vibrating String with Fixed Ends
Vibrating Membrane
Sturm-Liouville (SL) Eigenvalue Problems
Examples, SL Eigenvalue Problems
Heat Flow in A Nonuniform Rod without Sources
Self-Adjoint Operators, SL Eigenvalue Problems
Rayleigh Quotient
Vibrations of a Nonuniform String
Boundary Conditions of the Third Kind
Large Eigenvalues (Asymptotic Behavior)
Approximation Properties
Finite Difference Numerical Methods of Partial
Differential Equations
Finite Differences and Truncated Taylor Series
Heat Equation
Higher Dimensional Partial Differential Equations
Separation of the Time Variable
Vibrating Rectangular Membrane
Statements and Illustrations of Theorems
Green’s Formula, Self-Adjoint Operators, Multidimensional
Eigenvalue Problems
Rayleigh Quotient and Laplace’s Equation
Vibrating Circular Membrane, Bessel Functions
Laplace’s Equation in a Circular Cylinder
Spherical Problems and Legendre Polynomials
Nonhomogeneous Problems
Heat Flow with Sources and Nonhomogeneous
Boundary Conditions (BCs)
Method of Eigenfunction Expansion - Homogeneous BCs
(Differentiating Series of Eigenfunctions)
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Objectives/
Outcomes
Evaluated
APMA 3340 – Complex Variables
Section
1
1.1
1.2
1.3
1.4, 1.5
1.6, 1.7
2
2.1
2.2, 2.3
2.4, 2.5
2.6
3
3.1
3.2
3.3
3.4
3.5
4
4.1, 4.2
4.3, 4.4
4.5
4.6
5
5.1
5.2, 5.3
5.4, 5.5
5.6, 5.7
6
6.1
6.2
6.3,6.4,6.5
6.6
6.7
7
7.1
7.2,7.3,7.4
7.5
7.6
7.7
8
8.1
8.2, 8.3
8.4
8.5
Saff & Snider’s …Complex Analysis 3rd Ed
Problem
On Final
Exam
Topic
Complex Numbers
The Algebra of Complex Numbers
Point Representation of Complex Numbers
Vectors and Polar Forms
The Complex Exponential, Powers and Roots
Planar Sets, The Riemann Sphere
Analytic Functions
Functions of a Complex Variable
Limits and Continuity, Analyticity
The Cauchy-Riemann Equations, Harmonic Fct.s
Steady-State Temperature as a Harmonic Function
Elementary Functions
Polynomials and Rational Functions
The Exponential, Trigonometric, & Hyperbolic Fct.s
The Logarithmic Function
Washers, Wedges, and Walls
Complex Powers and Inverse Trigonometric Fct.s
Complex Integration
Contours, Contour Integrals
Independence of Path, Cauchy’s Integral Theorem
Cauchy’s Integral Formula and Its Consequences
Bounds for Analytic Functions
Series Representations for Analytic Functions
Sequences and Series
Taylor Series, Power Series
Convergence, Laurent Series
Zeros and Singularities, The Point at Infinity
Residue Theory
The Residue Theorem
Trigonometric Integrals
Improper Integrals, Indented Contours
Integrals Involving Multiple-Valued Functions
The Argument Principle and Rouche’s Theorem
Conformal Mapping
Invariance of Laplace’s Equation
Geometric Considerations, Mobius Transformations
The Schwarz-Christoffel Transformation
Applications: Electrostatics, Heat Flow, Fluid Mech.s
Further Physical Applications of Conformal Mapping
The Transforms of Applied Mathematics
Fourier Series ( The Finite Fourier Transform)
The Fourier Transform, The Laplace Transform
The z-Transform
Cauchy Integrals and the Hilbert Transform
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Wgt
%
Average
%
/
/
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA 5070 – Numerical Methods Cheney & Kincaid’s Num. Math & Comp. 6th Ed
Problem
On Final
Exam
Section
Topic
1
1.1, 1.2
2
2.1
2.2
3
3.1,3.2,
3.3
4
4.1
4.2
4.3
5
5.1
5.2, 5.3
6
6.1
6.2
7
7.1
7.2
7.3
10
10.1,
10.2
10.3
Introduction
Preliminary Remarks, Review of Taylor Series
Floating-Point Representation and Errors
Floating-Point Representation
Loss of Significance
Locating Roots of Equations
Bisection, Newton’s, and Secant Methods
