Week 1
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Wed, Sept. 26 
1^{st} order Linear ODEs (gen. solution) Separable Equations 
2.12.4, 2.6 (p.8993) 
2.1: 4(c), 11(c), 18, & 29 2.2: 6, 8, 10 
Fri., Sept. 28 
Exact Equations Modeling with Differential Eqs. 
Read Chp 1 for Background 3.13.3 
2.3: 3 & 13 2.6: 4 & 13 
Week 2
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Mon, Oct. 1 
Existence and Uniqueness Theorem Theory of 2nd Order LInear ODEs 
3.13.4 
2.4: 3,7,10, 15 & 25 3.1 2,6 & 21 
Wed. Oct 3 
A little more 2nd Order theory Char. Eqs. w/ distinct real or complex roots 
3.5, 3.6 
3.2: 3, 8, 14, 23 3.3: 28 3.4: 7, 12 
Fri., Oct 5 
Char. w/ repeated roots Method of Undetermined Coefficients 
3.6 (Skip proof of Method of Undetermined Coefficients) 3.7, 3.8 
2.1: 35 3.5: 2, 11, 14, 23 3.6: 14, 15 
Week 3
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Mon, Oct. 8 
Method of Undetermined Coefficients & Variation of Parameters 
4.1 & 3.8 
3.6: 32, 33 & 34 3.7: 13, 15 & 17 
Wed. Oct 10 
Setup for General n^{th} order linear Eqs. 
3.8 & 3.9 
3.3: 1, 4, 11, 21 & 24 3.8: 6, 7, 14 & 17 
Fri., Oct 12 
Applications of 2^{nd} order ODEs 
Start Reviewing & 5.1 
3.9: 5, 9 & 11 
Week 4
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Mon, Oct. 15 
Power Series 
Study for Exam I 

Wed. Oct 17 
Power Series 
Study for Exam I 

Thurs., Oct 18 
Exam I Rockefeller Center Room 2 68pm 


Fri., Oct 19 
Series Solutions 
5.2, 7.1 & 7.2 
5.1: 5, 7, 9, 16 & 28 
Week 5
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Mon, Oct. 22 
Series Solutions to ODEs Systems of First Oder Linear Equation 
7.3 & 7.4 
Due Friday 5.2: 2, 5, 6, 8, 15(a) and 16(a) 7.1: 3, 5 & 8 
Wed. Oct. 24 
Linear Algebra: What's a vector space?, linear independence, basis, linear transformation, Matrix representation of a linear transformation. 
7.3 & 7.4 Convince yourself that matrix mult. and composition of linear transformations correspond. For instance, consider the linear transformations on 2space given by T(x,y)=(3x + 5y, x+4y) and S(x,y) = (2x3y, 7x+y). Find their matrix representations A and B repsectively. Then show that the matrix AB corresponds to the matrix for the linear transformation T(S(x,y)) and show that the matrix BA corresponds to the linear transformation S(T(x,y)). 
7.2: 15, 21(c & d), 24 & 25 
Fri., Oct. 26 
Linear Algebra: eigenvalues & eigenvectors

7.4 & 7.5 
7.3: 2, 4, 6, 14, 15, 16 & 21 
Week 6
Date 
Class Topics 
Reading (due next class) 
Problems (due next class) 
Mon, Oct. 29 
General Theory of 1st order linear eqs Homogeneous Lin. System w/ constant coefficients 
7.6 (pay attention to the pictures) 
7.4: 2 & 4 7.5: 1, 7, 11, 18 (No need to draw the pictures) 
Wed. Oct. 31 
Systems with Complex Eigenvalues 
7.8 
7.6: 1, 3, 7 & 9 (No need to draw the pictures) 
Fri., Nov. 2 
Repeated Eigenvalues 
9.1 (pay attention to the pictures) 10.1 
7.8: 1, 3, 5, 9 & 17 (No need to draw the pictures) 
Week 7
Date 
Class Topics 
Reading (for next class) 
Problems (for next class) 
Mon, Nov. 5 
Phase plane 
10.1 & 10.2 
9.1: 1, 5, 6, 11 & 17 (Do only parts (a) (b) & (c) in the first four) 
Wed. Nov. 7 
Fourier Series 
10.3 & 10.4 

Fri., Nov. 9 
Fourier Series 
10.4 & 10.5 
10.2: 7, 8, 11, 13, 16 & 29 10.3: 5 & 6 
Week 8
Date 
Class Topics 
Reading (for next class) 
Problems (for next class) 
Mon, Nov. 12 
Separation of Variables 

10.1: 2, 5, 9, 11, 14 & 17 10.4: 1, 2, 5, 6, 7, 19 (Due Friday) 
Tues. Nov. 13 
Exam II, Rockefeller Center Rm. 2 68pm 


Wed. Nov. 14 



Fri., Nov. 16 
Separation of Variables 
10.6 & Appendix A of Chp. 10 Also, during class I made the assumption that in the BVP X'' + kX = 0, X(0) = 0 = X(L), that k has to be positive. Is this valid? 
10.4: 35 10.5: 1, 7, 9, 12 & 22 
Week 9
Date 
Class Topics 
Reading (for next class) 
Problems (for next class) 
Mon, Nov. 19 
More Heat Conduction & The Wave Equation 
10.7 & 10.8 
10.4: 39 10.6: 1, 3, 4, 9(a), 11(a) & 18 Due Nov. 28 
Wed., Nov. 21 
No Class (Thanksgiving Break) 


Fri., Nov. 23 
No Class (Thanksgiving Break) 


Week 10
Date 
Class Topics 
Reading (for next class) 
Problems (for next class) 
Mon, Nov. 26 
The Wave Equation 

10.7: 1(a), 4(a) & 8(a) plus see Nov. 19 assignment 
Wed., Nov. 28 
Laplace's Equation 

10.8: 1(a & b), 3(a& b) 
Fri., Nov. 30 
Laplace's Equation & Loose Ends 


Week 11
Date 
Class Topics 
Reading (for next class) 
Problems (for next class) 
Mon, Dec. 3 
Loose Ends/ Last Day of Class 


Wed., Dec. 5 



Fri., Dec. 7 



Sun. Dec 9 
Final Exam, 13pm 

