To introduce and develop advanced topics in applied engineering
mathematics. Specifically, students are to be able to
1. Solve engineering problems governed by ordinary and
partial differential equations.
2. Apply principles of linear algebra and matrix
operations to common engineering problems.
3. Apply principles of probability and statistics to
engineering problems.
4. Use mathematical software to solve the types of
problems described above (Outcomes 13).
5. Use numerical methods to solve problems governed by
ordinary differential equations and/or systems of algebraic equations.
6. Solve complex problems in multidisciplinary teams.
II. Instructor and Meeting Time:
Dr. WeiYin
Chen , Chemical Engineering Department
Office: Room 140, Anderson Hall
Telephone: 9155651
Fax: 9157023
Email: cmchengs@olemiss.edu
Regular Classes: 8:008:50 am Mondays, Tuesdays, Wednesdays and Fridays
Recitation Sessions: 8:008:50 am Thursdays
Office Hours for W. Chen: 3:005:30 pm, Wednesdays, and Fridays, or by
appointment
General
References:
Applications
and Advanced Materials:
V. Exams/Tests/Homework and General
Rules:
There will be two onehour exams, one midterm exam and one final exam. Homework will be assigned and collected every Friday. Late homework will be accepted only under unusual conditions uncontrollable by the students and only if special arrangements with the teacher has been made prior to the due date.
Homework will also include conducting projects in teams consisting of multidisciplinary members.
In accordance with Departmental policy, students missing more than 12 class periods are subject to direct grade penalties. Penalties may be assessed without regard to the student's performance.
Students are expected to keep up with the material as it is presented and submit assignments on time; most students find this difficult without regular class attendance.
Because the level of difficulties of the materials, attendance is very important for the course. In accordance with Departmental policy, students missing more than 3 class periods are subject to direct grade penalties. Penalties may be assessed without regard to the student's performance.
Students are expected to keep up with the material as it is presented and submit assignments on time; most students find this difficult without regular class attendance. Successful learning involves the following important steps
1. Attend all classes on time and listen
carefully
2. Do not fall sleep
3. Do not hesitate to ask questions in or out of the
classroom
4. Do not play crosswords
5. Practice, practice and practice
Final
grades will be given based on the overall performance of the homework, hourly
tests, midterm, and the final exam.
Homework 
200 
Hourly
Exams (2) 
200 
Midterm 
100 
Final
Exam 
200 
Total 
700 
For students taking ENGR310, grades will be given according to the following scale.
700>A>560
559>B>490
489>C>420
419>D>350
349>F
For students taking ENGR591, extra homework will be given and grades will be
given according to the following scale.
700>A>630
629>B>560
559>C>490
489>D>420
419>F
Depending on examination difficulty, this scale
may be relaxed.
Week
No. 
Week
of 
Topics 
Reading
Assignment 
1 
August
22 
FirstOrder
ODE, SecondOrder ODE 
Sec.
1.11.5, 2.12.5, 2.72.10 
2 
August
29 
Series
Solutions 
Sec.
5.15.3 
3 
September
5 
Series
Solutions 
Sec.
5.4 
4 
September
12 
Series
Solutions (Teacher in Pittsburgh), Exam I 
Sec.
5.75.8 
5 
September
19 
Fourier
Series and Integrals 
Sec.
11.111.3, 11.711.9 
6 
September
26 
Partial
Differential Equations 
Sec.
12.112.3 
7 
October
3 
Partial
Differential Equations, Midterm 
Sec.
12.512.6 
8 
October
10 
Partial
Differential Equations 
Sec.
12.712.8 
9 
October
17 
Probability
and Statistics 
Sec.
24.124.4 
10 
October
24 
Probability
and Statistics, Exam II 
Sec.
24.524.8, 25.1 
11 
October
31 
Matrix
and Linear Algebra 
Sec.
7.17.8 
2 
November
7 
AIChE
annual meeting :) (Teacher in Salt Lake City) 
Sec.
8.18.2 
13 
November
14 
Matrix
and Linear Algebra 
Sec.
19.119.3, 20.120.2 
14 
November
21 
Fall
Break :) 

15 
November
28 
Numerical
Methods 
Sec.
19.119.3, 20.120.2 
16 
December
5 
Final
Exam, 8:00 a.m., Monday, December 6? 
Note:
Late assignments will not be accepted except special arrangements between the
student and the teacher.
Chapter 1. FirstOrder Differential Equations
Request an account for the CadLab, as you will need to have access to the
software Mathcad for this course.
Problems 1, 7, 17 and 18 on page 8.
Problems 26 and 28 on page 18.
Problems 11 and 12 on page 25.
Problems 5 and 30 on page 32. For Problem 30, let the dependent variable
y be the fraction of infected.
Chapter 2. Linear Differential Equations of Second Order
Problems 2 and 14 on page 68.
Problem 5 and 12 on page 83. Use both the method of undetermined
coefficients and method of variation of parameters to solve these
problems. Moreover, use Mathcad to check your answers.
Problems 17 and 20 on page 90 Use Mathcad to graph the solutions.
Problems 1 and 13 on page 97.
Project 1. #24 on p.90
Chapter 5. Series Solutions of Differential Equations, Special
Functions
Problems 2 and 3 on page 170.
Problems 3, 5, 9, 16 and 17 on page 176.
