Mathematics 810 Download Page (Spring 2010)

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


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• Course Syllabus (size: unknown, not yet posted)

• Writing Assignment (size: unknown, not yet posted)
  
 
• Handouts

Integration by Parts (size: unknown, not yet posted)

Singularly Perturbed ODE (size: unknown, not yet posted)

Differing Widths (size: unknown, not yet posted)

Dependent Scaling (size: unknown, not yet posted)

Intermediate Layers (size: unknown, not yet posted)

Nonlinear ODEs (size: unknown, not yet posted)

Singular Boundary Problem (size: unknown, not yet posted)

Higher Order Example (size: unknown, not yet posted)

Linear Two-Timing (size: unknown, not yet posted)

Introduction to Mathieu's Equation (size: unknown, not yet posted)

Two-Timing for Mathieu's Equation (size: unknown, not yet posted)

Introduction to WKB (size: unknown, not yet posted)

Connection Formulas (size: unknown, not yet posted)

Stationary Phase (size: unknown, not yet posted)

Steepest Descents (size: unknown, not yet posted)

The Monkey Saddle (size: unknown, not yet posted)

• Homework Sets

Homework Set 1 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Order notation (section 7.1).

Homework Set 2 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Asymptotic expansions, perturbations for algebraic equations (sections 7.1 and 7.2).

Homework Set 3 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

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

Homework Set 4 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Singular perturbations for linear ordinary differential equations (section 9.7).

Homework Set 5 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Singular boundary value problems, higher-order examples (section 9.5).

Homework Set 6 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Two-timing problems (sections 11.1-11.3).

Homework Set 7 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Mathieu's equation (section 11.4).

Homework Set 8 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

The WKB method (sections 10.1, 10.2).

Homework Set 9 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Connection formulas, Watson's Lemma (sections 6.1-6.4, 10.4-10.6).

Homework Set 10 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Laplace's method, stationary phase (sections 6.4, 6.5).

Homework Set 11 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Steepest descent, saddle points (section 6.6).

Homework Set 12 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

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

Homework Set 13 (size: unknown, not yet posted), Solution Set (size: unknown, not yet posted)

Singular perturbations for partial differential equations.

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