Courses:

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Calculus of Several Variables (18.02) and Differential Equations (18.03) or Honors Differential Equations (18.034)

The full schedule, organized by session number. (PDF)

This course has three major topics:

• Second difference matrices K, T, B, C
• Positive definiteness: pivots, eigenvalues, energy
• A^TCA framework for equilibrium problems
  • Springs and masses
  • Least squares and covariance matrix
  • Graphs, networks, Kirchhoff's laws
  • Deformation of trusses (and mesh generation)
  • Minimum principles and constraints
  • Finite elements in one dimension

• Ordinary differential equations
  • Boundary conditions and delta functions
  • Dynamics: Mu'' + Ku = F(t)
  • Beam equations and cubic splines
• Partial differential equations
  • Laplace and poisson equations
  • Divergence, gradient, and curl
  • Special solutions from (x + iy)ⁿ and f(x + iy)
  • Potential, stream function, Cauchy-Riemann equations
  • Finite differences and boundary conditions
  • Finite element method and weak form

• Fourier series (and orthogonal polynomials)
  • Orthogonality and Parseval's formula
  • Laplace equation on a circle
• Discrete Fourier series
  • Fourier matrix and the fast Fourier transform
  • Convolution and filtering in signal processing
• Fourier integral
  • Shannon sampling theorem
  • Differential equations
  • Integral equations (convolution kernel)

This course has nine problem sets, three one-hour exams, and no final exam. You may use your textbook and notes on the exams.

The textbook for this course is:

Strang, Gilbert. Computational Science and Engineering. Wellesley, MA: Wellesley-Cambridge Press, 2007. ISBN: 9780961408817. (Table of Contents)

Information about this book can be found at the Wellesley-Cambridge Press Web site, along with a link to Prof. Strang's new "Computational Science and Engineering" Web page developed as a resource for everyone learning and doing Computational Science and Engineering.