11
11.1
11.2
11.3
13
13.1
13.2
13.3
14
14.1, 14.2
15
15.1
15.2
15.3
Interpolation and Numerical Differentiation
Polynomial Interpolation
Errors in Polynomial Interpolation
Estimating Derivatives and Richardson Extrapolation
Numerical Integration
Lower and Upper Sums
Trapezoid Rule, Romberg Algorithm
Additional Topics on Numerical Integration
Simpson’s Rule and Adaptive Simpson’s Rule
Gaussian Quadrature Formulas
Systems of Linear Equations
Naive Gaussian Elimination
Gaussian Elimination with Scaled Partial Pivoting
Tridiagonal and Banded Systems
Ordinary Differential Equations
Taylor-Series Methods
Runge-Kutta Methods
Stability and Adaptive Runge-Kutta and Multistep
Methods
Systems of Ordinary Differential Equations
Methods for First-Order Systems
Higher-Order Equations and Systems
Adams-Bashforth-Moulton Methods
Monte Carlo Methods and Simulation
Random Numbers
Estimation of Areas and Volumes by Monte Carlo
Techniques
Simulation
Boundary-Value Problems for Ordinary Differential
Equations
Shooting Method, A Discretization Method
Partial Differential Equations
Parabolic Problems
Hyperbolic Problems
Elliptic Problems
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Wgt
%
Average
%
/
/
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA 6410-Review.Beginning.Engr.Math.I Greenberg’s Adv.Engr.Math.
Section
1
1.1, 1.2, 1.3
2
2.1, 2.2, 2.3
2.4
2.5
3
3.1, 3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1, 4.2
4.3
4.4
4.5
4.6
5
5.1, 5.2
5.3
5.4
5.5
5.6
5.7
6
6.1, 6.2
6.3
6.4
6.5
7
7.1, 7.2
7.3, 7.4
7.5
7.6
8
8.1, 8.2
8.3
9
9.1, 9.2
9.3
9.4 ,9.5
9.6
9.7
9.8
9.9
9.10
Topic
Problem On
Beginning
Review Test
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
Introduction to Differential Equations
Definitions, Introduction to Modeling
Equations Of First Order
The Linear Equation, Applications
Separable Equations
Exact Equations and Integrating Factors
Linear Differential Equations of Second Order and
Higher
Linear Dependence and Linear Independence
Homogeneous Equation: General Solution
Solution of Homogeneous Equation: Constant Coefficients
Application to Harmonic Oscillator: Free Oscillation
Solution of Homogeneous Equation: Nonconstant Coeff.s
Solution of Nonhomogeneous Equation
Application to Harmonic Oscillator: Forced Oscillation
Systems of Linear Differential Equations
Power Series Solutions
Power Series Solutions
The Method of Frobenius
Legendre Functions
Singular Integrals; Gamma Function
Bessel Functions
Laplace Transform
Calculation of the Transform
Properties of the Transform
Application to the Solution of Differential Equations
Discontinuous Forcing Functions; Heaviside Step Function
Impulsive Forcing Functions; Dirac Impulse Function
Additional Properties
Quantitative Methods: Numerical Solution of Differential
Equations
Euler’s Method
Improvements: Midpoint Rule and Runge-Kutta
Application to Systems and Boundary Value Problems
Stability and Difference Equations
Qualitative Methods: Phase Plane and Nonlinear
Differential Equations
The Phase Plane
Singular Points and Stability, Applications
Limit Cycles, van der Pol equation, …
The Duffing Equation: Jumps and Chaos
Systems of Linear Algebraic Equations: Gauss
Elimination
Preliminary Ideas and Geometrical Approach
Solution by Gauss Elimination
Vector Space
Vectors; Geometrical Representation
Introduction of Angle and Dot Product
n-Space , Dot Product, Norm, and Angle for n-Space
Generalized Vector Space
Span and Subspace
Linear Dependence
Bases, Expansions, Dimension
Best Approximation
PAGE 1 of 2
APMA 6410-Review.Beginning.Engr.Math.I Greenberg’s Adv.Engr.Math.
