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2.087

Engineering Mathematics: Linear Algebra and ODEs

2-0-4 units · Undergraduate

Introduction to linear algebra and ordinary differential equations (ODEs), including general numerical approaches to solving systems of equations. Linear systems of equations, existence and uniqueness of solutions, Gaussian elimination. Initial value problems, 1st and 2nd order systems, forward and backward Euler, RK4. Eigenproblems, eigenvalues and eigenvectors, including complex numbers, functions, vectors and matrices.

Fall 2014 · Engineering Math: Differential Equations and Linear Algebra

Topics

  • Course introduction: What are differential equations and linear algebra? How do engineers use them? Four examples of first order differential equations.
  • First-order equations: Constant source, step function (Heaviside), delta (Dirac), exponentials, real and complex sinusoids.
  • Recitation
  • First-order equations (continued): Separable equations, exact equations.
  • Second-order equations: Second derivatives in engineering, complex numbers, constant coefficient equations.
  • Second-order equations (continued): Forced oscillations, examples in electrical and mechanical systems, Laplace transforms.
  • Laplace transforms (continued): Graphical Methods: Direction fields, nonlinear equations, sources, sinks, saddles, and spirals.
  • Graphical and numerical methods: Linearization, stability, Euler’s method.
  • Linear systems of equations: Gaussian elimination, matrix multiplication.
  • Linear systems of equations: Matrix inverse. Existence and uniqueness of solutions. Column, row, null space.
  • Linear systems of equations (continued): Mechanical engineering examples.
  • Eigenvalues and eigenvectors: The eigenvalue problem. Diagonalization, exponentiation of a matrix.
  • Least squares and projection: Positive definite matrices. Singular value decomposition.

Readings

Prerequisites & course information

Prereq: Calculus II (GIR) and Physics I (GIR) U (Fall; first half of term) Not offered regularly; consult department 2-0-4 units

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