Chabot College
Fall 2010
Course Outline for Physics 25
COMPUTATIONAL METHODS FOR ENGINEERS AND SCIENTISTS
(See also: Mathematics 25, Engineering 25)
Catalog Description:
25 – Computational Methods for Engineers and Scientists
3 units
Methodology and techniques for solving engineering/science problems using numerical-analysis
computer-application programs MATLAB and EXCEL. Technical computing and visualization using
MATLAB software. Examples and applications from applied-mathematics, physical-mechanics,
electrical circuits, biology, thermal systems, fluid systems, and other branches of science and
engineering. Prerequisite: Mathematics 1. Strongly recommended: Computer Science 8. May not
receive credit if Mathematics 25 or Physics 25 has been completed. 2 hours lecture, 3 hours
laboratory.
[Typical contact hours: lecture 35, laboratory 52.5]
Prerequisite Skills
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use delta notation;
explain limits and continuity;
use Newton’s method;
apply the definition of the derivative of a function;
define velocity and acceleration in terms of mathematics;
differentiate algebraic and trigonometric functions;
apply the chain rule;
find all maxima, minima and points of inflection on an interval;
sketch the graph of a differentiable function;
apply implicit differentiation to solve related rate problems;
apply the Mean Value Theorem;
demonstrate an understanding of the definite integral as the limit of a Riemann sum;
demonstrate an understanding of the Fundamental Theorem of Integral Calculus;
demonstrate an understanding of differentials and their applications;
integrate using the substitution method;
find the volume of a solid of revolution using the shell, disc, washer methods;
find the volume of a solid by slicing;
find the work done by a force;
find the hydrostatic force on a vertical plate;
find the center of mass of a plane region;
approximate a definite integral using Simpson’s Rule and the Trapezoidal Rule.
Expected Outcomes for Students
Upon completion of the course the student should be able to:
1. analyze engineering/science word problems to formulate a mathematical model of the problem;
2. express in MATLAB notation: scalars, vectors, matrices;
3. perform, using MATLAB or EXCEL, mathematical operations on vectors, scalars, and matrices
a. addition and subtraction;
Chabot College
Course Outline for Physics 25, Page 2
Fall 2010
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b. multiplication and addition;
c. exponentiation;
compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions
a. trigonometric functions;
b. exponential functions;
c. square-roots and absolute values;
create, store, and run MATLAB script files;
import data to MATLAB for subsequent analysis from data-sources
a. data-acquisition-system data-files;
b. spreadsheet files;
construct graphical plots for mathematical-functions in two or three dimensions;
formulate a fit to given data in terms of a mathematical curve, or model, based on linear,
polynomial, power, or exponential functions
a. assess the goodness-of-fit for the mathematical model using regression analysis;
apply MATLAB to find the numerical solution to systems of linear equations
a. uniquely determined;
b. underdetermined;
c. overdetermined;
perform using MATLAB or EXCEL statistical analysis of experimental data to determine the
mean, median, standard deviation, and other measures that characterize the nature of the data ;
compute, for empirical or functional data, numerical definite-integrals and discrete-point
derivatives;
solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous
ordinary differential equations;
assess, symbolically, using MATLAB
a. the solution to transcendental equations;
b. derivatives, antiderivatives, and integrals;
c. solutions to ordinary differential equations;
apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line
the: slope, intercept, and correlation-coefficient;
draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets
(multiple lines);
draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two
or three dimensions;
perform, using MATLAB and EXCEL, mathematical-logic operations;
plan, conceptually, computer-solutions to engineering/science problems using psuedocode and/or
flow-chart methods;
compose MATLAB script files that employ FOR and WHILE loops to solve engineering/science
problems that require repetitive actions.
Course Content (Lecture):
1. Engineering problem solving
a. construct Physical Model
b. construct Mathematical Model
c. solve using graphic-geometrical, analytical, or numerical methods
2. Using MATLAB
a. user interface and working-environment
b. writing MATLAB software-code using script or function files (“.m” files)
c. MATLAB Mathematical functions, including logical operations
d. graphical output
3. MATLAB linear algebra using arrays and matrices
a. array and Matrix mathematical operations: addition/subtraction, multiplication/division
exponentiation, transpose, inversion
Chabot College
Course Outline for Physics 25, Page 3
Fall 2010
4. MATLAB Files and Data Structures
a. importing data from ASCII and spreadsheet files
b. complex number formats, rectangular and polar
5. Programming with MATLAB
a. psuedocoding (written-english description of the intended program-function)
b. basic flow charting
c. conditional Branching using if/then/else techniques
d. fixed-termination loops (FOR loops)
e. dynamically-terminated conditional loops (WHILE loops)
f. DeBugging MATLAB programs
6. MATLAB graphical-output and curve-fitting
a. two dimensional Cartesian (XY) plots using multiple data-sets with proper scaling and
labeling
1) linear-linear
2) log-linear (semilog)
3) log-log
b. data-set curve fitting with regression analysis
1) linear
2) polynomial/power function
3) exponential function