Problems 5, 6 and 7 on page 180. In addition to the questions in the
textbook, for Problem #5, plot and compare the 3term and 10term
approximations, and the analytical expression for y2(x) for x between 0.99 and
0.99 in Mathcad. For Problem #6, plot and compare the 3term and 10term
approximations, and the analytical expression for y1(x)
for x between 0.99 and 0.99 in Mathcad. The approximate nature of the series
solutions should be illustrated in your graphic
representations; can you conclude that the series representations of these two
problems converge to the desired answers? Did you obtain better results
by including more terms in the series solutions?
Problems 1, 3 and 4 on page 187.
Problems 6, 9, 12 and 18 on page 209.
Problems 3 and 6 on page 216.
Project 2. #20 on p.209
Chapter 11. Fourier Series, Integrals and Transforms
Problems 8, 9, 13 and 18 on page 485.
Problems 1 and 8 on page 490  Derive the Fourier coefficients by hand first,
and then by Mathcad. Use MathCad to: 1) obtain the Fourier coefficients,
2)
plot the first 5 and 11 partial sums, and the given
function for both problems. Do you get better results when more terms are
included in the partial sums?
Problems 6, 7 and 16 on page 496  Derive the Fourier coefficients by hand
first, and then by MathCad. Use MathCad to: 1) obtain the Fourier
coefficients, 2) plot
the first 5 and 11 partial sums, and the given
function for both problems. Do you get better results when more terms are
included in the partial sums?
Problems 1, 6, 7 and 17 on page 512  For problems 7 and 17, derive the Fourier
coefficients by hand first, and then by MathCad. Use MathCad to: 1)
obtain the Fourier coefficients, 2) plot the first 5 and 11 partial sums, and
the given function. Do you get better results when more terms are
included in the partial sums?
Chapter 12. Partial Differential Equations
Problems 6, 8, 14, 19 and 23 on page 537.
Problems 1, 5, 14 (part a through d only) , 15 and 16 on page 546 (40 pints for
#14). For the first 2 problems, derive the Fourier coefficients by hand
first, and
then by MathCad. Plot five traces of the
deflection so that they demonstrate approximately the full cycle of the motion.
Problems 5, 6, 13, 14, 15 and 24 on page 560. For problems 5, and 6,
derive the Fourier coefficients by hand first, and then by MathCad. Plot
five traces of the u(x, t) so that they demonstrate approximately the initial
dynamics of the temperature variations.
Problems 3 and 4 on page 568. For these problems, derive the solutions by
hand first, and then by MathCad. Plot five traces of the u(x, t) so that
they
demonstrate the temperature variations over a wide
range of time.
Problems 6, 7 and 11 on page 578. For problem 11, derive the double
Fourier coefficients by hand first, and then by MathCad. Plot five traces
of the u(x, t) so
that they demonstrate approximately the first full
cycle of the motion.
Project 3. #30 on p.562
Chapter 24. Data Analysis, Probability Theory  Use MathCad for the
following problems, whenever the need arises.
Problems 1, 2, 3, 15, 16 and 17 on page 1005.
Problems 5, 8, 9, 14 and 18(d) on page 1010.
Problems 1, 2, 6, 7, 10 and 14 on page 1015.
Problems 1, 2, 6, 7, 10 and 11 on page 1019.
Problems 2, 3, 4, 10 and 11 on page 1025.
Problems 1, 3, 5, 6, and 8 on page 1031.
Chapter 25. Mathematical Statistics
Find the statistical quantities mentioned in the supplementary volume for the
data below and plot the histigram and cumulative frequency function.
90.60
80.40
83.50
86.20
82.40
79.80
84.30
82.40
82.60
84.30
79.10
83.20
88.10
90.30
85.40
81.80
80.50
87.20
82.10
87.80
Chapters 7, 8 and 20. Matrix Properties, Solution of Linear System of
Equations and the Numerical Methods
Problems 5, 7 and 13 on page 295. For all of these three problems: 1)
find the solutions by Gauss elimination, 2) use classical methods to calculate
the determinants, inverses, eigenvalues and eigenvectors of the coefficient
matrix A (if the determinant is not zero), 3) find the solutions by Cramer's
rule (if the determinant is not zero), and, 4) verify all of your calculations
with a software package, e.g., Mathcad (if the determinant is not zero).
Problems 13, 16 and 17 of Problem Set 13.1 in this notes (on partial pivoting
and scaling).
Problems 3, 8 and 20 of Problem Set 13.2 in this notes (on various methods of
LUfactorization).
Problems 5 and 12 on page 851 of the textbook (on Methods of GaussSeidel and
Jacobi)
Convert 4y'' + 16 y' + 17 y = 0 with y(0) = 0.5 and y'(0) = 1 to a system of
firstorder ordinary differential equations and prove that the eigenvalues
associated with the coefficient matrix of the converted system are essentially
the roots of the characteristic equation of the given ODE.
Chapter 19. Numerical Integration and Numerical Methods for
Differential Equations
Integrate the standardized Poisson distribution function between 0 and 2 by
1. Trapezoidal rule,
2. Simpson's 1/3 rule,
3. Simpson's rule with 7 points,
4. GaussLegendre Quadrature with 7 points, and,
5. Tabulated results from A7 on p.A89 of the textbook.
Compare the errors of these methods.
Given y ' = 3x/y 2xy and y(0) = 1, predict y(x) for 0 < x < 1 by using 1) Euler's method with h=0.25, b) Huen's method with h=0.25, and, c) the fourthorder RungeKutta Method with h=0.25. You can conduct these calculations in Mathcad.
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This page last updated 7/16/2010 by WYC