Syllabus for Math 23

Fall 2001

This is subject to change, so please check regularly

 

Week 1

Date

Class Topics

Reading (due next class)

Problems (due next class)

Wed, Sept. 26

1st order Linear ODEs (gen. solution)

Separable Equations

2.1-2.4, 2.6 (p.89-93)

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

3.1-3.3

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

3.1-3.4

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

Set-up for General nth 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 2nd 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 6-8pm

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 2-space given by T(x,y)=(3x + 5y, x+4y) and S(x,y) = (2x-3y, 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 6-8pm

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, 1-3pm