SM212 Differential Equations
Fall Semester 2014-2015
Text: Differential Equations with Boundary Value Problems, 8th ed., by Dennis G. Zill and
Warren S. Wright.
Lesson
Section/Topic
Problems
1 1.1 Introduction to differential equations
1,3,5,13,19,23,29,32,33
2 1.2 Initial value problems
1,3,7,9,11,16,17,25,27
3 2.2 Separable DE’s
1,3,5,6,7,17,23,25
4 2.3 First order linear DE’s
3,5,7,9,11,25,27
5 2.1.1 Direction fields; 2.6 Euler’s method
p. 43: 1,3; p.79: 1,2
6 3.1 Applications of linear models: Cooling and
13,17,21,23,25
mixing
7 Review
8 4.1.2 Homogeneous Linear Equations
15,17,21,23,25,27,40
9 4.3 Linear homogeneous DE’s: real roots
3,5,15,17,21,31,37
10 4.3 Linear homogeneous DE’s: complex roots
9,11,19,23,29,43-48
11 5.1.1 Mass-Spring Systems (free undamped
1,2,3,5
motion)
12 5.1.1 Free undamped motion continued
9,11
13 5.1.2 Mass-Spring Systems (free damped
17,19,21,23,25
motion)
14 Review
15 Review
16 Test 1
17 4.1.3 Non-Homogeneous Linear Equations
31,34,36
18
4.4 Undetermined Coefficients
1,4,5,8,11,12,13
19
4.4 Undetermined Coefficients
27,29,31,37
20 5.1.3 Mass-spring system with external force
29,31,33
21 5.1.3 Mass-spring system: Resonance
37,39
22 5.1.4 Series electrical circuits
45,47,53
23 Review
24 7.1 Laplace transform
5,7,11,25,31,38
SM212 Differential Equations
Lesson
Section/Topic
Fall Semester 2014-2015
Problems
25 7.2.1 Inverse LT
5,15,23,27
26 7.2.2 Solving DE’s using LT’s
33,35,39
27 7.3.1 First translation theorem
5,9,11,15,21,29
28 7.3.2 Unit step function
37,41,49,51,53
29 7.3.2 Unit step function in a DE
65,71,73
30 Review
31 Review
32 Test 2
33 7.4 Derivative of LT, convolution
1,3,11,19,25,33
34 7.5 Dirac delta function
1,3,9,11
35 Appendix II.1 Matrices
1,3,4,7,11,15,25,29
36 Appendix II.2 Solving linear systems by row
31,35,39
reduction
37 7.6 Solving systems of DE’s using LT’s
1,3,5,7,9
38
13,14
7.6 Coupled Mass-Spring Systems
39 3.3,7.6 Electrical networks
15,16
40 Appendix II.3 Eigenvalues and eigenvectors
47,48,49,50,55
41 8.1 Linear systems of DE’s
1,11,13,17,21,23
42 8.2.1 Systems with real, distinct eigenvalues
1,3,5,7
43 8.2.3 Linear systems with complex eigenvalues
33,35,37,39
44 Review
45 8.3.2 Nonhomogeneous systems
11,13,15,29
46 9.4 Euler’s method for linear systems and
1,2
higher order DE’s
47 Review
48 Test 3
49 11.2 Fourier Series
1,3,5,7,9 For each problem
graph the function to which the
series converges over three
periods
SM212 Differential Equations
Lesson
Section/Topic
Fall Semester 2014-2015
Problems
50 11.3 Even and Odd Functions
1,3,5,7,8,11,12,13,15
51 11.3 Half-Range Expansions
25,29,31
52 12.1 Separable Partial Differential Equations (1
1,3,5
order)
53 12.1 Separable Partial Differential Equations
10,11,13,15
nd
(2 order)
54 12.3 Heat Equation (ends held at 0 degrees)
1,2
55 12.3 Heat Equation (ends insulated)
3,4
56 Review
57 Review
58 Test 4
59 Review for Final Examination
Notes:
1. The problems assigned, and the number and timing of the exams, may be altered by your
instructor.
2. WebAssign: Your instructor may wish that you use the online homework system WebAssign
in place of paper submissions. Access codes for WebAssign come bundled with your
textbook. Consult your instructor for more details.
3. Calculator: Midshipmen will need a calculator capable of symbolic computations, such as
the TI-Nspire. Your instructor, however, may prohibit its use on some quizzes and all or
parts of hour exams.
4. Getting help: In addition to EI from your instructor, you can visit Math Lab (CH130), which
is staffed by USNA Math Department faculty every academic period of every academic day.
Finally, you may avail yourself of various programs offered by the Center for Academic
Excellence (MGSP, Professional Evening Tutoring, Supplemental Instruction, etc.).
5. Final Exam: SM212 has a common Final Exam, which is 50% multiple choice and 50% freeresponse. Use of a calculator on the multiple choice part may be forbidden. Old final
exams and their solutions are available from the Math Department website: http://
www.usna.edu/MathDept/resources/course-materials.php
Course coordinator: Prof J. Buchanan, jlb@usna.edu