Mathematical and Computational Methods

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Course
en
English
126 h
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  • From www.edx.org
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  • 18 Sequences
  • Advanced Level
  • Starts on January 29, 2022
  • Ends on June 8, 2022

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Course details

Syllabus

  • Be able to apply techniques of calculus (learned in the first three semesters of a calculus sequence) to solve problems that arise in physics.
  • Derive and use the geometric series in calculations.
  • Manipulate power series expressions and employ them in physics contexts.
  • Calculate Taylor polynomials/series of common functions and use them in approximating functions
  • Follow the development for how one integrates polynomials, rational functions of polynomials, square roots of quadratics, rational functions with square roots of quadratics, and why the procedure cannot solve integrals with square roots of quartics.
  • Solve integrals via parametric methods (differentiating under the integral sign) including techniques for introducing the parameter into the integrand
  • Set up and integrate multidimensional integrals with variable mass density and for moments of inertia.
  • Solve problems in multivariable integrals via the different integral theorems
  • Solve Laplace's equation for simple geometries
  • Compute the curl or divergence of a vector field and the gradient of a scalar function
  • Solve complex numbers arithmetic problems
  • Use calculus of residues to solve integrals
  • Use row reduction to solve simultaneous linear equations
  • Calculate the determinant, inverse, and eigenvalues of matrices
  • Construct abstract vector spaces using the definitions of a vector space and generalized inner products
  • Solve any first-order linear differential equation
  • Solve the six classes of nonlinear first-order differential equations
  • Solve higher-order differential equations with constant coefficients (homogeneous and inhomogeneous)
  • Construct representations of curves in three dimensions using the Frenet-Serret apparatus
  • Construct Fourier series of periodic functions

Prerequisite

None.

Instructors

James Freericks
Professor
Georgetown University

Platform

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