Section
10
10.1, 10.2
10.3, 10.4
10.5
10.6
10.7, 10.8
11
11.1, 11.2
11.3, 11.4
11.5
11.6
12
12.1, 12.2
12.3
13
13.1,13.2
13.3
13.4
13.5
13.6
13.7
13.8
14
14.1, 14.2
14.3
14.4
14.5
14.6
15
15.1, 15.2
15.3
15.4
15.5
15.6
16
16.1, 16.2, 16.3
16.4, 16.5
16.6
16.7
16.8
16.9
16.10
Topic
Problem On
Beginning
Review Test
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
Matrices and Linear Equations
Matrices and Matrix Algebra
The Transpose Matrix, Determinants
Rank; Application to Linear Dependence, to Existence and
Uniqueness for Ax = c
Inverse Matrix, Cramer’s Rule, Factorization
Change of Basis, Vector Transformation
The Eigenvalue Problem
Solution Procedure and Applications
Symmetric Matrices, Diagonalization
Application to First Order Systems with Constant Coefficients
Quadratic Forms
Extension to Complex Case
Complex n-Space
Complex Matrices
Differential Calculus of Functions of Several Variables
Preliminaries
Partial Derivatives
Composite Functions and Chain Differentiation
Taylor’s Formula and Mean Value Theorem
Implicit Functions and Jacobians
Maxima and Minima
Leibniz Rule
Vectors In 3-Space
Dot and Cross Product
Cartesian Coordinates
Multiple Products
Differentiation of a Vector Function of a Single Variable
Non-Cartesian Coordinates
Curves, Surfaces, and Volumes
Curves and Line Integrals
Double and Triple Integrals
Surfaces
Surface Integrals
Volumes and Volume Integrals
Scalar and Vector Field Theory
Preliminaries; Divergence
Gradient; Curl
Combinations; Laplacian
Non-Cartesian Systems; Div, Grad, and Laplacian
Divergence Theorem
Stokes’s Theorem
Irrotational Fields
PAGE 2 of 2
APMA 6410 – Engineering Math. I Haberman’s Appl.PDEs…4th Ed
Section
1
1.1, 1.2
1.3
1.4
1.5
2
2.1, 2.2
2.3
2.4
2.5
3
3.1, 3.2
3.3
3.4
3.5
4
4.1, 4.2
4.3
4.4
4.5
5
5.1, 5.2, 5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
6
6.1, 6.2
6.3
7
7.1, 7.2
7.3
7.4
7.5
7.6
7.7, 7.8
7.9
7.10
8
8.1, 8.2
8.3
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
Heat Equation
Derivation of the Conduction of Heat in a 1D Rod
Boundary Conditions
Equilibrium Temperature Distribution
Derivation of the Heat Equation in 2D and 3D
Method of Separation of Variables
Linearity
Heat Equation with Zero Temperatures at Finite Ends
Heat Equation: Other Boundary Value Problems
Laplace’s Equation: Solutions and Properties
Fourier Series
Statement of Convergence Theorem
Fourier Cosine and Sine Series
Term-by-Term Differentiation of Fourier Series
Term-by-Term Integration of Fourier Series
Wave Equation: Vibrating Strings and Membranes
Derivation of a Vertically Vibrating String
Boundary Conditions
Vibrating String with Fixed Ends
Vibrating Membrane
Sturm-Liouville (SL) Eigenvalue Problems
Examples, SL Eigenvalue Problems
Heat Flow in A Nonuniform Rod without Sources
Self-Adjoint Operators, SL Eigenvalue Problems
Rayleigh Quotient
Vibrations of a Nonuniform String
Boundary Conditions of the Third Kind
Large Eigenvalues (Asymptotic Behavior)
Approximation Properties
Finite Difference Numerical Methods of Partial
Differential Equations
Finite Differences and Truncated Taylor Series
Heat Equation
Higher Dimensional Partial Differential Equations
Separation of the Time Variable
Vibrating Rectangular Membrane
Statements and Illustrations of Theorems
Green’s Formula, Self-Adjoint Operators, Multidimensional
Eigenvalue Problems
Rayleigh Quotient and Laplace’s Equation
Vibrating Circular Membrane, Bessel Functions
Laplace’s Equation in a Circular Cylinder
Spherical Problems and Legendre Polynomials
Nonhomogeneous Problems
Heat Flow with Sources and Nonhomogeneous
Boundary Conditions (BCs)
Method of Eigenfunction Expansion - Homogeneous BCs
(Differentiating Series of Eigenfunctions)
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Page 1 of 2
