Chabot College
Fall 2005
Replaced Fall 2010
Course Outline for Mathematics 25
COMPUTATIONAL METHODS FOR ENGINEERS AND SCIENTISTS
(See also: Engineering 25, Physics 25)
Catalog Description:
25 – Computational Methods for Engineers and Scientists
3 units
Methodology and techniques for solving engineering/science problems using numerical-analysis computerapplication 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 Application Systems 8 or Computer Science 8. May not
receive credit if Engineering 25 or Physics 25 has been completed. 2 hours lecture, 3 hours laboratory.
[Typical contact hours: lecture 35, laboratory 52.5]
Prerequisite Skills:
Before entering the course the student should be able to:
1. apply the methods of the Theory of Equations (synthetic division, Rational Roots Theorem, etc.) to
factor polynomials and to solve algebraic equations;
2. graph algebraic functions and relations;
3. solve equations involving logarithmic, exponential and trigonometric functions;
4. prepare detailed graphs of conic sections;
5. create mathematical models using algebraic or transcendental functions;
6. use sign graphs to solve non-linear inequalities;
7. construct a proof using mathematical induction;
8. graph using translations, reflections and distortions;
9. identify and use the trigonometric functions in problem solving;
10. prove trigonometric identities;
11. develop and use exponential, logarithmic and trigonometric formulas;
12. graph exponential and trigonometric functions and their inverses;
13. graph polar equations.
Expected Outcome 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;
b. multiplication and addition;
c. exponentiation;
4. compute, using MATLAB or EXCEL, the numerical-value of standard mathematical functions
a. trigonometric functions;
b. exponential functions;
c. square-roots and absolute values;
5. import data to MATLAB for subsequent analysis from data-sources
a. data-acquisition-system data-files;
b. spreadsheet files;
6. construct graphical plots for mathematical-functions in two or three dimensions;
7. 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;
8. apply MATLAB to find the numerical solution to systems of linear equations
a. uniquely determined;
b. underdetermined;
Chabot College
Course Outline for Mathematics 25, Page 2
Fall 2005
c. overdetermined;
9. 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 ;
10. compute, for empirical or functional data, numerical definite-integrals and discrete-point derivatives;
11. solve numerically, using MATLAB, linear, second order, constant-coefficient, nonhomogenous ordinary
differential equations;
12. assess, symbolically, using MATLAB
a. the solution to transcendental equations;
b. derivatives, antiderivatives, and integrals;
c. solutions to ordinary differential equations;
13. apply, using EXCEL, linear regression analysis to xy data-sets to determine for the best-fit line the:
slope, intercept, and correlation-coefficient;
14. draw using MATLAB or EXCEL two-dimensional Cartesian (xy) line-plots with multiple data-sets
(multiple lines);
15. draw using EXCEL qualitative-comparison charts such as Bar-Charts and Column-Charts in two or three
dimensions;
16. perform, using MATLAB and EXCEL, mathematical-logic operations;
17. compose EXCEL Visual-Basic MACRO programs/functions to automate repetitive spreadsheet tasks.
Course Content:
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
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. state transition diagrams
d. conditional Branching using if/then/else techniques
e. conditional Loops
f. DeBugging MATLAB programs using the Editor/Debugger
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
Chabot College
Course Outline for Mathematics 25, Page 3
Fall 2005
8.
9.
10.
11.
12.
13.
14.
15.
16.
b. matrix inversion decomposition
c. cramer’s method
d. underdetermined systems and the minimum-norm solution
e. overdetermined systems and the least-squares solution
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
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
MATLAB solutions for ordinary differential equations
a. Runge-Kutta based ODE solvers
1) stiff and nonstiff systems
2) low, medium, and variable order solvers
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
EXCEL user-interface and working-environment
EXCEL mathematical functions including logical operations
EXCEL graphical output
a. bar and column charts
b. line and xy plots
c. three dimensional surface plots
EXCEL statistical analysis, and curve fitting including linear regression
Creating EXCEL software-code using the MACRO technique
a. record-macro tool
b. write macros using Microsoft visual basic
Methods of Presentation:
1.
2.
3.
4.
5.
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
Assignments and Methods of Evaluating Student Progress:
2. Typical Assignments
a. Read chapter-2 in the text on MATLAB’s Array and Matrix handling functions
b. 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 voltage-source
values
Chabot College
Course Outline for Mathematics 25, Page 4
Fall 2005
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
Where







Va
V-I Relation
-
I  0;

Va  0
I  I sat e
qVa
nkT

 1 ; Va  0
Va  the Applied Electrical Potential in Volts (V)
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)
Chabot College
Course Outline for Mathematics 25, Page 5
Fall 2005
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
H
7) The height, H, reached by a bubble rising through a
liquid in time r may be calculated using the double
integral equation*.

H
0

r  tA 
0.375 K1vr  K 2 vr5 3  K 3vr3 2
dy  H      g 
0
0
ro
 
 dt dt
 
 
A
y
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
ro, CD, and g, determine for the specified rise time the
value of H.
3. Methods of Evaluating Student Progress
a. Weekly homework assignments
b. Examinations
c. Final examination
Textbook(s) (Typical):
Introduction to MATLAB 7, Dolores Etter, David Kuncicky, Holly Moore, Prentice Hall, 2004
Introduction To MATLAB 7 For Engineers, William Palm, McGraw-Hill 2005
MATLAB, an Introduction with Applications, Amos Gilat, John Wiley, 2004
Guide to Microsoft Excel 2002 for Scientists and Engineers (3rd Edition), Bernard Liengme, ButterworthHeinemann (Elsevier Science), 2002
Spreadsheet Tools For Engineers: Excel, Second Edition, Byron S. Gottfried, McGraw-Hill, 2003
EXCEL for Engineers and Scientists, S. C. Bloch, John Wiley, 2003
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
*
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Course Outline for Mathematics 25, Page 6
Fall 2005
Special Student Materials:
Software: MATLAB and Simulink student version with the Symbolic Math Toolbox
Software: Microsoft Office 2003 Student and Teacher Edition; includes EXCEL
Bruce Mayer, PE • PHYS25_F05.doc
New Sep04