# SF1637Differential Equations and Transforms III6.0 credits

## Differentialekvationer och transformer III

This course is in the process of being cancelled.

Basic course in differential equations and Fourier analysis.

First cycle

C
• #### Subject area

Mathematics
Techonology

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.

• 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