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18.303

Linear Partial Differential Equations: Analysis and Numerics

3-0-9 units · Undergraduate

Provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science and engineering, including heat/diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Studies operator adjoints and eigenproblems, series solutions, Green's functions, and separation of variables. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems, including stability and convergence analysis and implicit/explicit timestepping. Some programming required for homework and final project.

Fall 2014

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The {{% resource_link "89413e98-0330-4d6f-a3a9-e20c19726f5f" "Julia Language" %}} (a free, open-source environment) is introduced and used in homework for simple examples.

Readings

Fall 2006 · Linear Partial Differential Equations

This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green's functions.

Readings

  • Guenther, R. B., and J. W. Lee. Partial Differential Equations of Mathematical Physics and Integral Equations . New York, NY: Dover Publications, 1996. ISBN: 0486688895.
    Listed reading
  • Myint-U, Tyn, and Lokenath Debnath. Linear Partial Differential Equations for Scientists and Engineers. 4th ed. Boston, MA: Birkhauser, 2006. ISBN: 0817643931.
    Listed reading

Prerequisites & course information

Prereq: 18.06 or 18.700 U (Fall) 3-0-9 units

Sources