## Mathematics 617-010Techniques of Applied Mathematics Spring 2019Department of Mathematical Sciences University of Delaware

### As of November 22, 2021, large portions of this site are offline.

• Course Syllabus (size: 126K)
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• Writing Assignment (size: 78K)
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• Handouts
•  Review (size: 247K) Fourier and Laplace Series (size: 195K) revised version posted 4/11/19 Classification (size: 202K) Standing Waves (size: 159K) Fourier Series (size: 191K) Frobenius Series Review (size: 214K) Sine and Cosine Series (size: 224K) Bessel Functions (size: 191K) Pointwise Convergence (size: 159K) Legendre Polynomials (size: 191K) Sturm-Liouville Completeness (size: 157K) The Navier-Stokes Equations (size: 163K) revised version posted 5/7/19 The Delta Function (size: 202K) revised version posted 3/13/19 The Blasius Solution (size: 186K) The Green’s Function (size: 157K) The Elastica (size: 119K) Fourier Transforms (size: 206K)
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• Homework Sets
Homework Set 1 (size: 102K), Solution Set (size: 236K)
Classification of second-order PDEs, separation of variables, orthogonality (section G2-6, G5-1, G7.6, L5.1).
Homework Set 2 (size: 199K) revised version posted 2/28/19, Solution Set (size: 130K)
Fourier series the heat equation (sections G3-1—G3-3, G5-1, G7-6, L5.1, L5.3, L6.4.2).
Homework Set 3 (size: 89K), Solution Set (size: 135K)
Maximum principle, Sturm-Liouville theory (sections G5-2, G7-1, G7-6, G7-10, L5.1, L5.2).
Homework Set 4 (size: 112K), Solution Set (size: 219K) revised version posted 3/26/19
Delta and Green’s functions (sections G7-2, L5.5, and L5.6).
Homework Set 5 (size: 104K), Solution Set (size: 219K)
Fredholm alternative, advanced ODEs (sections G7-7, L5.5, L5.6).
Homework Set 6 (size: 184K), Solution Set (size: 131K)
Fourier and Laplace transforms, heat and wave equations (sections G3-4, G3-5, G4-1, G5-1, L6.1, L6.2, L6.5, L7.4.1, L7.4.2).
Homework Set 7 (size: 215K), Solution Set (size: 152K)
Wave equation, Bessel functions (sections G4-2, G4-3, G10-1, G10-2, L7.4).
Homework Set 8 (size: 116K), Solution Set (size: 135K) revised version posted 5/14/19
Laplace’s equation, Poisson’s integral formula, spherical harmonics (sections G8-1, G8-2, G8-4, L6.3).
Homework Set 9 (size: 144K), Solution Set (size: 160K)
Legendre polynomials, unidirectional flows, lubrication theory (sections G12-1, L8.4).
Supplemental Study Material (size: 118K) revised version posted 5/20/19, Solution Set (size: 96K)
Inviscid flows, Fredholm integral equations (sections G7-5, G12-1, L5.4.2, L5.4.3, L8.4).