mechanical engineering

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EGR 2323 Applied Engineering Analysis I

Summer 2014

Syllabus

Part A- Course Outline

Required Course in Engineering

Catalog Description:

(3-1) 3 hours credit.

Application of mathematical principles to the analysis of engineering problems using linear algebra and

ordinary differential equations (ODEs). Topics include: mathematical modeling of engineering problems;

separable ODE’s; first-, second-, and higher-order linear constant coefficient ODE’s; characteristic equation

of an ODE; systems of coupled first-order ODE’s; matrix addition and multiplication; solution of a linear

system of equations via Gauss elimination and Cramer’s rule; rank, determinant, and inverse of a matrix;

eigenvalues and eigenvectors; solution of an ODE via Laplace transform; numerical solution of ODE’s.

Prerequisites: Mat 1223 Calculus II

Textbooks:

Advanced Engineering Mathematics, Equations, Erwin Kreyszig, 10 th

ed., 2011, John Wiley & Sons

Reference: Schaum's Outline of Differential Equations, Richard Bronson, Paperback, 3 rd

ed., 2009

Introduction to Linear Algebra, Gilbert Strang, 4 th

ed., 2009

Major Prerequisites by Topic:

1. Algebra 2. Calculus 3. Geometry 4. Trigonometry

Course learning outcomes

The student will learn to:

1. Solve ordinary differential equations by analytical techniques 2. Learn concepts of linear algebra related to ordinary differential equations

Course Objectives: a) Identify engineering problems. b) Solve analytically ODEs commonly used to model engineering systems. c) Associate ODEs with physical phenomena descriptive of a variety of engineering problems.

Topics Covered:

1. Mathematical modeling of engineering problems 2. Separable ODE’s 3. Integrating factor 4. First-, second-, and higher-order linear constant coefficient ODEs 5. Characteristic equation of an ODE

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6. Systems of first-order ODE’s 7. Solution of a linear system of algebraic equations via Gauss elimination and Cramer’s rule,

determinant, and inverse of a matrix;

8. Eigenvalues and eigenvectors 9. Solution of an ODE via Laplace transform

Class/Laboratory Schedule:

Lecture: Two 115 minute sessions per week.

Recitation: Four 85 minute sessions per week.

Laboratory: Not applicable.

Contribution of course to meet the professional component:

This course contributes to the student’s ability to:

1. Understand the need to model engineering problems with ordinary differential equations 2. Solve ordinary differential equations analytically 3. Learn linear algebra concepts

Relationship to Engineering Program Outcomes: This course primarily contributes to Engineering program outcomes that develop the student abilities to:

 Use principles from mathematics in engineering

Evaluation Methods:

1. 3 in-class exams totally 50% of the course grade

2. Comprehensive Final Exam comprising 50% of the course grade

3. Homework can add up to 10% extra credit if the student’s total test score average exceeds 65%

Exam Assistant: NO electronic devices and NO cheat/formula sheets allowed during exams

Homework: The percentage grade for all your homework will be divided by ten and added to your course

percentage grade AS LONG AS total test percentage is 65% OR BETTER

Late Homework: NO late homework will be accepted. Homework must be turned in by the end of class on the day it is due. Once I walk out

of the classroom door it is too late. (Sorry, but the class is too large to make any exceptions.)

Performance Criteria:

Course Objectives will be evaluated by methods 1, 2 and possibly 3.

Course Content: 100% Engineering Science

UTSA policies and services regarding disabilities, dishonesty, counseling, tutoring, and the Roadrunner

Creed can be found online at provost.utsa.edu/syllabus.asp

I encourage you to utilize the academic support services available to you through the Tomás Rivera Center

(TRC) to assist you with building study skills and tutoring and Supplemental Instruction in course content.

These services are available at no additional cost to you. The TRC has several locations at the Main

Campus and is also located at the Downtown Campus. For more information, visit the web site at

www.utsa.edu/trcss or call (210) 458-4694 on the Main Campus and (210) 458-2838 on the Downtown

Campus.

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Part B: Syllabus* Instructor: Liang Sun, BSE 1.534, (210) 458-5588, [email protected]

Lectures: TR 2-3:55 pm, MH 2.01.36

Office Hours: TR 11 am – noon or by appointment.

Teaching Assistants: Jaya Chaitanya ([email protected]),

Sai Madhuri Malladi ([email protected]), Swathi Babulal ([email protected]).

Recitations: TR 10-11:25am, EB 2.04.02; W 8-9:25am, AET 0.214; F 12-1:25pm, EB 2.04.02

Content:

Schedule:

6/3 Intro, 6/5 1.1, 1.2, 1.3 6/10 Pre-req test, 1.3, 6/12 1.4,1.5 6/17 1.5,1.6 6/19 2.1,2.2 6/24 Test#1, 2.2,2.4 6/26 2.4,2.5,2.7 7/1 2.7,2.8,2.9 7/3 6.1,6.2 7/8 Test#2, 6.2

7/10 6.3,6.4 7/15 6.5 7/17 7.1,7.2,7.3 7/22 Test#3, 7.3, 7/24 7.4, 7.5 7/29 7.6, 7.7 7/31 7.8, 8.1 8/5 8.2, Model Analysis

8/7 Model Analysis

8/14 Final

*Subject to change

Section Topic Assigned Problems Due Date

Intro Calculus Hand-outs Jun 12

1.1 I order ODE: Concepts 1,3,5,7,11,12,18 Jun 12

1.2 Direction fields 1,3,5,12 Jun 12

1.3 Separable ODEs 1,3,5,9,11,13,15,19,21,24,25,27 Jun 19

1.4 Exact ODEs 1,3,5,7,9,11,13 Jun 19

1.5 Linear ODEs 1,2,3,5,7,9,15,16,17,18,19,20,31,33, 35 Jun 26

1.6 Orthogonal Trajectories 1,3,4,7,9 Jun 26

2.1 II Order ODE: Homogeneous 3,9,13,15,17,19 Jun 26

2.2 Homogeneous 1,3,5,7,9,11,1317,19,21,23,25 Jul 3

2.4 Mass-spring system 1,3,5,6,11,13 Jul 3

2.5 Euler-Cauchy equations 1,3,5,13,15 Jul 3

2.7 Non-homogenous 1,3,5,7,9,11,13,15,17 Jul 10

2.8, 2.9 Resonance 3,7,9,11,17 (2.8); 9,11 (2.9) Jul 10

6.1 Laplace Transforms 1,3,5,7,9,13,15,25,29,33,35,37,39 Jun 10

6.2 Derivatives, Integrals, ODEs 2,3,4,5,8,23,25,27 Jun 17

6.3 t-shifting 3,5,7,9,11,14,15,16,29,31 Jun 17

6.4 Dirac delta 3,5,11 Jun 17

6.5 Convolution 1,3,5,7,9,11,13,17,21,23,26 Jun 24

7.1, 7.2 Matrices: Addition, Multiplication 1,2,3,4,5,6,9,11,13 (7.1), 11,13,15,17 (7.2) Jun 24

7.3 Gauss elimination 1,3,5,8,11,13 Jun31

7.4, 7.5 Rank, Linear equations 1,3,5,7 (only rank), Hand-outs Jun31

7.6, 7.7 Determinants 1,3,7,9,11,21,23 Aug 7

7.8 Inverse 1,3,5,7,9 Aug 7

7.9 (o) Vector space Hand-outs Aug 7

8.1, 8.2 Eigenvalue problem 1,3,5,7,9,11,13 (8,1); 1,3,5, Ex. 4 (8.2)

Modal analysis Hand-outs