• Differential Equations
    • Department of Physics and Astronomy
    • Credit. 3
    • MA256
    • Enroll
    • Spring , 2015
    • 964
    • Course Description:
    • ( Exchange Programme )
    • Modelling the world in terms of ordinary and partial differential equations, solving these equations and interpreting the solutions are fundamentally important for physicists. The course “Differential Equations” for first-year undergraduate students is designed to make students familiar with the basic methods to solve linear ordinary and partial differential equations with typical boundary value problems. Topics include: solution of ODE’s with constant and non-constant coefficients; Bessel’s functions and Legendre polynomials; Fourier series; solutions of PDE’s in rectangular, cylindrical, and spherical coordinates by method of eigenfunction expansions.
    • Course Syllabus:
    • Learn the standard technique for solving ordinary differential equations with power series expansions, and be familiar with Bessel functions and Legendre polynomials. Study the approach that how to construct the partial differential equations from physical problems. Understand the basic approach called the method of separation of variables, and obtain the power series solution by the method of eigenfunction expansion in various coordinate systems.
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Introduction to Ordinary Differential Equations / 5 Credit hours / lecture / homework

      2.Series Solutions of Linear Second-Order Ordinary Differential Equations / 6 Credit hours / lecture / homework

      3.Orthogonal Functions and Fourier Series / 6 Credit hours / lecture / homework

      4.Introduction to Partial Differential Equations / 6 Credit hours / lecture / homework

      5.Partial differential equations in rectangular coordinates / 8 Credit hours / lecture / homework

      6.Partial Differential Equations in Polar and Cylindrical Coordinates / 7 Credit hours / lecture / homework

      7.Partial Differential Equations in Spherical Coordinates / 7 Credit hours / lecture / homework

      8.Fourier and Laplace transforms and their applications to partial differential equations / 3 Credit hours / lecture / homework
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • 罗旭东
    • Associate Professor
    • Read more
    • Male
    • E-mail:
    • luoxd@sjtu.edu.cn
    • Profile
  • Prerequisite Course:

    Advanced Mathematics

  • Textbooks:

    Partial differential equations and boundary value problems with Fourier series, by N H Asmar, Pearson Education.
  • Grading:

    30% Homework
    70% Final exam
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