Monday 
Wednesday 
Friday 
Jan 16 
Jan 18 (Jan 17: Autumn Classes Begin)
1.1 Introduction
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Jan 20
1.2 Derivation of the Conduction of Heat Equation
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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
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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
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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 Termbyterm 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 SturmLiouville 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 SturmLiouville Eigenvalue Problems
5.2 Examples: Heat flow in nonuniform rod
5.3: General sturmLiouville 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 Selfadjoint 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 Fouriervon 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 selfadjoint 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 timeindependent problems
9.2 Onedimensional 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
