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SF1637 Differential Equations and Transforms III 6.0 credits

Differentialekvationer och transformer III

Please note

This course is in the process of being cancelled.

Basic course in differential equations and Fourier analysis.

  • Educational level

    First cycle

  • Academic level (A-D)

    C

  • Subject area

    Mathematics
    Techonology

  • Grade scale

    A, B, C, D, E, FX, F

Last planned examination: Spring 15

At present this course is not scheduled to be offered.

Learning outcomes

To provide the students with

  • Knowledge of basic theory of ordinary differential equations
  • Ability to solve certain types of (systems of) ordinary differential equations with standard methods
  • Ability to investigate (systems of) ordinary differential equations with elementary geometrical and qualitative methods
  • Ability to compute Fourier series and Fourier transforms
  • Ability to solve separable partial differential equations and to find solutions to boundary value problems using Fourier methods.
  • Possibilities of further studies of related topics specific to their educational programme
  • Ability to use suitable software for symbolic as well as graphical investigations of the types of problems mentioned above
  • Ability to apply these skills to mathematical modelling.

Course main content

  • First order ordinary differential equations: Basic theory and concepts. Modelling. Direction fields and solution curves. Autonomous equations, stationary solutions and stability. Separable equations. Linear equations. Substitutions.
  • Linear ordinary differential equations of higher order: Basic theory. Methods for solving equations with constant coefficients. The harmonic oscillator.
  • Systems of linear ordinary differential equations: Basic theory and concepts. Solutions to linear systems with constant coefficients using the eigenvalue method (homogeneous systems) and ”variation of parameters” (particular solutions to non-homogeneous systems).
  • Autonomous systems of ordinary differential equations: Basic concepts. Stationary solutions and stability. Brief discussion about global phase portraits. Modelling
  • Fourier series and Fourier transforms with applications.
  • Linear partial differential equations: Separation of variables. Solutions to classical boundary value problems (the wave equation, the heat equation, Laplace’s equation) using Fourier methods.
  • Program specific contents.

Eligibility

Basic knowledge in linear algebra and calculus equivalent to 5B1143/SF1623 Mathematics 1 for teachers and 5B1123/SF1613 Mathematics 2 for teachers, or 5B1104/SF1600 + 5B1105/SF1601 Calculus I, part 1 + 2 and 5B1109/SF1604 Linear algebra.

Literature

Zill-Cullen/Differential Equations with Boundary-Value Problems, 6:th ed.

Examination

  • TEN1 - Examination, 6.0 credits, grade scale: A, B, C, D, E, FX, F

Requirements for final grade

TEN1, 6 hp. Final oral and/or written exam and continuous examination.

Offered by

SCI/Mathematics

Examiner

Version

Course plan valid from: Autumn 07.
Examination information valid from: Autumn 07.