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18.085

Computational Science and Engineering I

3-0-9 units · Undergraduate

Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications.

Summer 2020

Topics

  • Review of Linear Algebra
  • Review of Linear Algebra (cont.)
  • Differences, Derivatives, and Boundary Conditions
  • Inverses and Delta Functions
  • Eigenvalues and Eigenvectors
  • Positive Definite Matrices and Least Squares
  • Numerical Linear Algebra: LU, QR, SVD
  • Equilibrium and the Stiffness Matrix
  • Oscillation by Newton’s Law I
  • Oscillation by Newton’s Law II
  • Graph Models and Kirchhoff’s Laws
  • Damped Harmonic Oscillators and the Laplace Transform I
  • Damped Harmonic Oscillators and the Laplace Transform II
  • [no lecture]
  • Review of Vector Calculus I
  • Review of Vector Calculus II; Fourier Series
  • Fourier Series (cont.)
  • Polar Coordinates and Laplace’s Equation
  • Laplace’s Equation and Separation of Variables
  • Laplace’s Equation and Finite Difference
  • The Finite Element Method I
  • The Finite Element Method II
  • The Discrete Fourier Transform and the FFT I
  • The Discrete Fourier Transform and the FFT II
  • Convolution and Signal Processing
  • Fourier Integrals
  • Course Review
  • Guest Lectures
  • Special Topic: Deep Learning/Double Descent

Readings

Fall 2008

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications. Note: This course was previously called "Mathematical Methods for Engineers I."

Readings

Prerequisites & course information

Subject meets with 18.0851 Prereq: Calculus II (GIR) and ( 18.03 or 18.032 ) U (Fall, Summer) 3-0-9 units

Sources