MATH 231-DIFFERENTIAL EQUATIONS-SPRING 2015-COURSE LOG

1/8 Introduction, syllabus/ linear first-order equations (2.3)
HW: (2.3) 8,12,15, 19, 20

1/13separable equations (2.2), implicit solutions
HW: (2.2) 7,9,17,19

1/15 Existence-uniqueness theorem/Autonomous equations and the phase line (Project C, p. 32)
Geometric analysis of autonomous equations
HW1 (due Th 1/22: read the handout, solve the examples on p.3)
HW1 From text: (1.2) 27, 28

1/20 exact equations (2.4)
HW2 (due Th 1/29): (2.4) 10, 13, 25

1/22 substitutions/transformations (2.6): homogeneous type, Bernouilli
HW2 (due Th 1/29): (2.6) 10, 17, 23 (find the solution in explicit form when possible).

1/27 substitutions/transformations (2.6): linear forms, examples (42, 46, 47)

1/29 solution of homework problems/ review problems from Ch.2 (p.77): 1, 31, 39, 3, 33, 5
HW3 (due Th 2/6): (p.77) 7, 9, 38/ p.99 5,6

2/4 Applications: section 3.2 (mixing problems, population growth)
HW4 (due  Tu 2/11): sect 3.2: 15, 24

2/6 Applications: section 3.3 (radioactive decay, heating/cooling)
HW4 (due Tu  2/11) 3.3  7, 9, 11

2/10 Review/questions (HW4 due)

2/12 Exam 1 (with solutions)

included: sections 1.2, 2.2, 2.3, 2.4, 2.6, 3.2, 3.3 and the online handout.
Closed book, closed notes, no calculators

2/17 University closed due to inclement weather

2/19 Second-order linear equations: homogeneous, constant coefficients.
HW5 (now due Tu 3/3): (4.2) 3, 15 (for 15, sketch the graph of the solution)/ (4.3) 13, 21 (for 21, write the solution in amplitude/phase form, with a time-dependent amplitude; then sketch its graph.)

2/24 University closed due to inclement weather

2/26 Non-homogeneous second-order equations: undetermined coefficients (4.4), (4.5)
HW6 (also due Tu 3/3): (4.4) 13, 21 (4.5) 21, 29, 41

3/3 (4.6) Variation of parameters
HW7 (due 3/10): (4.6) 12, 17

3/5 (4.7) Variable-coefficient equations
HW7 (due 3/10): (4.7) 13, 21, 37, 48

3/10 (4.9) Free mechanical vibrations
HW8  (due 3/26): (4.9) 11, 16, 18

3/12 (4.10) Forced mechanical vibrations
HW8 (due 3/26): (4.10) 3, 9, 15

3/17, 3/19: Spring Break

3/24: Laplace transform: definition, first properties (7.1-7.3)

3/26: Laplace transform: inverse transform, solution of IVP (7.4-7.5)
HW9 (7.5)1, 6, 11; (7.6) 3, 7, 19

3/31: Laplace transform: convolution theorem
HW9 due

4/2: Exam 2: Chapters 4 and 7
Exam 2 (with solutions)

4/7 Ch. 8: Taylor approximations, power series, analytic functions (8.1, 8.2)
Practice problems (8.1) 5 (8.2) 3, 6, 17, 21, 31, 33

4/9 Ch.8 : DEs with analytic coefficients: power series solutions (8.3, 8.4)
HW 10: (8.3) 15, 25, 27 (8.4) 3, 9, 15

4/14 Power series solutions-examples/ Laplace transforms (review)
HW10 due

4/16 Exam 3 (Ch.7, 8)
Exam 3 (with solutions)

4/21 first-order linear systems: solution by substitution
Practice problems: (5.2) 7, 19, 23, 36, 38

4/23 (last day) systems (practice problems), discussion of test 3

FINAL EXAM:  Tuesday, May 5th, 2:45 PM (comprehensive)
Based on the three tests and on section 5.2

Final Exam (with solutions)