Mathematics 535-010Introduction to Partial Differential Equations Spring 2024Department of Mathematical Sciences University of Delaware

• Course Syllabus (size: 148K)
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• References
• Laplace Transforms and PDEs:
Texas Tech
Manitoba
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• Resources
•  Fourier Series (size: 202K) Traveling Waves Sine and Cosine Series (size: 264K) Handout (size: 228K) revised version posted 4/24 Standing Waves 1-D Movie (size: 533K) Handout (size: 196K) 2-D Movie (α=1, V=4) (size: 1.4M) Mathematical Animation (size: 2M) The Stefan Problem Mathematica Notebook (size: 6K) Handout (size: 209K) Standing Wave Video 1 Movie (St=1) (size: 431K) Standing Wave Video 2 First-Order Linear Equations Reflected Wave Video 1 Handout (size: 182K) Reflected Wave Video 2 Movie: Constant Speed (size: 372K) The Laplace Transform (size: 230K) revised version posted 4/12 Movie: Exponential Speed (size: 311K) The Error Function (size: 250K) revised version posted 4/8 Quasilinear Equations Fourier and Laplace Series (size: 230K) Handout (size: 220K) Fourier Transforms (size: 265K) revised version posted 4/17 Movie (size: 260K) Similarity Solutions (size: 202K) revised version posted 4/19 Envelopes Handout (size: 238K) Movie (size: 275K)
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• Homework Sets
Homework Set 1 (size: 139K), Solution Set (size: 164K)
Review material.
Homework Set 2 (size: 114K), Solution Set (size: 131K)
The heat equation, separation of variables, general Fourier series (sections 1.1, 1.2, 2.1-2.3).
Homework Set 3 (size: 130K), Solution Set (size: 151K)
Trigonometric Fourier series, sine and cosine series (sections 3.1-3.4).
Homework Set 4 (size: 151K) revised version posted 3/5, Solution Set (size: 153K)
Fourier series for the heat equation, maximum principle (sections 1.3, 1.4, 8.1-8.3).
Homework Set 5 (size: 139K), Solution Set (size: 146K)
Classification, the wave equation (sections 4.1, 4.2, 4.4, 4.5, 12.3-12.5).
Homework Set 6 (size: 94K) revised version posted 3/22, Solution Set (size: 178K)
Wave and Laplace’s equation (sections 2.5, 2.5.4, 7.1, 7.2.1, 7.3).
Homework Set 7 (size: 146K) revised version posted 4/9, Solution Set (size: 151K)
Laplace’s equation, Poisson integral formula, Laplace transforms (sections 2.5.1, 2.5.2, 13.1-13.3).
Homework Set 8 (size: 125K) revised version posted 4/12, Solution Set (size: 140K)
Laplace and Fourier transforms (sections 10.1, 10.3, 13.2).
Homework Set 9 (size: 136K), Solution Set (size: 145K) revised version posted 5/1
Fourier transforms, sine and cosine transforms (sections 10.3-10.5).
Homework Set 10 (size: 140K) revised version posted 5/3, Solution Set (size: 139K)
Similarity solutions, traveling waves, Stefan problem (sections 10.4.1, 14.7.3).
Homework Set 11 (size: 113K), Solution Set (size: 145K)
First-order linear and nonlinear equations (sections 12.1, 12.2, 12.6).
Supplemental Study Material (size: 139K) revised version posted 5/16, Solution Set (size: 125K)
Discontinuities (sections 12.6.4, 12.6.5).