MA3560 

Mathematical Modeling with Differential Equations

 

Instructor:     Dennis Lewandowski

Office:             Fisher 301A

Phone:            487-2793

e-mail:            dtlewand@mtu.edu

Web Site:       http://www.math.mtu.edu/~dtlewand

Course list:    ma3560-l@mtu.edu

WebCT page: MA3560 Spring 2003

Office Hours: MWF 10-11, TR 2-3

 

 

 

Text:   A First Course in Differential Equations with Modeling Applications, 7th ed by Dennis G. Zill

 

Objectives:      This course develops ODE based mathematical models for numerous physical situations. In addition to the development of the models, the course presents fundamental material on solution methods and applications of ordinary differential equations. This material motivated the development of calculus by Newton and Liebnitz and forms the foundation of a large fraction of engineering and science curricula.

 

Required Background:         Be able to: differentiate, integrate, and use the techniques of linear algebra. Have access to and know how to operate a calculator which can compute the roots of a 5th degree polynomial and the eigenvalues and eigenvectors of a 5x5 matrix

 

Topics:          Fundamental physical principles. Newtons laws of motion. What is an ordinary differential equation? Why should I care what an ODE is? An introduction to first order solution techniques. Linear constant coefficient equations. Systems of ordinary differential equations. This material corresponds to chapters: 1,2,3,4,5,7,8, and 9 of the text.

 

Reading:   Reading is assigned for each class meeting. It should be completed before the next class. It is critical to compete the readings so that you pick up details not covered in class.

 

Homework:    Homework will consist of problems from the text and problem sets handed out in class. Drop the lowest score. There will be a 10% per day fine for late homework. No homework will be accepted for text sections after they have been tested on.

 

Projects:  Experiments and projects will be assigned. Each group is to complete and turn in experiments and projects.

 

Hour Exams: There will be 2 (or 3) hour exams scheduled during the semester.

 

Final Exam: There will be a two hour comprehensive final exam.

 

 

Grading:         Homework=        20%

                        Project Reports= 15%

                        Hour Exams=     40%

                        Final Exam=       25%

                        Total=                100%

 

Grading Scale:                     A= [90%, 100%]     C=  [70%, 75%)

                                    AB= [85%, 90%)     CD= [65%, 70%)

                                    B=   [80%, 85%)      D=   [60%, 65%)

                                    BC= [75%, 80%)      F=   (0%, 60%)

 

 


Homework Assignments: 

 

Chapter #1:

Introduction to Differential Equations

1.1:  6, 8, 10, 12, 13, 19, 26, 27

1.2:  2, 4, 5, 8, 17, 18, 20, 22, 23

1.3:  2, 3, 4, 7, 9

 

Chapter#2:

 First Order Differential Equations

2.1: 2,4,6,10,14,16,18,20

2.2: 2,6,11,17,21,24,26,28,30

2.3: 5,6,8,9,11,13,14,17,21,24,26,27,29,31

2.4: 2,3,4,7,8,10,12,22,25,28

2.5: 2,5,11,13,15,19,21,30

2.6: 1,2,4

 

Chapter #3:

Modeling with First-Order ODE’s

3.1: 4,5,8,14,17,19,20,24,26,29,35

3.2: 1,2,3,7,8,22

3.3: 4,5,6

 

Chapter #4:

ODE’s of Higher Order

4.1: 2,3,16,17,19,21,23,26,31,32  

4.2: 3,6,9,11,19      

4.3: 3,6,8,9,15,19,21,23,28,32,36,38       

4.4: 5,6,11,13,16,22,26     

4.5: 2,8,13,19,21,23,45,49,53,57,61,69   

4.6: 2,4,5,6,15

4.9: 2,4,5,6,8,14,15,16

 

Chapter #5:

Modeling with Higher-Order ODE’s

5.1.1: 3,4,6,8,11

5.1,2: 21,23,25,26

5.1.3: 30,35,37

5.1.4: 46,47,52

5.2: 10,14,17,20

5.3:

 

Chapter #7:

The Laplace Transform

7.1:

7.2:

 

Chapter #8:

Systems of 1st Order Linear ODE’s

8.1: 4,5,8,10,11,15,17,22   

8.2.1:  2,3,8,12,14

8.2.2:  20,24,25,29

8.2.3:  34,36,39,43

8.3:

 

Chapter #9:

Numerical Solutions of ODE’s

9.1:

9.2: