SM286

Differential Equations

with

Examples from Quantum Mechanics

 

Last Updated:  04/12/2011 11:56

 

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Block I

1st Order DEs

Cooling and Mixing Problems

2nd Order Homogeneous DEs

Mass-Spring Systems

Block II

2nd Order Non-homogeneous DEs

Intro to Matrix Algebra

Systems of DEs

Block III

Power Series Solutions

Fourier Series

Intro to PDEs

Block IV

Time Independent Schrödinger Equation

Hydrogen Wave Function

Particle in a Box

Harmonic Oscillator

Particle on a Ring

Rigid Rotor

Block 1

Module

Day/Date

Reading Assignment

PROBLEMS

NOTES

1st Order DEs

1

Tue

1/11

1.1 Introduction to differential equations

(10) 1,2,13,19,27,29

 

2

Wed

1/12

1.2 Initial value problems

2.2 Separable variables

(17) 1,9,13,14,17,25,26

(50) 1,6,7,17,25;

 

3

Fri

1/14

2.3 Linear equations

(60) 3,5,10,23,27,28

 

H

Mon

1/17

Martin Luther King Day

 

 

4

Tue

1/18

2.1.Direction fields

2.6 Euler’s method

(41) 1,3

(79) 1,2

2.1 Template

5

Wed

1/19

3.1 Applications: Cooling and mixing

(89) 13,17,21,25

 

2nd Order Homogeneous DEs

6

Fri

1/21

4.1 Higher order DE’s: Existence and uniqueness

(128) 3,5,7,9,10

 

7

Mon

1/24

4.1 Higher order DE’s: Linear independence, non-homogeneous DE’s

(128) 15,18,23,25,31

 

8

Tue

1/25

4.3a Linear homogeneous constant coefficient DE’s: real roots

(139) 3,5,15,31,35

Add Deadline

9

Wed

1/26

4.3b Linear homogeneous constant coefficient DE’s: complex roots

(139) 9,11,25,29,43-48

 

10

Fri

1/28

5.1.1 Undamped mass-spring systems

(194) 1,2,3,5

(194) 9,11

 

11

Mon

1/31

5.1.2 Damped mass-spring systems

(194) 17,19,21,23,25

 

12

Tue

2/1

Test 1

 

Prereg 2,3/C

Block 2

2nd Order Non-homogenous DEs

13

Wed

2/2

4.5 Undetermined Coefficients

(156) 15-26

Prereg 2,3/C

14

Fri

2/4

4.5 Non-homogeneous DE’s by Undetermined Coef

(148)1,4,12,19,28

Prereg 2,3/C

15

Mon

2/7

5.1.3 Mass-spring system with external force

(194) 31,39

Prereg 2,3/C

16

Tue

2/8

5.1.4 Series electrical circuits

(194) 45,47,53

 

Intro to Matrix Algebra

17

Wed

2/9

Appendix II.1 Matrices

(A18) 1,3,4,7,11,15,25

 

18

Fri

2/11

Appendix II.2 Solving linear systems by row reduction

(A18) 31,35,39

 

19

Mon

2/14

Appendix II.3 Matrix inverse by row reduction

(A18) 41,43

Ac Res

20

Tue

2/15

Solving Chemical Formulae using Matrices

Supplementary Notes A

Ac Res

21

Wed

2/16

Appendix II.4 Eigenvalues and eigenvectors

(A18) 47,49,53

Ac Res

Systems of DEs

22

Fri

2/18

8.1 Systems of DEs

( 310) 1,11,13,17,21,23

Ac Res

H

Mon

2/21

Washington’s Birthday

   

23

Tue

2/22

8.2.1 Linear systems with real, distinct eigenvalues

(324) 1,3,5,7

 

24

Wed

2/23

9.4 Euler’s method for linear systems

(357) 8,9 (use Euler’s method with h = 0.1)

6 Wk Grades

25

Fri

2/25

9.4 Euler’s method for higher order DEs

(357) 1,2  (don’t do analytic solution for #2)

 

26

Mon

2/28

Test 2

 

 

 

Block 3

Module

Day/Date

Reading Assignment

PROBLEMS

NOTES

Power

Series

27

Tue

3/1

6.1.1a Review of Power Series

(230) 1,3,8,10,11,13

 

28

Wed

3/2

6.1.1b Review of  Maclaurin Series

Supplementary Notes 1

HW Solutions

 

29

Fri

3/4

6.1.1b Review of  Taylor Series

 

 

30

Mon

3/7

6.1.1c Power Series Solutions

(230) 17,27

Declare Maj

31

Tue

3/8

Power Series Continued

 

Declare Maj

32

Wed

3/9

The ‘Gaussian’ DE   

Supplementary Notes

HW Solutions

Declare Maj

33

Fri

3/11

Review

 

Early Sched

 

H

3/12-3/19

Spring Break

 

 

Fourier Series

34

Mon

3/21

11.1 Orthogonal functions

(402) 1,10,12,17

 

35

Tue

3/22

11.2 Fourier series

(407) 1,3,5,9

Prereg 4/C

36

Wed

3/23

11.2 Convergence of FS

(407) Graph FS(x) for 7,11; 17,19

Prereg 4/C

37

Fri

3/25

11.3 Sine and cosine series

(414) 1,3,5,7,11,13

Prereg 4/C

38

Mon

3/28

11.3 Half-range expansions

(414) 25,29

Prereg 4/C

Intro to PDEs

39

Tue

3/29

12.1 Separation of variables for PDEs

(436) 1,3,5,11

 

40

Wed

3/30

12.3.1 Heat equation, ends held at 0 degs

(445) 1,6

 

41

Fri

4/1

12.3.2 Heat equation, ends insulated

(445) 3,5

 

42

Mon

4/4

12.4 Wave Equation

(448) 1,2

Ac Res

43

Tue

4/5

Review

 

Ac Res

44

Wed

4/6

Test 3

 

Ac Res

Block 4

Applications

of DEs

to

Quantum

Mechanics

45

Fri

4/8

A Brief Introduction to Quantum Mechanics

Supplementary Notes 2

Ac Res

46

Mon

4/11

Time Dependent vs. Time Independent Schrödinger Equation

Supplementary Notes 3

Homework Solutions

 

47

Tue

4/12

Solution to Particle in a Box (1D)

Supplementary Notes 4

HW Solutions

12 wk grade

48

Wed

4/13

The Hermite DE

Supplementary Notes 6

HW Solutions

 

49

Fri

4/15

The Hermite DE (cont)

 

Drop Course Deadline

50

Mon

4/18

The Harmonic Oscillator

Supplementary Notes 7

 

51

Tue

4/19

Solution to the Harmonic Oscillator

 

 

52

Wed

4/20

Solution to the Harmonic Oscillator

 

 

53

Fri

4/22

Particle in a Box (2d)

Supplementary Notes 8

 

54

Mon

4/25

Particle in a Box (3d)

Team Project

 

55

Tue

4/26

4.3b DE Solutions in complex exponential forms

Supplementary Notes 9

 

56

Wed

4/27

13.1 Laplacian in Polar Coordinates

Supplementary Notes 10

 MS Word File

57

Fri

4/29

Rotational Motion in 2 Dimensions

Supplementary Notes 11

 

58

Mon

5/2

The Rigid Rotor (Separation of Variables)

Supplementary Notes 12

 MS Word File

Final

59

Tue

5/3

Review

 

 

R

Wed

5/4

Reading Day

 

 

E

TBD

TBD

Final Exam