SM212 Differential Equations Fall Semester 2009-2010


Text: Differential Equations with Boundary Value Problems, 7th ed., by Dennis G. Zill and Michael R. Cullen. Some quizzes and hour exams may require use of the USNA Mathematical Tables in lieu of a calculator. Your instructor will determine this.

LESSON/PAGES

SECTION/TOPIC

PROBLEMS

  1. 2-10

1.1 Introduction to differential equations

p. 10: 1,2,13,19,27,29

  1. 13-16

1.2 Initial value problems

p. 17: 1,9,13,14,15,17,25,26

  1. 44-50; 53-58

2.2 Separable variables; 2.3 Linear equations

p. 50: 1,6,7,17,25; p.60: 3,5,10,23,27,28

  1. 35-37, 75-79

2.1.1 Direction fields; 2.6 Euler’s method

p. 41: 1,3; p.79: 1,2

  1. 85-87

3.1 Applications of linear models: Cooling and mixing

p. 89: 13,17,21,25

Review


  1. 118-120

4.1 Higher order DE’s: Existence and uniqueness

p. 128: 3,5,7,9,10

  1. 120-127

4.1 Higher order DE’s: Linear independence, non-homogeneous DE’s

p. 128: 15,18,23,25,31

  1. 133-138

4.3 Linear homogeneous constant coefficient DE’s: real roots

p. 139: 3,5,15,31,35

  1. 133-138

4.3 Linear homogeneous constant coefficient DE’s: complex roots

p. 139: 9,11,25,29,43-48

Review


Test 1


  1. 150-156

4.5 Annihilators

p. 156: 5,17,21,23,31,33

  1. 150-156

4.5 Non-homogeneous DE’s by annihilators

p. 156: 39,47,51,67

Review


  1. 182-186

5.1.1 Undamped mass-spring systems

p. 194: 1,2,3,5

  1. 182-186

5.1.1 Undamped mass-spring systems

p. 194: 9,11

  1. 186-189

5.1.2 Damped mass-spring systems

p. 194: 17,19,21,23,25

  1. 189-191

5.1.3 Mass-spring system with external force

p. 194: 31,39

  1. 87-88,192-193

5.1.4 Series electrical circuits

p. 194: 45,47,53

  1. Review



  1. 256-258

7.1 Laplace transform

p. 261: 5,7,11,25,31,38

  1. 262-265

7.2.1 Inverse LT

p. 269: 5,15,23,27

  1. 265-269

7.2.2 Solving DE’s using LT’s

p. 269: 33,35,39

  1. 270-274

7.3.1 First translation theorem

p. 278: 5,9,11,15,21,29

  1. 274-277

7.3.2 Unit step function

p. 278: 37,41,49,51,53

  1. 274-277

7.3.2 Unit step function in a DE

p. 278: 65,71,73

  1. Review



  1. 282-286

7.4 Derivative of LT, convolution

p. 289: 1,3,11,19,25,33

  1. 292-294

7.5 Dirac delta function

p. 295: 1,3,9,11

  1. 295-297

7.6 Solving systems of DE’s using LT’s

p.299: 1,3,14

Review


Test 2


  1. App-3-App-10

Appendix II.1 Matrices

p. App-18: 1,3,4,7,11,15,25

  1. App-10-App-14

Appendix II.2 Solving linear systems by row reduction

p. App-18: 31,35,39

  1. App-10-App-14

Appendix II.2 Matrix inverse by row reduction

p. App-18: 41,45

  1. App-14-App-18

Appendix II.3 Cramer’s rule, eigenvalues and eigenvectors

p. App-18: 47,49,53

Review


  1. 304-310

8.1 Systems of DE’s

p. 310: 1,11,13,17,21,23

  1. 311-315

8.2.1 Linear systems with real, distinct eigenvalues

p.324: 1,3,5,7

  1. 320-324

8.2.3 Linear systems with complex eigenvalues

p.324: 33,35,37,39

  1. 329-332

8.3.2 Nonhomogeneous systems by variation of parameters

p.332: 11,13,15,29

  1. 109-110,297-298

3.3,7.6 Electrical networks

p. 299: 15,16 [use LT’s for this one]; p. 332: 33

  1. 353-355

9.4 Euler’s method for linear systems and higher order DE’s

P.357: 1,9 (use Euler’s method with h = 0.1)

Review


Test 3


  1. 398-402

11.1 Orthogonal functions

p.402: 1,10,12,17

  1. 403-405

11.2 Fourier series

p.407: 1,3,5,9

  1. 405-407

11.2 Convergence of FS’s

p. 407: Graph FS(x) for 7,11; 17,19

  1. 408-411

11.3 Sine and cosine series

p.414: 1,3,5,7,11,13,25,29

  1. 433-435

12.1 Separation of variables for partial differentials equations

p.436: 1,3,5,11

  1. 443-444

12.3 Heat equation, ends held at 0 degrees

p.445: 1,6

12.3 Heat equation, ends insulated

p.445: 3,5

Review


Review


Test 4


Final examination review


Final examination review






Course webpage for Prof. Joyner's sections:

http://www.usna.edu/Users/math/wdj/teach/sm212/

Old exams and quizzes (with solutions) and class lecture notes and videos are there.



Course coordinator: Prof Buchanan, jlb@usna.edu