APMA 6410 – Engineering Math. I Greenberg’s Adv.Engr.Math…2nd Ed
Section
17
17.1
17.2
17.3
17.3.1
17.3.2
17.3.3
17.3.4
17.4
17.7
17.7.1
17.7.2
17.8
18
18.1
18.2
18.2.1
18.2.2
18.2.3
18.3
18.3.1
18.3.2
18.3.3
19
19.1
19.2
19.2.1
19.2.2
19.2.3
19.3
19.4
19.4.1
20
20.1
20.2
20.3
20.3.1
20.3.2
20.3.3
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
Fourier Series, Fourier Integral, Fourier
Transform
Introduction
Even, Odd, and Periodic Functions
Fourier Series of a Periodic Function
Fourier series
Euler’s formulas
Applications
Complex exponential form for Fourier series
Half- and Quarter- Range Expansions
The Sturm-Liouville Theory
Sturm-Liouville problem
Lagrange identity and proofs
Periodic and Singular Sturm-Liouville Problems
Diffusion Equation
Introduction
Preliminary Concepts
Definitions
Second-order linear equations and their classification
Diffusion equation and modeling
Separation of Variables
The method of separation of variables
Verification of solution
Use of Sturm-Liouville theory
Wave Equation
Introduction
Separation of Variables; Vibrating String
Solution by separation of variables
Traveling wave interpretation
Using Sturm-Liouville theory
Separation of Variables; Vibrating Membrane
Vibrating String; d’Alembert’s Solution
d’Alembert’s solution
Laplace Equation
Introduction
Separation of Variables; Cartesian Coordinates
Separation of Variables; Non-Cartesian Coordinates
Plane polar coordinates
Cylindrical coordinates
Spherical coordinates
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Poor (< 60 %)
Page 2 of 2
APMA 6420 – Engineering Mathematics II Haberman’s Applied PDEs … 4th Ed
Section
6
6.1, 6.2
6.3
8
8.1, 8.2
8.3
8.4
8.5
8.6
9
9.1, 9.2
9.3
9.4
9.5
10
10.1, 10.2
10.3
10.4
10.5
10.6
11
11.1, 11.2
11.3
13
13.1, 13.2
13.3
13.4
13.5
13.6
13.7
13.8
Problem
On Final
Exam
Topic
Finite Difference Numerical Methods for Partial
Differential Equations
Finite Differences and Truncated Taylor Series
Heat Equation
Nonhomogeneous Problems
Heat Flow with Sources and Nonhomogeneous
Boundary Conditions (BCs)
Method of Eigenfunction Expansion - Homogeneous
BCs (Differentiating Series of Eigenfunctions )
Method of Eigenfunction Expansion Using Green’s
Formula (With or Without Homogeneous BCs)
Forced Vibrating Membranes and Resonance
Poisson’s Equation
Green’s Functions for Time-Independent Problems
One-dimensional Heat Equation
Green’s Functions for Boundary Value Problems for
Ordinary Differential Equations
Fredholm Alternative and Generalized Green’s
Functions
Green’s Functions for Poisson’s Equation
Infinite Domain Problems: Fourier Transform
Solutions of Partial Differential Equations
Heat Equation on an Infinite Domain
Fourier Transform Pair
Fourier Transform and the Heat Equation
Fourier Sine and Cosine Transforms
Worked Examples Using Transforms
Green’s Functions for Wave and Heat Equations
Green’s Functions for the Wave Equations
Green’s Functions for the Heat Equation
Laplace Transform Solution of Partial Differential
Equations
Properties of the Laplace Transform
Green’s Functions for Initial Value Problems for
Ordinary Differential Equations
A Signal Problem for the Wave Equation
A Signal Problem for a Vibrating String of Finite Length
The Wave Equation and its Green’s Function
Inversion of Laplace Transforms Using Contour
Integrals in the Complex Plane
Solving the Wave Equation Using Laplace Transforms
(with Complex Variables)
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Wgt
%
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
/
/
Fair (60 – 74 %)
Poor (< 60 %)
Page 1 of 2
APMA 6420 – Engineering Math. II Greenberg’s Adv.Engr.Math..2nd Ed
Section
21
21.1
21.2
21.3
21.3.1
21.3.2
21.3.3
21.3.4
Problem
On Final
Exam
Topic
24.1
24.2
24.2.1
24.2.2
24.3
24.4
