Mathematics 810 Download Page (Spring 2002)

As of October 15, 2009, large sections of this site are offline.

• 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: 12K) revised version posted 2/13/02

• Writing Assignment (size: 10K)
  
 
• Handouts

Integration by Parts (size: 31K) revised version posted 2/11/02

Singularly Perturbed ODE (size: 19K)

Differing Widths (size: 19K)

Dependent Scaling (size: 28K)

Intermediate Layers (size: 27K)

Nonlinear ODEs (size: 53K)

Singular Boundary Problem (size: 19K)

Higher Order Example (size: 28K) revised version posted 3/7/02

Linear Two-Timing (size: 18K)

Introduction to Mathieu's Equation (size: 36K)

Two-Timing for Mathieu's Equation (size: 40K)

Introduction to WKB (size: 27K)

Connection Formulas (size: 45K)

Stationary Phase (size: 31K)

Steepest Descents (size: 61K) revised version posted 4/19/02

The Monkey Saddle (size: 86K) revised version posted 4/26/02

• Homework Sets

Homework Set 1 (size: 34K), Solution Set (size: 60K)

Order notation, asymptotic expansions (section 7.1).

Homework Set 2 (size: 29K) revised version posted 2/20/02, Solution Set (size: 65K)

Singular perturbations for algebraic and linear ordinary differential equations (sections 7.2, 7.4, 9.1, 9.2, 9.4).

Homework Set 3 (size: 22K), Solution Set (size: 66K)

Singular perturbations for linear and nonlinear ordinary differential equations (sections 9.5-9.7).

Homework Set 4 (size: 21K), Solution Set (size: 73K)

Nonlinear ODEs, singular BVPs (sections 9.5-9.7).

Homework Set 5 (size: 37K) revised version posted 3/12/02, Solution Set (size: 76K)

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

Homework Set 6 (size: 51K), Solution Set (size: 69K)

Two-timing problems, Mathieu's equation (chapter 11).

Homework Set 7 (size: 40K) revised version posted 4/10/02, Solution Set (size: 85K)

Mathieu's Equation, WKB method (section 6.4, chapter 10, section 11.4).

Homework Set 8 (size: 43K) revised version posted 4/22/02, Solution Set (size: 64K)

Connection formulas, Laplace integrals (sections 6.1-6.4, 10.4-10.6).

Homework Set 9 (size: 35K), Solution Set (size: 74K)

Moving maxima, stationary phase, steepest descents (sections 6.4-6.6).

Homework Set 10 (size: 38K), Solution Set (size: 73K) revised version posted 5/7/02

The saddle point method (section 6.6).

Homework Set 11 (size: 33K), Solution Set (size: 63K)

Asymptotic expansions of sums, singular perturbations for partial differential equations (section 6.7).

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