 | 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) |
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Course Description: Fourier Series, Fourier Transforms, Distributions. Partial Differential Equations: Heat, Wave, Laplace's, Transport, Schrödinger, Reaction- diffusion equations, solitons, and numerical methods. Prerequisites: Math 60 and Math 111. |
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Office Hours: MWF 10:00-11:00am @ Adams 206 and by appointment |
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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. |
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Policy: NO make-up exams without doctor's excuse. Late Homework will be no credit. |
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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
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Jan 20
1.2 Derivation of the Conduction of Heat Equation Click here for HW today in a PDF file
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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 Click here for HW today in a PDF file
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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.
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| 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)
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Feb 3
2.4 Examples of the heat equations problems Click here for HW today in a PDF file
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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
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Feb 8
2.5 Laplace equation HW 2.5 book questions: 2.5.1(c)(e), 2.5.6(a)
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Feb 10
2.5 Laplace equation
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| 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
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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
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| 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)
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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
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| 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)
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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
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Mar 7
Section 5.6 Rayleigh Quotient HW 5.6: 5.6.2
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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
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| 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
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Mar 23
Section 6.1 Finite difference 6.2 Truncated Taylor Series HW: 6.2.1,6.2.3
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| Mar 26
6.3 Heat equations HW: 6.2.5, 6.2.6
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Mar 28
6.3 Heat equations HW: 6.3.1 |
Mar 30
Cesar Chavez Holiday (observed)
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| 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
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| 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)
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| 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
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May 11
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