Functions of a Complex Variable
Introduction
Complex Numbers and the Complex Plane
Elementary Functions
Preliminary ideas
Exponential function
Trigonometric and hyperbolic functions
Application of complex numbers to integration and
the solution of differential equations
Polar Form, Additional Elementary Functions, and
Multi-valuedness
Polar form
Integral powers of z and de Moivre’s formula
Fractional powers
The logarithm of z
General powers of z
Obtaining single-valued functions by branch cuts
More about branch cuts
The Differential Calculus and Analyticity
The Complex Integral Calculus
Introduction
Complex Integration
Definition and properties
Bounds
Cauchy’s Theorem
Fundamental Theorem of the Complex Integral
Calculus
Cauchy’s Integral Formula
Taylor’s Series, Laurent Series, and the Residue
Theorem
Introduction
Complex Series and Taylor Series
Complex Series
Taylor Series
Laurent Series
Classification of Singularities
24.5
24.5.1
24.5.2
24.5.3
Residue Theorem
Residue theorem
Calculating residues
Applications of the residue theorem
21.4
21.4.1
21.4.2
21.4.3
21.4.4
21.4.5
21.4.6
21.4.7
21.5
23
23.1
23.2
23.2.1
23.2.2
23.3
23.4
23.5
24
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
Wgt
%
Average
%
Proficiency
Rating
Objectives/
Outcomes
Evaluated
Poor (< 60 %)
Page 2 of 2
APMA 6430 – Statistics for Engr.s & Sci. Milton & Arnold’s Intr. Prob. & Stat.s
Section
1
1.1, 1.2, 1.3
2
2.1, 2.2
2.3, 2.4
3
3.1, 3.2
3.3, 3.4
3.5 - 3.9
4
4.1, 4.2
4.3, 4.4
4.5, 4.6, 4.7
4.8, 4.9
5
5.1, 5.2
5.3, 5.4, 5.5
7
7.1, 7.2
7.3, 7.4
8
8.1
8.2
8.3 - 8.6, 8.7
9
9.1, 9.2
9.3, 9.4
10
10.1
10.2
10.3, 10.4
10.5
10.6
11
11.1, 11.2
11.3
11.4 - 11.6
13
13.1
13.2 - 13.4
13.5 - 13.9
16
16.1 - 16.3
16.4 - 16.7
Problem
On Final
Exam
Topic
Wgt
%
Average
%
Introduction to Probability and Counting
Sample Spaces, Events, Permutations, Combinations
Some Probability Laws
Axioms, Conditional Probability
Independence, Bayes’ Theorem
Discrete Distributions
Random Variables, Discrete Probability Densities
Expectation, Geometric Distr., Moment Generating Fct.
Binomial, Neg. Binom., Hypergeom., Poisson Distr.s, ...
Continuous Distributions
Densities, Expectation, Distribution Parameters
Gamma, Exponential, Chi-Squared, Normal Distr.s
Chebyshev’s Inequality, Weibull Distr. and Reliability
Transform. of Variables, Simulating a Continuous Distr.
Joint Distributions
Joint Densities, Independence, Expectation, Covariance
Correlation, Conditional Densities, Regression, …
Estimation
Point Estimation, Method of Moments, Max. Likelihood
Functions of Random Var.s, Interval Estimation, CLT
Inferences on the Mean & Variance of a Distribution
Interval Estimation of Variability
Estimating the Mean, the Student-t Distribution
Hypothesis Testing, Significance Testing, …
Inferences on Proportions
Estimating & Testing Hypotheses on a Proportion
Comparing Proportions: Estimation, Hypothesis Testing
Comparing Two Means and Two Variances
Point Estimation: Independent Samples
Comparing Variances: The F Distribution
Comparing Means: Variances Equal and Unequal
Comparing Means: Paired Data
Alternative Nonparametric Methods
Simple Linear Regression and Correlation
Model - Parameter Estimation, Least-Squares Estimators
Confidence Interval Estimation and Hypothesis Testing
Rep. Meas.s, Lack of Fit, Residual Analysis, Correlation
Analysis of Variance
One-Way Classification Fixed-Effects Model
Comparing Variances, Pairwise Comp.s, Test Contrasts
Randomized Block Design, Random-Effects Models, …
Statistical Quality Control
Control Charts
Tolerance Limits, Acceptance Sampling, …
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
Excellent (≥ 90 %)
Good (75 – 89 %)
Fair (60 – 74 %)
/
/
Poor (< 60 %)
Proficiency
Rating
Objectives/
Outcomes
Evaluated
APMA-Math.Prep.for.Grad.Engr.
