MAT 204

Differential Equations

Spring 2014

 

Instructor: Bruce Armbrust, ph: 541-4660 x314, email: bruce.armbrust@hotmail.com

 

Office Hours: Room A210,   Mon., Wed., Thurs.     12:00  – 1:00 PM

Tues.                           10:00 – 11:00 AM

MSC A201,     Fri.                               11:00 AM – 12:00 PM

And as always, by appointment.

 

Class Time and Location: Mon., Wed., Fri.  1:00  – 2:40 PM, E106

 

Textbook: Elementary Differential Equations, 9th Edition, by Boyce & DiPrima

 

Course Description: This course covers techniques of solving ordinary differential equations including: exact, separable, and linear equations, integrating factors, the method of undetermined coefficients, variation of parameters, Laplace transforms, series solutions, systems of differential equations, and applications.

 

Prerequisite: MAT107 with a grade of “C” or better or equivalent.

 

Student Learning Outcomes:

1. Apply ordinary differential equations to problems from physics, biology, and other scientific disciplines.
2. Employ the technique of transformations in finding solutions to ordinary differential equations.
3. Prove results from the field of differential equations.
4. Sketch direction fields for first-order ordinary differential equations.
5. Solve differential equations using sequences, series, and matrices.

 

Course Grade: Your final letter grade will be based on the usual grading scale:

A 90-100%, B 80-89.99%, C 70-79.99%, D 60-69.99%, F 0-59.99%

The following items will make up the course grade:

 

Homework:                             15%

Poster Project:                        10%

Exam1 (May 2):                      20%

Exam2 (June 2):                     20%

Final Exam (June 25):                        35%

 

You may check your grades at any point in the quarter by using Passport.

 

Registration Information: You may drop the class with a full refund and no penalty or mark on your record on or before April 18.  After April 18, you may drop the class and receive a grade of W until May 23.  After May 23, if still enrolled, you will receive a grade of A, B, C, D, F or I.

 

 

Homework: Homework will be due by 3PM the class day after it is assigned.  Homework not turned in at this time will be considered late. You may turn in homework up to one week after it is assigned for half credit.  If all homework is completed (at least 50% of each assignment) and no more than two are late, you do not need to take the final exam. 

 

Poster Project: Our class will join with the 1st year calculus class as well as the calculus- based physics classes in the creation of posters demonstrating the use of calculus & physics in every-day life.  The requirements and due dates for the project will be provided at a later point.  Poster presentations will be held at a date TBD.

 

Exams:  Students are to bring a pencil and blank scratch paper to each exam.  If you cannot make it to an exam (final not included), you may take it up to 2 school days prior to the scheduled date with proper arrangements.  Otherwise, the exam may be made up after the scheduled date with a penalty of 10% per day.  The final exam must be taken no later than June 25th.

 

How to Succeed in a Math Class: I am often asked how to successfully pass a math class, and here is my advice:

 

I) Come to every class session.  Be prepared, and plan on participating.

II) Do your homework.  Remember that what I assign is what I consider a bare minimum.  If you need more practice, do it.

III) Read the book.  You paid good money for it, so you might as well use it.

IV) Make use of available tutors and my office hours.  You will find tutors who know the subject matter in this course at the MSC.

V) Do math every day.  Math is just like everything else: if you don’t practice, you become rusty.

 

Learning Disabled Students: Students with disabilities who may need accommodations for this class are encouraged to notify me and contact the Disability Resource Center (DRC) early in the quarter so that reasonable accommodations may be implemented as soon as possible.  Students may contact the DRC by visiting the Center (located in room A205) or by phoning 541-4660, ext. 249 (voice) or 542-1870 (TTY for deaf students).  All information will remain confidential.

 

Technology in the Classroom:  All cell phones, headphones, MP3 players, iPods, etc, must be turned off and put away prior to the start of each class.  No electronic devices (other than calculators) may be used during quizzes and exams.

 

Academic Dishonesty: Academic dishonesty of any form will not be tolerated.  Students caught cheating on an exam will receive a score of zero on the assignment and the ability to skip the final exam will be forfeit.  Students may work together on homework assignments (and, in fact, are encouraged to) as long as all students understand the material covered.

 

 

Course Schedule:

The following is a tentative schedule.  If things change (and I have money that says they will), I will let you know.

 

April

7          Chapter 1                    Introduction to Differential Equations

9          2.1/2.2                         Integrating Factors and Separable Equations

11        2.3                               Modeling with First Order Equations

14        2.4/2.5                         Linear vs. Nonlinear, Autonomous Equations

16        2.6                               Exact Equations and Integrating Factors

18        2.8                               The Existence and Uniqueness Theorem

21        2.9                               First Order Difference Equations

23        3.1                               Homogeneous Equations with Constant Coefficients           

25        3.2                               Linear Homogeneous Equations

28        3.3/3.4                         Complex and Repeated Roots

30        3.5                               Nonhomogeneous Equations

 

May    

2          Exam I

5          3.6                               Variation of Parameters

7          3.7                               Mechanical and Electrical Vibrations

9          3.8                               Forced Vibrations

12        4.1                               General Theory of nth Order Linear Equations

14        4.2                               Higher Order Homogeneous Equations

16        4.3                               Method of Undetermined Coefficients

19        4.4                               Method of Variation of Parameters

21        5.1                               Power Series

23        5.2                               Series Solutions near an Ordinary Point

26        NO CLASS                 MEMORIAL DAY

28        5.3                               More Series Solutions

30        5.4                               Euler Equations          

 

June

2          Exam II

4          6.1                               The Laplace Transform

6          6.2                               Initial Value Problems

9          6.3                               Step Functions

11        6.4                               Discontinuous Forcing Functions

13        7.2/7.3                         Matrices/Systems of Linear Algebraic Equations

16        7.4                               Systems of First Order Linear Equations

18        7.5                               Homogeneous Linear Systems

20        7.6                               Complex Eigenvalues

25        Final Exam                 Note: The final is from 12:00 - 1:50 PM

 

 

The following is a list of all homework assignments for this course.  The due dates for the various sections will be given in class.

 

Section

Assignment

1.1

3,16-19,22,24

1.2

3,9,12

1.3

1-6,7,12,17,20

2.1

13,15,20,31

2.2

3,6,12,17,21,25

2.3

3,10,17,27

2.4

1-6,9-12,15,16

2.5

2,12,15,17

2.6

3,8,11,15,22,25,28

2.8

1,2,3,6,9

2.9

2,5,12,14

3.1

4,7,12,15,23,24

3.2

1,5,8,12,25

3.3

7,12,15,20,22,26

3.4

2,5,12,13,25,28

3.5

2,5,6,14,17,25

3.6

9,10,13,15,29

3.7

6,8,18,26

3.8

6,8,15,16

4.1

13,16,22,23,27

4.2

14,21,25,31,34

4.3

4,7,10,14-17

4.4

1,6,11,13

5.1

2-5,11,14,21,26

5.2

2,6,15,16,21,23

5.3

1-3,6-8

5.4

2,3,6,7,14,20,24,29

6.1

5,8,19,26

6.2

5-8,12,18,22

6.3

1,5,9,12,15,22

6.4

2,4,10,13

7.2

11,12,17,18,23-26

7.3

7-10,20-23

7.4

6,7

7.5

3,9,11,15,18,30

7.6

2,5,7,15,28