Advanced Engineering Math

Fall 2009 Syllabus

Instructor: Ken Bosworth

Textbook: Draft chapters from the instructor's textbook.

Topics to be covered (these may be slightly amended after consultation with the NE program, and preferences of students enrolled this semester):

Fall 2009

• Quick review of calculus, basic linear algebra, and multivariate differential calculus

• 1-d linear differential equations:

  • the variation of parameters formula and the superposition principle

• 1-d nonlinear differential equations:

  • models

  • phase portraits,

  • equilibrium points,

  • stability analysis,

  • local linearizations,

  • bifurcation diagrams

• systems of ODE's:

  • models

  • linear systems

    • the matrix exponential

    • variation of parameters

    • stability of linear systems

    • transient vs. long-term solutions

    • phaseportraits

  • nonlinear systems

    • equilbrium points

    • stability analysis,

    • local linearizations,

    • Lyaponov functions

    • phase portraits

    • chaotic systems

• approximation techniques for ODE's:

  • power series

    • review of power series,

    • power series as approx. techniques,

  • Bessel-Fourier series

    • Bessel functions

    • Bessel series as approx. techniques,

  • problems depending on a small parameter

    • non-dimensionalization

    • regular perturbation