Section
1
1.1, 1.2, 1.3
2
2.1, 2.2, 2.3
2.4
2.5
3
3.1, 3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1, 4.2
4.3
4.4
4.5
4.6
5
5.1, 5.2
5.3
5.4
5.5
5.6
5.7
6
6.1, 6.2
6.3
6.4
6.5
7
7.1, 7.2
7.3, 7.4
7.5
7.6
8
8.1, 8.2
8.3
9
9.1, 9.2
9.3
9.4 ,9.5
9.6
9.7
9.8
9.9
9.10
Greenberg’s Adv. Engr. Math. 2nd Ed
Topic
Problem
On Final
Exam
Problem
Average
Proficiency
Rating
Goals
Evaluated
Introduction to Differential Equations
Definitions, Introduction to Modeling
Equations Of First Order
The Linear Equation, Applications
Separable Equations
Exact Equations and Integrating Factors
Linear Differential Equations of Second Order and
Higher
Linear Dependence and Linear Independence
Homogeneous Equation: General Solution
Solution of Homogeneous Equation: Constant Coefficients
Application to Harmonic Oscillator: Free Oscillation
Solution of Homogeneous Equation: Nonconstant Coeff.s
Solution of Nonhomogeneous Equation
Application to Harmonic Oscillator: Forced Oscillation
Systems of Linear Differential Equations
Power Series Solutions
Power Series Solutions
The Method of Frobenius
Legendre Functions
Singular Integrals; Gamma Function
Bessel Functions
Laplace Transform
Calculation of the Transform
Properties of the Transform
Application to the Solution of Differential Equations
Discontinuous Forcing Functions; Heaviside Step Function
Impulsive Forcing Functions; Dirac Impulse Function
Additional Properties
Quantitative Methods: Numerical Solution of Differential
Equations
Euler’s Method
Improvements: Midpoint Rule and Runge-Kutta
Application to Systems and Boundary Value Problems
Stability and Difference Equations
Qualitative Methods: Phase Plane and Nonlinear
Differential Equations
The Phase Plane
Singular Points and Stability, Applications
Limit Cycles, van der Pol equation, …
The Duffing Equation: Jumps and Chaos
Systems of Linear Algebraic Equations: Gauss
Elimination
Preliminary Ideas and Geometrical Approach
Solution by Gauss Elimination
Vector Space
Vectors; Geometrical Representation
Introduction of Angle and Dot Product
n-Space , Dot Product, Norm, and Angle for n-Space
Generalized Vector Space
Span and Subspace
Linear Dependence
Bases, Expansions, Dimension
Best Approximation
PAGE 1 of 2
APMA-Math.Prep.for.Grad.Engr.
Section
10
10.1, 10.2
10.3, 10.4
10.5
10.6
10.7, 10.8
11
11.1, 11.2
11.3, 11.4
11.5
11.6
12
12.1, 12.2
12.3
13
13.1,13.2
13.3
13.4
13.5
13.6
13.7
13.8
14
14.1, 14.2
14.3
14.4
14.5
14.6
15
15.1, 15.2
15.3
15.4
15.5
15.6
16
16.1, 16.2, 16.3
16.4, 16.5
16.6
16.7
16.8
16.9
16.10
Greenberg’s Adv. Engr. Math. 2nd Ed
Problem
On Final
Exam
Topic
Problem
Average
Proficiency
Rating
Goals
Evaluated
Matrices and Linear Equations
Matrices and Matrix Algebra
The Transpose Matrix, Determinants
Rank; Application to Linear Dependence, to Existence and
Uniqueness for Ax = c
Inverse Matrix, Cramer’s Rule, Factorization
Change of Basis, Vector Transformation
The Eigenvalue Problem
Solution Procedure and Applications
Symmetric Matrices, Diagonalization
Application to First Order Systems with Constant Coefficients
Quadratic Forms
Extension to Complex Case
Complex n-Space
Complex Matrices
Differential Calculus of Functions of Several Variables
Preliminaries
Partial Derivatives
Composite Functions and Chain Differentiation
Taylor’s Formula and Mean Value Theorem
Implicit Functions and Jacobians
Maxima and Minima
Leibniz Rule
Vectors In 3-Space
Dot and Cross Product
Cartesian Coordinates
Multiple Products
Differentiation of a Vector Function of a Single Variable
Non-Cartesian Coordinates
Curves, Surfaces, and Volumes
Curves and Line Integrals
Double and Triple Integrals
Surfaces
Surface Integrals
Volumes and Volume Integrals
Scalar and Vector Field Theory
Preliminaries; Divergence
Gradient; Curl
Combinations; Laplacian
Non-Cartesian Systems; Div, Grad, and Laplacian
Divergence Theorem
Stokes’s Theorem
Irrotational Fields
PAGE 2 of 2
Final Exam Average
Number of Students Who Passed Final Exam/Course
Number of Students Who Failed Final Exam/Course
/
/
„
Assessing mathematics ability / quantitative
reasoning?
