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.


• Suggestion Box

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• Course Syllabus (size: 108K)

• Writing Assignment (size: 72K)
  
 
• Handouts

Integration by Parts (size: 136K)

Singularly Perturbed ODE (size: 124K)

Dependent Scaling (size: 116K)

Differing Widths (size: 100K)

Intermediate Layers (size: 116K)

Nonlinear ODEs (size: 148K) revised version posted 3/4/10


Singular Boundary Problem (size: 116K)

Higher Order Example (size: 124K)

Linear Two-Timing (size: 72K)

Introduction to Mathieu's Equation (size: 108K)

Two-Timing for Mathieu's Equation (size: 140K)

Introduction to WKB (size: 104K)

Connection Formulas (size: 148K) revised version posted 4/20/10

Stationary Phase (size: 124K)

Saddle Points (size: 148K)

The Monkey Saddle (size: 152K)

• Homework Sets

Homework Set 1 (size: 112K), Solution Set (size: 128K)

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

Homework Set 2 (size: 92K), Solution Set (size: 136K)

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

Homework Set 3 (size: 80K) revised version posted 3/5/10, Solution Set (size: 140K)

Singular perturbations for linear ordinary differential equations (sections 9.1-9.7).

Homework Set 4 (size: 96K), Solution Set (size: 176K)

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

Homework Set 5 (size: 116K), Solution Set (size: 132K)

Two-timing problems (sections 11.1-11.3).

Homework Set 6 (size: 96K), Solution Set (size: 128K)

Mathieu's equation (section 11.4).

Homework Set 7 (size: 104K) revised version posted 4/11/10, Solution Set (size: 136K)

The WKB method (sections 10.1, 10.2).

Homework Set 8 (size: 136K), Solution Set (size: 160K)

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

Homework Set 9 (size: 116K), Solution Set (size: 156K)

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

Homework Set 10 (size: 124K), Solution Set (size:152K)

Steepest descent, saddle points (section 6.6).

Homework Set 11 (size: 132K), Solution Set (size: 204.4K)

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

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