c. three dimensional plots: line, surface mesh, contour
7. solutions to systems of linear equations
a. gaussian elimination
b. matrix inversion decomposition
c. cramer’s method
d. underdetermined systems and the minimum-norm solution
e. overdetermined systems and the least-squares solution
8. MATLAB and EXCEL statistical analysis for empirical data
a. calculate standard statistical metrics: mean, median, mode, standard deviation, minimum,
maximum, range
b. generate random numbers
c. linear interpolation
9. MATLAB numerical integration and differentiation
a. trapezoidal integration
b. simpson’s rule integration
c. numerical differentiation
1) forward difference
2) backward difference
3) central difference
10. MATLAB solutions for ordinary differential equations
a. Runge-Kutta based ODE solvers
1) stiff and nonstiff systems
2) low, medium, and variable order solvers
11. MATLAB symbolic mathematics
a. mathematical-expressions and algebra
b. solve algebraic and transcendental equations
c. ordinary and partial differentiation
d. antiderivatives and definite integrals
e. solve linear and nonlinear ordinary differential equations
12. EXCEL user-interface and working-environment
13. EXCEL mathematical functions including logical operations
14. EXCEL graphical output
a. bar and column charts
b. line and xy plots
c. three dimensional surface plots
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Course Outline for Physics 25, Page 4
Fall 2010
15. EXCEL statistical analysis, and curve fitting including linear regression
Course Content (Laboratory):
1. Use MATLAB’s interactive mode to compute numerical results for scalar, vector, matrix, can array
operations
2. compose user-defined, special-purpose, MATLAB programs
3. plan computer-code (“m” file) solutions to engineering/science problems using
a. psueodcode
b. diagrams and/or tables
c. flow-charts
4. design, in detail, computer-code solutions to engineering/science problems using – run, test, and
check the solutions
5. import into MATLAB and EXCEL data generated by data-acquisition systems to
a. analyze the data statistically
b. evaluate the data using visualization tools such as plots, charts, and tables
6. compose MATLAB script-files to solve engineering/science problems that employ
a. logical variables
b. relational operations
c. FOR and/or WHILE loops
d. user-defined MATLAB functions
7. Create from experimental or theoretical data visualization objects
a. XY Cartesian plots: linear, semilog, and log-log
b. XYZ three-dimensional plots
c. Comparison charts: bar, column, pie, area, line, radar
d. Histograms
8. Numerically Determine using MATLAB the maxima, minima, and zeros of single-variable
functions
9. Use MATLAB to solve numerically and symbolically systems of linear equations
10. Use MATLAB to solve numerically and symbolically ordinary differential equations
11. Use MATLAB to perform numerically and symbolically mathematical differentiation and
integration
12. Use MATLAB and EXCEL to analyze empirical data using linear regression analysis
13. Use MATLAB and EXCEL to analyze empirical data using higher-order regression analysis
14. Create MATLAB SIMULINK models for time-varying systems that employ feedback loops
Methods of Presentation:
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Formal lectures using PowerPoint and/or WhiteBoard presentations
Computer demonstrations
Reading from the text
Laboratory use of computers
Class discussion of problems, solutions, and student’s questions
Engineering/Science Problem Solving tutorials using this progression
a. Use diagrams, charts, and tables to analyze the problem
b. Formulation of a mathematical model for the problem
c. Translate, conceptually, the math model for computer implementation using psuedocode or
flow-charts
d. Implement the solution using a MATLAB script-file
e. Run and Check the MATLAB solution
f. Output the solution in the form of a properly constructed table, chart, or graph
Chabot College
Course Outline for Physics 25, Page 5
Fall 2010
Assignments and Methods of Evaluating Student Progress:
1. Typical Assignments
b. Read chapter-2 in the text on MATLAB’s Array and Matrix handling functions
c. Exercises from the text book, or those created by the instructor
1) A set of three equations defines the mesh currents in shown in Text Figure 5.5. Write at
MATLAB program to compute the mesh currents using the given resistor and voltagesource values
2) The Useful life of a machine bearing depends on its operating temperature as indicated
by the following data:
Temperature (°F)
Bearing Life (kHr)
100
28
120
21
140
15
160
11
180
8
200
6
220
4
Obtain a functional description (curve fit) for this data. Plot the function and the data on
the SAME plot. Also estimate bearing life for a 150 °F operating temperature.
3) Given that i = √-1, let y = -3 + ix. For x = 0, 1, 2 use MATLAB to numerically evaluate the
following expressions. Hand check your answers.
(a) |y|
(b) √y
(c) (-5-7i)y
(d) y/(6-3i)
4) Consider an Ordinary Differential Equation (ODE) and its analytical solution:
Ordinary Differential Equation
dx
 ax  b;
dt
x0   c
Solution
xt  
b 
b
  c  e  at
a 
a
Verify the solution using two methods
(a) By hand take the analytical derivative of x(t) and substitute in to the ODE.
(b) Solve the ODE symbolically using MATLAB’s dsolve function
5) Given a set of deflection vs. load data for a cantilever beam use EXCEL to plot the data
and calculate the slope of the best straight line through the data.
6) A DIODE is an electronic component that essentially acts as “check valve” for electrical
current; i.e., the diode allows current flow in one direction, but not the other. The electrical
circuit symbol, and the theoretical equation relating the diode current to the electrical
potential (or pressure) in applied across the diode:
Circuit Symbol
+
I
Va
V-I Relation
-
I  0;