How competent are our
SEAS undergraduates?
„
In the 2008 University-wide Mathematics
Quantitative Reasoning Test / Assessment,
SEAS students scored the highest and were
Number 1 across the University
(Office
of Institutional Assessment and Studies).
Excellence demonstrated by SEAS students: Highest Score and Number 1 Rating in
the 2008 University-wide Mathematics Quantitative Reasoning Testing / Assessment
This past year in the 2008 University-wide Mathematics Quantitative Reasoning Testing /
Assessment, the School of Engineering and Applied Science students scored the highest
and excelled with the Number 1 rating among the students in all Schools across the
University – spanning Architecture [ARCH], Continuing and Professional Studies [BIS],
Commerce [COMM], Engineering and Applied Science [SEAS], Nursing [NU],
Humanities and Fine Arts [CLAS], Science/Mathematics [CLAS], and Social Science
[CLAS]. The bar graph, that follows, illustrates the “Mean” and “Median” total scores
and the highest performance and Number 1 rating demonstrated by the SEAS students in
comparison with other Schools’ students, such as Science/Mathematics majors in CLAS.
U.Va. Quantitative Reasoning, 2008
ARCHITECTURE
24.00
BIS
22.00
COMMERCE
20.00
ENGINEERING /
APPLIED SCIENCE
18.00
NURSING
16.00
14.00
HUMANITIES /
FINE ARTS
12.00
SCIENCE /
MATHEMATICS
10.00
SOCIAL SCIENCE
1
MEAN TOTAL SCORE- 1
2
MEDIAN TOTAL SCORE - 2
( MAXIMUM TOTAL SCORE = 30.00 )
ALL 4th YEAR
STUDENTS
„
In the student evaluations completed online
at the end of each semester, are APMA
courses and the professors teaching APMA
courses rated highly on average?
„
Final Exams in APMA Courses available
(representative final exams), if requested?
Information Exchange, after today?
High Ratings of APMA Courses and the Professors teaching APMA Courses
SEAS students generally seem to appreciate the APMA Program and on the whole give
high ratings to the APMA Courses and to the Professors teaching APMA Courses in their
course/instructor evaluations. The four bar graphs that follow, with data taken from the
SEAS students’ course/instructor evaluations, illustrate the high ratings of APMA
courses and the Professors teaching APMA courses during 2008-09 and also over the
five-year period 2004-09, since Summer of 2004 when considerable APMA
improvements were initiated.
Specifically in the first bar graph that follows, a comparison of the APMA Course
Means” reveals that 75 percent, 73 percent, 73 percent, 70 percent, and 76 percent of the
“APMA Course Means” were greater than or equal to the “long-term” average value of
3.97 / 5.00 for the 2008-09, 2007-08, 2006-07, 2005-06, and 2004-05 academic years
respectively, compared to a corresponding 7 percent and 19 percent for the 2003-04 and
2002-03 academic years.
Similarly in the second bar graph that follows, a comparison of the “APMA Professor
Means” reveals that 56 percent, 66 percent, 57 percent, 66 percent, and 68 percent of the
“APMA Professor Means” were greater than or equal to the “long-term” average value of
3.97 / 5.00 for the 2008-09, 2007-08, 2006-07, 2005-06, and 2004-05 academic years
respectively, compared to a corresponding 43 percent and 33 percent for the 2003-04
and 2002-03 academic years.
In the third and fourth bar graphs that follow, similar comparisons are made with respect
to the baseline of the SEAS means, which vary somewhat from semester to semester,
rather than with respect to the baseline of the “long-term” average value of 3.97 / 5.00.
Again striking are the high ratings for APMA courses and the Professors teaching APMA
courses during 2008-09 and also over the five-year period 2004-09.
