MATH 810 Download Page

• Textbook:
• Bender, C. M., and Orszag, S. A. Advanced Mathematical Methods for Scientists and Engineers. New York: Springer-Verlag, 1999.
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• Suggestion Box

• Course Syllabus (size: 125K)
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• Writing Assignment (size: 73K)
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• Inverted Pendulum Video
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• Handouts

  Integration by Parts (size: 136K)

  Singularly Perturbed ODE (size: 155K) revised version posted 2/24/16

  Two Layers (size: 137K) revised version posted 2/24/16

  Dependent Scaling (size: 117K) revised version posted 2/24/16

  Differing Widths (size: 132K) revised version posted 2/24/16

  Intermediate Layers (size: 148K) revised version posted 3/2/16

  Nonlinear ODEs (size: 163K) revised version posted 2/26/16

  Singular Boundary Problem (size: 118K) revised version posted 3/3/16

  Higher Order Example (size: 140K)

  Linear Two-Timing (size: 158K) revised version posted 3/10/16

  Nonlinear Two-Timing (size: 140K) revised version posted 3/17/16

  Introduction to Mathieu’s Equation (size: 121K) revised version posted 3/22/16

  Two-Timing for Mathieu’s Equation (size: 142K)

  Introduction to WKB (size: 127K) revised version posted 3/25/16

  Connection Formulas (size: 148K) revised version posted 4/7/16

  Stationary Phase (size: 123K)

  Steepest Descents (size: 129K)

  Saddle Points (size: 1.4M) revised version posted 4/26/16

  The Monkey Saddle (size: 511K)

  Elliptic PDEs (size: 144K)

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• Homework Sets

  Homework Set 1 (size: 106K), Solution Set (size: 124K)

  Order notation, asymptotic expansions (sections 6.3 and 7.1).

  Homework Set 2 (size: 97K), Solution Set (size: 132K)

  Singular algebraic equations, linear ordinary differential equations (sections 7.1, 7.2, 9.1, 9.2).

  Homework Set 3 (size: 74K), Solution Set (size: 128K)

  Singular perturbations for linear ordinary differential equations (sections 9.1-9.6).

  Homework Set 4 (size: 79K), Solution Set (size: 126K)

  Singular boundary value problems, nonlinear ODEs (section 9.7).

  Homework Set 5 (size: 87K), Solution Set (size: 171K)

  Higher order ODEs, linear two-timing problems (sections 9.5, 11.1-11.3).

  Homework Set 6 (size: 128K), Solution Set (size: 133K)

  Nonlinear two-timing, Mathieu’s equation (sections 11.1-11.4).

  Homework Set 7 (size: 96K), Solution Set (size: 166K)

  Mathieu’s equation (section 11.4).

  Homework Set 8 (size: 128K) revised version posted 4/13/16, Solution Set (size: 137K)

  The WKB method (sections 10.1, 10.2, 10.4-10.6).

  Homework Set 9 (size: 105K), Solution Set (size: 128K)

  Watson’s Lemma (sections 6.1-6.4).

  Homework Set 10 (size: 106K), Solution Set (size: 141K)

  Laplace’s method, stationary phase (section 6.5).

  Homework Set 11 (size: 119K) revised version posted 5/4/16, Solution Set (size: 145K)

  Steepest descent, saddle points (section 6.6).

  Homework Set 12 (size: 125K) revised version posted 5/5/16, Solution Set (size: 212K)

  Saddle points, asymptotic expansions of sums, singular perturbations for partial differential equations (sections 6.6, 6.7).

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