Va  0
I  I sat e
qVa
nkT

 1 ; Va  0
Where
 Va  the Applied Electrical Potential in Volts (V)
Chabot College
Course Outline for Physics 25, Page 6
Fall 2010

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
I  the Diode Current in Amps
Isat  the Diode SATURATION Current, a
PRACTICAL constant, in Amps
q  the ELECTRONIC CHARGE, a
UNIVERSAL constant = 1.6 x10-19 Coulombs
k  BOLTZMANN’S value, a UNIVERSAL
constant = 1.3805 x10-23 J/K
n  the Diode IDEALITY FACTOR, a
PRACTICAL constant without units
T  the Thermodynamic Temperature in
Kelvins (K)
H
An instrument called a Digital MultiMeter, or DMM (which
we will use in ENGR43) can be used to collect Va vs. I
data. The CSV (Comma Separated Values) data file
provided by the instructor contains Va  0 data for a
1N4123 silicon diode.
 Use these data to create a SOME TYPE of Plot to
reveal the values of the practical constants:
o Isat
o n
 Based on your analysis, comment on the
quality/reliability of the values for Isat and n
y
7) The height, H, reached by a bubble rising through a
liquid in time r may be calculated using the double
integral equation1.

H
0

r  tA 
0.375 K1vr  K 2 vr5 3  K 3vr3 2
dy  H      g 
0
0
ro
 
 dt dt
 
 
A
Find the rise velocity, vr, from

v r t A 
0
tA 
3C v 2 t  
dvr  vr (t A )    g  D r dt
0
8ro 

Using the instructor-provided values for the constants r o, CD, and g, determine for the
specified rise time the value of H.
8) Create a SimuLink model to plot the solution of the following equation for 0 < t < 10
10 y  7 sin 4t  5 cos 3t
y0  4 y 0  1
2. Methods of Evaluating Student Progress
a. Weekly homework assignments
b. Examinations
B. Mayer, C. C. Collins, M. Walton, “Transient Analysis of Carrier Gas Saturation in Liquid Source Vapor
Generators”, Journal of Vacuum Science Technology A, vol. 19, no.1, pp. 329-344, Jan/Feb 2001
1
Chabot College
Course Outline for Physics 25, Page 7
Fall 2010
c.
Final examination
Textbook(s) (Typical):
Engineering Computation with MATLAB, 2/E, David M Smith, Addison-Wesley, 2010
Introduction To MATLAB 7 For Engineers, William Palm, McGraw-Hill 2005
MATLAB®, Katsuhiko Ogata, Prentice Hall, 2008
Mastering MATLAB 7, Duane C. Hanselman and Bruce L. Littlefield, Prentice Hall, 2005
MATLAB: An Introduction with Applications, 3rd Edition, Amos Gilat, John-Wiley, 2008
Engineering Computation: An Introduction Using MATLAB and Excel, Joseph Musto, William
E. Howard, and Richard R. Williams, McGraw-Hill 2009
Special Student Materials:
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4.
Laboratory access to MATLAB and EXCEL Software
Software: MATLAB and Simulink student version with the Symbolic Math Toolbox
Software: Microsoft Office Student and Teacher Edition; includes EXCEL
USB Computer Storage Drive
Bruce Mayer, PE •
C:\WorkingFiles\Bruce_Files\Chabot\Curriculum_Analysis\Curriculum_Proposal_Fa09\ENGR25_Outline0
2_090821.doc
Revised 08/21/2009