0.19
0.07
0.76
0.70
0.73
0.73
0.75
2002-03
0.80
0.70
2003-04
0.60
2004-05
0.50
0.40
2005-06
0.30
2006-07
0.20
0.10
2007-08
0.00
APMA COURSE MEAN > 3.97/5.00
2008-09
0.33
0.43
0.68
0.66
0.57
0.66
0.56
0.70
2002-03
2003-04
0.60
2004-05
0.50
2005-06
0.40
2006-07
2007-08
0.30
APMA PROF MEAN > 3.97/5.00
2008-09
0.56
0.70
0.81
0.85
0.83
0.80
0.73
2002-03
0.80
2003-04
2004-05
0.70
2005-06
0.60
2006-07
2007-08
0.50
APMA COURSE MEAN > SEAS COURSE MEAN
2008-09
0.41
0.54
0.64
0.62
0.55
0.63
0.52
0.70
2002-03
2003-04
0.60
2004-05
0.50
2005-06
0.40
2006-07
2007-08
0.30
APMA PROF MEAN > SEAS PROF MEAN
2008-09
„
Caution:
What is the importance of
insuring high quality VCCS mathematics
instruction?
„
Caution: Uncertainty in the quality of the
mathematics instruction for some summer
transfer credit courses, where the coverage
is limited and sometimes compressed or
crammed into as few as 10 to 12 meeting
times of 3 to 4.5 hours each?
Cautions: Uncertainty
There is considerable uncertainty in the quality of the mathematics instruction provided
by summer transfer-credit courses taken by SEAS students at a number of community
colleges in VCCS and other institutions, particularly where in the summer the coverage is
limited and the effective instruction is compressed into as few as 10 to 12 meeting times
of crammed lecture sessions of 3 to 4.5 hours each. Complaints have been received from
a number of our SEAS students, upon returning from such transfer-credit summer
instruction, that they have found themselves not well prepared for our higher-level SEAS
courses.
In efforts to look out for the best interests of our SEAS students and to avoid complaints
on the weakness of their transfer-credit backgrounds both from these students and from
our faculty teaching higher-level SEAS courses, there is some discussion toward asking
(1) that all such compressed and crammed summer transfer-credit mathematics courses
be removed from the transfer-credit-course approval list (where those courses referenced
are actually corresponding academic-year courses, which are not the ones compressed
and crammed during regular academic semesters and which are not the cause of concern)
and (2) that such compressed and crammed summer transfer-credit mathematics courses
not be granted approvals in the future starting with Summer 2010.
For those students who insist on taking such compressed and crammed summer
mathematics courses or insist on taking summer mathematics courses online where the
proctoring of Tests and Final Exams are not guaranteed to be proctored by the
institutions, it requested that these students be asked to take, upon their return, one or
another of the APMA Placement Exams and be required to pass in order to gain such
transfer credit approvals.
As an example from a previous semester, one such complaint came from a SEAS faculty
member who complained that the students in his MEC 321 Fluid Mechanics course were
weak in their background in Vector Calculus. After calling a meeting of all instructors of
APMA 212, where the Vector Calculus is taught, for the purpose of airing the complaint,
the APMA Director’s Office worked to revise the APMA 212 Course Summary Table
and implemented it in future semesters with an additional extra week of focus on the
Vector Calculus included. Also, in a follow-up effort to try to understand more fully the
complaint, the APMA Director’s Office retrieved the final letter grades received by the
MAE 321 students at the end of that semester, converted them into equivalent MAE 321
GPAs for all the MAE 321 students, and then reordered the students into the following
subgroups: (1) those SEAS students starting in APMA 109 (22 students), those SEAS
students starting in APMA 111 (42; their somewhat stronger mathematics backgrounds
qualified them to start with APMA 111 as entering first year students), and transfer
students (33 students). The bar graph, that follows, illustrates the equivalent MAE 321
students’ average GPA in each of these three subgroups.
MAE 321 Fluid Mechanics
2.50
2 .4 2
2.30
2 .15
2.10
1.90
1.8 7
1.70
Transfer
APMA 109
APMA 111
Of the 33 transfer students, 22 had not taken APMA 212 in SEAS but instead had been
granted approval for transfer-credit multivariable Calculus taken elsewhere, ten others
had been granted transfer-credit approval for both APMA 109 and 111 taken elsewhere,
and the remaining one had been granted transfer-credit approval for only APMA 111
taken elsewhere. It is evident that the group of students, who performed most weakly in
MAE 321 Fluid Mechanics, was the group of transfer students (average GPA of only
1.87 / 5.00 in the D to C range).