CHELOGO

ENGR310 and ENGR591

Engineering Analysis I; Fall, 2010


 

I. Course Objectives

  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 1-3).
     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. Wei-Yin Chen , Chemical Engineering Department
Office: Room 140, Anderson Hall
Telephone: 915-5651
Fax: 915-7023
Email: cmchengs@olemiss.edu

Regular Classes: 8:00-8:50 am Mondays, Tuesdays, Wednesdays and Fridays
Recitation Sessions: 8:00-8:50 am Thursdays
Office Hours for W. Chen: 3:00-5:30 pm, Wednesdays, and Fridays, or by appointment
 
 

III. Textbook:

IV. References:

General References:

Applications and Advanced Materials:


 

V. Exams/Tests/Homework and General Rules:

There will be two one-hour 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
 

 

VI. Grading Policy and Current Grades:

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.
   

 

VII. Tentative Course Schedule

 

Week No. 

Week of 

Topics

Reading Assignment

1 

August 22

First-Order ODE, Second-Order ODE

Sec. 1.1-1.5, 2.1-2.5, 2.7-2.10

2 

August 29

Series Solutions 

Sec. 5.1-5.3

3 

September 5

Series Solutions

Sec. 5.4

4 

September 12

Series Solutions (Teacher in Pittsburgh), Exam I

Sec. 5.7-5.8

5 

September 19

Fourier Series and Integrals

Sec. 11.1-11.3, 11.7-11.9

6 

September 26

Partial Differential Equations

Sec. 12.1-12.3

7 

October 3

Partial Differential Equations, Mid-term

Sec. 12.5-12.6

8 

October 10

Partial Differential Equations

Sec. 12.7-12.8

9 

October 17

Probability and Statistics

Sec. 24.1-24.4

10 

October 24

Probability and Statistics, Exam II

Sec. 24.5-24.8, 25.1

11 

October 31

Matrix and Linear Algebra

Sec. 7.1-7.8

2 

November 7

AIChE annual meeting :) (Teacher in Salt Lake City)

Sec. 8.1-8.2

13 

November 14

Matrix and Linear Algebra

Sec. 19.1-19.3, 20.1-20.2

14 

November 21

Fall Break :)

15 

November 28

Numerical Methods 

Sec. 19.1-19.3, 20.1-20.2

16 

December 5

Final Exam, 8:00 a.m., Monday, December 6?


 

VIII. Homework Assignment

Note: Late assignments will not be accepted except special arrangements between the student and the teacher.

Chapter 1. First-Order Differential Equations
Request an account for the Cad-Lab, 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 3-term and 10-term 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 3-term and 10-term 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 LU-factorization).
Problems 5 and 12 on page 851 of the textbook (on Methods of Gauss-Seidel and Jacobi)
Convert 4y'' + 16 y' + 17 y = 0 with y(0) = -0.5 and y'(0) = 1 to a system of first-order 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. Gauss-Legendre 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 fourth-order Runge-Kutta 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