# SF1629 Differential Equations and Transforms II 9.0 credits

## Differentialekvationer och transformer II

## Please note

This course has been cancelled.

A course of (mostly) ordinary differential equations and transform methods, including Fourier series.

#### Education cycle

First cycle#### Main field of study

Mathematics

Technology

#### Grading scale

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

Last planned examination: autumn 19.

At present this course is not scheduled to be offered.

## Intended learning outcomes

After the course, the students should be able to

- solve first order ordinary differential equations (especially separable, linear and exact equations)
- solve second order linear differential equations using reduction of order and variation of parameters
- solve second order linear differential equations using power series
- solve differential and integral equations using Laplace transforms
- solve systems of first order linear differential equations, classify critical points of autonomous systems, determine the trajectories and phase portraits for autonomous systems and investigate the stability of critical points (especially by linearization)
- calculate Fourier series and their sums
- use summation kernels
- solve approximation problems using orthogonal projections in inner product spaces
- solve problems using systems of orthogonal polynomials
- solve partial differential equations using separation of variables
- solve the Dirichlet problem in the unit disc
- solve Sturm-Liouville problems
- calculate Fourier transforms, use Fourier transforms and convolutions in order to carry out computations (including applications to partial differential equations) and use the Z-transform
- carry out computations using distributions and their derivatives and Fourier Transforms

## Course main content

First order differential equations. Second order linear equations. The Laplace transform. Systems of differential equations. Qualitative methods for non-linear differential equations. Analysis at critical points. Long termbehaviour. Stability. Existence- and uniqueness theorems.

Fourier series, orthogonal systems of functions. Sturm-Liouville problems.

The Fourier transform. Discrete transforms. Distributions. Partial differential equations. Separation of variables. Applications to ordinary and partial differential equations.

## Eligibility

SF1602 + SF1603 Differential and integral calculus II, parts 1 and 2, as well as SF1604 Linear Algebra.

## Literature

Boyce-Diprima:Elementary Differential Equations and Boundary Value Problems, 10:th ed.

Anders Vretblad: FOURIERANALYSIS and Its Applications.

## Examination

- TEN1 - Examination, 4.5, grading scale: A, B, C, D, E, FX, F
- TEN2 - Examination, 4.5, grading scale: A, B, C, D, E, FX, F

## Requirements for final grade

Two written exams (TEN1;4,5 cr, TEN2;4,5 cr).

## Offered by

SCI/Mathematics

## Examiner

Anders Szepessy <szepessy@kth.se>

John Andersson <johnan@kth.se>

## Version

Course syllabus valid from: Autumn 2013.

Examination information valid from: Autumn 2007.