Mathematics 23
Winter 2004
Syllabus
Date
Topic
Homework (Do not
hand in the starred problems.)
15 
1.1 Direction
fields; 2.1 FOL equations 
2.1: 8(c),
9, 16, 22*, 26 
17 
2.2 Separable
equations; 2.3 Applications 
2.2: 7,
10, 12*, 14*; 2.3: 1*, 14, 18*, 19, 25(a) 
19 
2.4 Linear vs.
nonlinear equations 
2.4: 1,
3, 5*, 7, 9*, 10*, 14, 15*, 22ab 
112 
p.73 Bernoulli equations;
2.6 Exact equations and integrating factors

2.4: 28*, 29*,
30; 2.6: 1*, 2*, 10, 13, 19*, 20, 26*, 29 
114 
3.1, 3.2 Second
order linear homogenous equations 
3.1: 1*, 2, 5,
10, 21*, 29; 3.2: 3, 6*, 8*, 9, 14, 16* 
116 
3.2, 3.3 Abel's theorem;
3.4 complex roots 
3.2: 23*, 26;
3.3: 17, 18*, 22*, 24, 25*, 27* (Ignore the first
sentence.) 3.4: 2, 3* 
120 
3.4, 3.5 Reduction of order,
complex roots 
3.4: 7, 9*, 12*, 27;
3.5: 2, 11, 14*, 25, 28* due Thursday, the 22nd by 4:00pm. 
121 
3.6 Nonhomogeneous
equations, undetermined coefficients 
3.6: 1*, 2, 3, 9, 14, 15* 
123 
More 3.6, 3.7 Variation
of parameters 
3.6: 17, 18; 3.7:
3*, 7, 8, 10*, 13, 17 
126 
5.1, 5.2 Series solutions 
5.2: 2, 15(a) 
128 
5.2, 5.3 More series solutions 
5.2: 5, 6, 16(a), 10*(Since
one solution is a polynomial, you might want to think about getting
the other using reduction of order.); 5.3: 5*, 6*, 7,
12(The first three nonzero terms are enough.) 
130 
7.1, 7.2 FOL systems,
matrices 
7.1: 5, 8, 11*; 7.2:
1*, 10, 17*, 21(c)*, 22, 24, 25* 
The first exam on Wednesday,
Feb. 4, in Rockefeller Room 1, from 6:00 to 8:00pm covers up
to and including material from class on 130.
Solutions to the
first exam.
22 
7.3 Linear algebra 
7.3: 2*, 4, 5, 6, 7*, 11*,
12*, 14 (Due Wed. or Friday) 
24 
7.3 Eigenvalues and eigenvectors 
7.3: 15, 16, 21 
26 
7.1, 7.4 Theory of FOL systems 
7.4: 3, 4, 5*, 6, 7* 
29 
7.5 Homogeneous systems 
7.5: 1*, 5, 7, 11, 16, 18* 
210 
7.6 Complex roots 
7.6: 1, 2*, 3, 7, 9, 10*
(due Friday, the 13th at 12:35pm) 
211 
7.8 Repeated roots 
7.8: 1*, 3, 5, 9, 17ad, 18ad*
(due Monday, the 16th) 
216 
10.5, 10.1 The heat equation 
Problem 1 here;
10.1: 1, 3, 4*; 10.5: 1, 4, 5* 
218 
10.5, 10.2 Fourier series 
Problem 2,
10.1: 11, 15*; 10.5: 7, 8* 
220 
10.2 More Fourier series 
10.2: 13, 16*, 17 (On 13 and 16, also
graph the first three partial sums of the Fourier series you find.) 
223 
10.3, 10.4 Fourier convergence thm.,
sine and cosine series 
10.3: 1, 3b*, 6b; 10.4: 7, 11*, 17*,
18*, 27abc, 35*, 36 
225 
10.5 The heat equation again 
10.5: 9, 12*, 13*; 10.6: 14(a)* 
227 
10.7 The wave equation 
10.7: 1abc, 8abc* 
31 
More wave equation, D'Alembert's solution 
10.7: 20 
33 
10.8 Laplace's equation 
10.7: 4ab (Use D'Alembert's method with L = 6,
not 10. Sketch u(x,t) at times t when the two traveling waves making
up D'Alembert's solution have moved 1, 2, 3 and 4 units.) 
35 
10.8 More Laplace's equation 
10.8: 1ab, and the following problem: Find the steadystate temperature, to the nearest degree, at the center of a square metal plate if three edges are kept at 0 degrees and the fourth at 100 degrees. Assume that the steadystate temperature function of the plate satisfies Laplace's equation. 