ENGR310 and ENGR591

Engineering Analysis I; Fall, 2009

COURSE OBJECTIVES
INSTRUCTOR, TEACHING ASSISTANT, AND MEETING TIME
TEXTBOOK
REFERENCES
EXAMS/TESTS/HOMEWORK
GRADING POLICY AND CURRENT GRADES
TENTATIVE SCHEDULE
DOWNLOAD LECTURE NOTES
HOMEWORK ASSIGNMENT

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: 10:00-10:50 am Mondays, Tuesdays, Wednesdays and Fridays
Recitation Sessions: 10:00-10:50 am Thursdays
Office Hours for W. Chen: 3:00-5:30 pm, Mondays, Wednesdays, and Fridays, or by appointment

III. Textbook:

Advanced Engineering Mathematics, 9th Edition, by Erwin Kreyszig, Wiley, New York, 2006.
ENGR310/591 Engineering Analysis I - Supplementary Volume, by Wei-Yin Chen, University of Mississippi, 2007.

IV. References:

Mathcad: A Tool for Engineering Problem Solving, by Pritchard, Philip J., WCB McGraw-Hill, 1998. (available in the book store for ChE307).

General References:

Your textbook for the Ordinary Differential Equation course.
References on pp. A.1-A.5 (Appendix A) of your text.
Advanced Engineering Mathematics, by A. Jeffrey, Harcourt/Academic Press, Burlington, MA, 2002.
Advanced Engineering Mathematics, 6th edition, by C. Ray Wylie and Louis C. Barrett, McGraw-Hill, New York, 1995.
Advanced Engineering Mathematics, by D.G. Duffy, CRC Press, Boca Roton, FL, 1997.
Advanced Engineering Mathematics, 3rd edition, by Peter V. O'Neil, Wadsworth, 1991.
Advanced Engineering Mathematics, 2nd edition, by Michael D. Greenberg, Prentice-Hall, New Jersey, 1998.
Advanced Engineering Mathematics, 2nd edtion, by Dennis G. Zill and Michael R. Cullen, Jones and Bartlett, Boston, MA, 2000.
Applied Numerical Methods, by B. Carnahan, H.A. Luther, and J.O. Wilkes, Wiley, 1969.
Introductory Probability and Statistical Applications, 2nd ed., by Paul L. Meyer, Addison-Wesley, Reading, Mass., 1972.

Applications and Advanced Materials:

References on pp. A.1-A.4 (Appendix A) of your text.
Mathematical Methods in Chemical Engineering, by Arvind Varma and Massimo Morbidelli, Oxford University Press, 1997.
Applied Mathematics and Modeling for Chemical Engineers, by Richard Rice and Duong D. Do, Wiley, New York, 1994.
Mathematical Methods in Chemical Engineering, by Victor G. Jenson and G.V. Jeffreys., 2d ed. London, New York, Academic Press, 1977.
An Intriduction to Ordinary Differential Equations, by E. A. Coddington, Prentice-Hall, Englewood Cliffs, New Jersey, 1961.
Applied Linear Algebra, by B. Noble, Prentice-Hall, Englewood Cliffs, New Jersey, 1969.
Conduction of Heat in Solids, by H.S. Carslaw and J.C. Jaeger, Oxford University Press, 1959.

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.

Except for excessive absenteeism, student attendance is not directly factored into grades.

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 23	First-Order ODE, Second-Order ODE	Sec. 1.1-1.5, 2.1-2.5, 2.7-2.10
2	August 30	First-Order ODE, Second-Order ODE, Series Solutions	Sec. 5.1-5.3
3	September 6	Series Solutions	Sec. 5.4
4	September 13	Series Solutions, Exam I	Sec. 5.5-5.8
5	September 20	Fourier Series and Integrals	Sec. 11.1-11.3, 11.7-11.9
6	September 27	Partial Differential Equations	Sec. 12.1-12.3
7	October 4	Partial Differential Equations	Sec. 12.5-12.6
8	October 11	Partial Differential Equations, Mideterm	Sec. 12.7-12.8
9	October 18	Partial Differential Equations	Sec. 12.9-12.10
10	October 25	Probability and Statistics	Sec. 24.1-24.4
11	November 1	Probability and Statistics	Sec. 24.5-24.8, 25.1
12	November 8	teacher away at AIChE annual meeting :), Exam II	Sec. 7.1-7.8, 8.1-8.2
13	November 15	Matrix and Linear Algebra	Sec. 7.1-7.8, 8.1-8.2
14	November 22	Fall Break :)	Sec. 7.1-7.8, 8.1-8.2
15	November 29	Numerical Methods	Sec. 19.1-19.3, 20.1-20.2
16	December 26	Final Exam, 8:00 a.m., Monday, December 7

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 4, 14, 19 and 22 on page 8.
Problems 27 and 29 on page 18.
Problems 13 and 16 on page 25.
Problems 7 and 29 on page 32.

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 4. 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 7, and 15 on page 197.
Problems 2, 9 and 12 on page 202.
Problems 6, 7 and 16 on page 209.
Problems 7, 10 and 11 on page 216.

Project 2. #17 on p.216

Chapter 11. Fourier Series, Integrals and Transforms
Problems 10, 12, 15 and 19 on page 485.
Problems 3, 7 and 17 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 5, 12 and 19 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 2, 5, 8 and 14 on page 512 - For problems 5 and 14, 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 3, 6, 15, 21 and 25 on page 537.
Problems 2, 7, 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 7, 8, 12, 13, 16 and 18 on page 560. For problems 7 and 8, 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 5 and 7 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 8 and 12 on page 626. For problem 12, 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.
Problems 6(d), 11, 23, and 24 through 29 on page 585.

Project 3. #30 on p.562. For Part b, use the Leibnits formula to derive the expansion. Use Mathcad for plots and calculations.

Chapter 24. Data Analysis, Probability Theory - Use MathCad for the following problems, whenever the need arises.
Problems 2, 4, 9 and 18(d) on page 1010.
Problems 1, 3, 8, 11, and 13 on page 1015.
Problems 1, 2, 8, 9, 11 and 12 on page 1019.
Problems 2, 5, 7, 10 and 12 on page 1025.
Problems 2, 4, 7 and 9 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.
81.40
84.50
84.80
87.30
79.70
85.10
81.70
83.70
84.50
84.70
86.10
83.20
91.90
86.30
79.30
82.60
89.10
83.70
88.50

Chapters 7, 8 and 20. Matrix Properties, Solution of Linear System of Equations and the Numerical Methods
Problems 4, 5 and 8 on page 295. If the given problem dose have a unique solution, 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.
Problems 13, 14 and 15 of Problem Set 13.1 in this notes (on partial pivoting and scaling).
Problems 2, 7 and 19 of Problem Set 13.2 in this notes (on various methods of LU-factorization).
Problems 7 and 13 on page 850 of the textbook (on Methods of Gauss-Seidel and Jacobi)
Convert y'' + 4 y' + 7/4 y = 0 with y(0) = 2 and y'(0) = -2.109 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 normal 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.A98 of the textbook.
Compare the errors of these methods.

Given y ' = yx² - y 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 7/29/2009 by WYC