18.085/0851 - Computational Science and Engineering I (Fall 2016)

NOTE: Please check the Stellar site for up-to-date information: https://stellar.mit.edu/S/course/18/fa16/18.085/

Syllabus

Part 1: Applied Linear Algebra

  1. Four Special Matrices

  2. Differences, Derivatives, and Boundary Conditions

  3. Elimination Leads to K = LDLT

  4. Inverses and Delta Functions

  5. Eigenvalues and Eigenvectors

  6. Positive Definite Matrices

  7. Numerical Linear Algebra: LU, QR, SVD

Part 2: A Framework for Applied Mathematics

  1. Equilibrium and the Stiffness Matrix

  2. Oscillation by Newton’s Law

  3. Least Squares for Rectangular Matrices

  4. Graph Models and Kirchhoff’s Laws

  5. Networks and Transfer Functions

  6. Nonlinear Problems

  7. Structures in Equilibrium

Part 3: Boundary Value Problems

  1. Differential Equations of Equilibrium

  2. Cubic Splines and Fourth Order Equations

  3. Gradient and Divergence

  4. Laplace’s Equation

  5. Finite Differences and Fast Poisson Solvers

  6. The Finite Element Method

  7. Elasticity and Solid Mechanics

Part 4: Fourier Series and Integrals

  1. Fourier Series for Periodic Functions

  2. Chebyshev, Legendre, and Bessel

  3. The Discrete Fourier Transform and the FFT

  4. Convolution and Signal Processing

  5. Fourier Integrals

  6. Deconvolution and Integral Equations

  7. Wavelets and Signal Processing