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Syllabus: Click here for details in a PDF file

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Matlab code: Click here for the matlab m-files for figures in the books

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Course: Math 182, Partial Differential Equations, MWF 11:00am Roberts North 103

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Texts: Applied Partial Differential Equations, Fourth Edition, by Richard Haberman. (required)

bullet Course Description: Fourier Series, Fourier Transforms, Distributions. Partial Differential Equations: Heat, Wave, Laplace's, Transport, SchroŐądinger, Reaction- diffusion equations, solitons, and numerical methods. Prerequisites: Math 60 and Math 111.
bullet Office Hours: MWF 10:00-11:00am @ Adams 206  and by appointment
bullet Grading: first midterm (Fri. Feb 24, 20%), second midterm (Wed. Apr. 4, 20%), final exam( Mon. May 7 9:00am, 30%), class participation (5%), and homework and quiz (25%). The letter grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale.
bullet  Policy: NO make-up exams without doctor's excuse. Late Homework will be no credit.
bullet Tentative Schedule: updated regularly

The HW problems need to be turned in. HW due every Wednesday in class. It includes all assignments given in the previous week (Mon, Wed, Fri). 

 

 

 

 

 

Monday Wednesday Friday
Jan 16 Jan 18 (Jan 17: Autumn Classes Begin)

1.1 Introduction

Click here for HW today in a PDF file

 

Jan 20

1.2 Derivation of the Conduction of Heat Equation

Click here for HW today in a PDF file

 

Jan 23

1.3 Boundary Conditions; 1.4 Equilibrium Temperature Distribution

1.4 Equilibrium Temperature Distribution ;1.5 Derivation of the Heat Equation in dimensions two and three

Jan 25

1.5 Derivation of the Heat Equation

Click here for HW today in a PDF file

 

Jan 27

HW2: book questions: 1.4.7(turn in), 1.5.9(a)(turn in), and make sure you understand how to derive (1.5.20), (1.5.22) for Laplacian in cylindrical and spherical coordinates respectively (Don't turn in).

2.1,2.2 Method of separation of variables. Linearity and superposition principle.


Jan 30 (Last day to add)

Class rescheduled due to the talk

Feb 1

2.3 Solutions of the heat equation by separation of variables method.

HW2.3(book questions): 2.3.1, 2.3.2(b)(c),2.3.3(a)

 

 

Feb 3

2.4 Examples of the heat equations problems

Click here for HW today in a PDF file

 

Feb 6

HW 2.4 book questions:2.4.1 (a,b,c,d),2.4.3

2.5 Laplace equation

 

Feb 8

2.5 Laplace equation

HW 2.5 book questions: 2.5.1(c)(e), 2.5.6(a)

 

Feb 10

2.5 Laplace equation

 

Feb 12

2.5 Laplace equation

HW 2.5: book questions: 2.5.5.(d), 2.5.7(b), 2.5.8(a)

3.1 Fourier Series: Introduction

3.2 Convergence theorem for Fourier series

HW 3.2: book questions: 3.2.1(b),3.2.2(a),3.2.3,3.2.4

 

Feb 15

3.3 Fourier cosine and sine series

HW 3.3 book questions:3.3.1(d),3.3.13

3.4 Term-by-term differentiation

HW3.4 book questions:3.4.3(a),3.4.12

Feb 17

4.1 Introduction to wave equation

4.4 Vibrating string with fixed ends

 

 

Feb 19

4.2 Wave equation: vibrating string

4.4 Vibrating string with fixed ends

HW 4.4.1(a,b), 4.4.2 (c), 4.4.3(b)

 

Feb 22

5.1 Sturm-Liouville Eigenvalue Problems

Review

Feb 24

First Exam: Ch 1 - Ch 3

exercise: 1.4.1,1.4.2,1.4.7,1.5.3,1.5.5,1.5.10,1.5.11,1.5.13

2.2.1,2.2.4,2.3.2,2.3.3,2.3.5,2.3.6,2.3.8,2.4.4,

2.5.2,2.5.3,3.3.18,3.4.9

 

Feb 27

5.1 Sturm-Liouville Eigenvalue Problems

5.2 Examples: Heat flow in nonuniform rod

5.3: General sturm-Liouville Eigenvalue Problems

HW 5.3.3, 5.3.4(a,b), 5.3.9(a,b,c)

 

Feb 29 (Low grade resports due to Registrar)

5.4 Heat Flow

HW 5.4: 5.4.2,5.4.3,5.4.6

Mar 2

Section 5.5 Self-adjoint operators

HW 5.5: 5.5.1g,5.5.9

Section 5.6 Rayleigh Quotient

HW 5.6:5.6.1c

Mar 5

Class is rescheduled due to AMS meeting

 

Mar 7

Section 5.6 Rayleigh Quotient

HW 5.6: 5.6.2

 

Mar 9

Section 5.7 Worked Example: Vibrations of a nonuniform string

HW 5.7: 5.7.1

Mar 12

Spring break

Mar 14

Spring break

Mar 16

Spring break

 

Mar 19

Section 5.8 Boundary Conditions of the Third Kind

HW 5.8: 5.8.2(c), 5.8.3(b), 5.8.7

Mar 21

Section 5.8 Boundary Conditions of the Third Kind

HW: 5.8: 5.8.8

make up class on Mar 22

Section 6.1 Finite difference

6.2 Truncated Taylor Series

 

Mar 23

Section 6.1 Finite difference

6.2 Truncated Taylor Series

HW: 6.2.1,6.2.3


Mar 26

6.3 Heat equations

HW: 6.2.5, 6.2.6

 

Mar 28

6.3 Heat equations

HW: 6.3.1
Mar 30

Cesar Chavez Holiday (observed)

 

 

 


Apr 2

6.3 Simulation of heat equation

Apr 4

Second Exam: Ch 4- 6.2

Apr 6

6.3.4 Fourier-von Neumann Stability Analysis

HW: 6.3.7,6.3.8,6.3.17

 


Apr 9

7.1 -7.2 Higher dimensional PDE

7.3 Vibrating membrane

HW: 7.3.1(c), 7.3.2(b),7.3.4(b),7.3.6(b)

Apr 11

7.4 General eigenvalue problem : Helmholtz equation

Apr 13

7.5 Green formula and self-adjoint operators

7.6 Rayleigh quotient and Laplace equation

HW:7.4.1(a),7.5.1,7.6.4(b)

 

 


Apr 16

8.1,8.2 Nonhomogeneous problems: Heat equation with sources and nonhomogeneous boundary conditions

HW 8.2: 8.2.1(a), 8.2.2(c),8.2.6(a)

Apr 18

8.3, 8.4 Method of eigenfunction expansion

Apr 20

8.3, 8.4 Method of eigenfunction expansion

HW: 8.3.1(c),8.3.5,8.3.7,8.4.1(b)

Apr 23

9.1 Green's functions for time-independent problems

9.2 One-dimensional heat equation Example

HW: 9.2.1(d), 9.2.3

Apr 25

9.3 Green's functions for boundary value problems for Ordinary Differential Equations

Apr 27

9.3 Green's functions for boundary value problems for Ordinary Differential Equations

HW: 9.3.5,9.3.9,9.3.14(d)(this question is related to dirac function and is not due!)

Apr 29

Class in RN12

May 2

9.3.4 Green's function

May 4

Review Day

May 7


May 7: Final Exam @ 9:00am

May 9


May 11