course information

Mathematics 23                              Winter 2004                           Syllabus

Date                              Topic                                                                 Homework (Do not hand in the starred problems.)

 1-5 1.1 Direction fields;  2.1 FOL equations 2.1:  8(c), 9, 16, 22*, 26 1-7 2.2 Separable equations;  2.3 Applications 2.2:  7, 10, 12*, 14*;  2.3: 1*, 14, 18*, 19, 25(a) 1-9 2.4 Linear vs. nonlinear equations 2.4:  1, 3, 5*, 7, 9*, 10*, 14, 15*, 22ab

 1-12 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 1-14 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* 1-16 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*

 1-20 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. 1-21 3.6  Nonhomogeneous equations, undetermined coefficients 3.6: 1*, 2, 3, 9, 14, 15* 1-23 More 3.6,  3.7 Variation of parameters 3.6:  17, 18;  3.7:  3*, 7, 8, 10*, 13, 17

 1-26 5.1, 5.2  Series solutions 5.2:  2, 15(a) 1-28 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.) 1-30 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 1-30.
Solutions to the first exam.

 2-2 7.3  Linear algebra 7.3:  2*, 4, 5, 6, 7*, 11*, 12*, 14  (Due Wed. or Friday) 2-4 7.3  Eigenvalues and eigenvectors 7.3:  15, 16, 21 2-6 7.1, 7.4  Theory of FOL systems 7.4: 3, 4, 5*, 6, 7*

No class Friday the 13th.  Class meets Tuesday the 10th during X-hour 1:00-1:50.

 2-9 7.5  Homogeneous systems 7.5: 1*, 5, 7, 11, 16, 18* 2-10 7.6  Complex roots 7.6:  1, 2*, 3, 7, 9, 10*    (due Friday, the 13th at 12:35pm) 2-11 7.8  Repeated roots 7.8:  1*, 3, 5, 9, 17a-d, 18a-d*       (due Monday, the 16th)

 2-16 10.5, 10.1  The heat equation Problem 1 here;  10.1: 1, 3, 4*;  10.5:  1, 4, 5* 2-18 10.5, 10.2  Fourier series Problem 2,  10.1:  11, 15*;  10.5:  7, 8* 2-20 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.)

The second exam on Thursday,  Feb. 26, in Rockefeller Room 1, from 6:00-8:00pm
emphasizes material from classes on 2-2 through 2-20.
Solutions to the second exam.

 2-23 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 2-25 10.5 The heat equation again 10.5:  9, 12*, 13*;  10.6:  14(a)* 2-27 10.7  The wave equation 10.7:  1abc, 8abc*

 3-1 More wave equation, D'Alembert's solution 10.7:  20 3-3 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.) 3-5 10.8 More Laplace's equation 10.8: 1ab, and the following problem: Find the steady-state 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 steady-state temperature function of the plate satisfies Laplace's equation.