CME 261F - Engineering Mathematics I
Detailed Syllabus
Academic Year ‘13/’14
September 9, 2013
Instructor
Prof. Kaiwen Xia, Department of Civil Engineering
Office
GB 314A
Email
kaiwen.xia@utoronto.ca
Teaching Assistants
Tamer Abdulazim (tamer.abdulazim@utoronto.ca)
Glareh Amirjamshidi (glareh.amirjamshidi@mail.utoronto.ca)
Mohamed Elshenawy (mohamed.elshenawy@utoronto.ca)
Patrick Paskalis Kanopoulos (patrick.kanopoulos@mail.utoronto.ca)
Mona A. Qouqa (mona.qouqa@mail.utoronto.ca)
Bangbiao Wu (wubangbi@utoronto.ca)
Wei Yao (wei.yao@mail.utoronto.ca)
Course Schedule
Monday
Lecture
Tuesday
Wednesday
Thursday
13:00-14:00
LM159
Friday
9:00-11:00
SF1105
Practice*
11:00-12:00
10:00-11:00
WB255/GB150 GB150/GB144
**
Tutorial
14:00-15:00
BA1130
* Practice sessions will be used for office hour and practice with Matlab.
** Tutorial sessions will be used for quizzes (in examination center) or general
assistance to students.
Course Website
Blackboard will be used for announcements, posting problems, handouts, grades and any other
information for the course. See http://portal.utoronto.ca for login instructions.
Course Description
This course deals with both numerical methods for engineering analysis and advanced topics in
analytical calculus. Within the numerical methods portion of the course emphasis is placed on
problem formulation, solution algorithm design and engineering applications. Within the
analytical calculus portion emphasis is placed on the vector calculus.
Evaluation Scheme
CME261 Syllabus
Component
Percentage
Matlab Projects
Two Quizzes
Final
20%
30%
50%
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Prof. Kaiwen Xia
Exams
All exams will be Type A (close book, no aids other than the information supplied on the
examination paper) and calculators must be nonprogrammable.
Classroom Rules
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Late appearance and early leave are discouraged.
Cell phones should be always off or set in the quiet mode during the lecture.
No noise should be made in the classroom except for the discussion periods.
Questions during the lecture are encouraged.
Repeated disruptive behaviors will be reported to the appropriate authorities.
Textbook
S.C. Chapra, Applied Numerical Methods with MATLAB, (3rd ed.), McGraw Hill
C.H. Edwards & D.E. Penney, Calculus: Early Transcendentals (7th ed.), Prentice Hall
Table of Contents
The references to Chapters (Ch) and Sections (Sec) are from the following texts:
C = S.C. Chapra, Applied Numerical Methods with MATLAB, (3rd ed.), McGraw Hill
E&P = C.H. Edwards & D.E. Penney, Calculus: Early Transcendentals (7th ed.), Prentice Hall
Topic I: Basics of Matlab and Sources of Numerical Errors (1 week)
(C, 2.1 – 2.4, 3.1 – 3.5, 4.1 – 4.3)
Covered: Matlab Fundamentals, programming in Matlab, data uncertainty, round off and
truncation errors
Discussed: Model errors
Topic II: Solution of Nonlinear Equations in One Variable (2 weeks)
(C, 5.1 – 5.5, 6.1 - 6.4)
Covered: Graphic method, Bisection, Fixed-Point Iteration, Newton’s Method, convergence
characteristics, assessing precision of answer at each iteration
Discussed: Engineering motivations for nonlinear equations, False Point and Secant methods,
solving nonlinear equations with Matlab
Examples: Design of a model submarine and a dam
Topic III: Solution of Systems of Equations (2 weeks)
(C, 9.1 – 9.3, 10.1 – 10.2, 11.1-11.2, 12.1)
Covered: Building on material from MAT188 (intro to Gauss and LU), Naïve Gauss
Elimination, LU Decomposition, Gauss-Seidel iteration
Discussed: engineering motivations for systems of equations (e.g., stiffness matrices for plane
frame structures), Gauss with pivoting, system conditioning and methods for assessing
reliability of computed answer, solution of nonlinear systems using iterative techniques
Example: Structural mechanics and pollution of the five lakes
CME261 Syllabus
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Prof. Kaiwen Xia
Topic IV: Partial Differentiation (2 weeks)
(E&P, Ch 12)
Covered: Building on material from MAT187, Functions of several variables; functions of two
variables and contour maps over a base plane; limits and continuity; partial derivatives in the
ordinate directions, directional derivative in a specified direction, gradient (maximum
directional derivative) and normal vectors
Discussed: engineering motivations
Examples: Vibration of strings and wave propagation in bars
Topic V, Part I: Least-Squares Approximation (1.5 weeks)
(C, 14.1 -14.3, 15.1, 15.3, 15.5)
Covered: Building on material in MAT188, Error measure for a given data point [ei = yi – f(xi)]
and entire data set [Sr = (ei)2]; linear regression (with and without intercept), linearization of
nonlinear functions, nonlinear regression
Discussed: engineering motivations (e.g., best-fit predictive models for data with uncertainty
such as compressive strength data, exponential growth/decay models, power laws, saturation
growth rate models, traffic data)
Example: Fitting of rock fracture data
Topic V, Part II: Interpolation and Polynomial Approximation (1.5 weeks)
(C, 17.1, 17.3, 17.5, 18.1 - 18.4)
Covered: Building on material in MAT188, method of undetermined coefficients (set of linear
equations to determine polynomial coefficients), Lagrange Polynomials, problems with
oscillations and extrapolation; linear, quadratic and cubic splines, implications of extrapolating
spline fits beyond the given range of data
Discussed: engineering motivation (e.g., curve fits for use as predictive models for data such as
stream flow and population change)
Example: Annual temperature change
Topic VI: Numerical Integration (2 weeks)
(C, 19.1 – 19.6, 20.1 – 20.4)
Covered: Building on material from MAT186 (intro to Trapezoid and Simpson’s rules),
Trapezoid Rule, Simpson’s 1/3 and 3/8 rules, Gauss 2-point Quadrature, Error estimates and
“n-2n” (Richardson) extrapolation for improved estimates
Discussed: engineering motivations (e.g., numerical analogues to the analytic approach
described in the previous section Multiple Integrals, such as surface areas and volumes of
slopes described by point-wise data coming from a land surveying program)
Topic VII: Ordinary Differential Equation (1 week)
(C, 23.1 – 23.6)
Covered: Euler’s method, Improvements of Euler’s method, Runger-Kutta methods
Discussed: Systems of equations
CME261 Syllabus
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Prof. Kaiwen Xia