Course syllabus for Applied mathematics

The course syllabus contains changes
See changes

Course syllabus adopted 2024-02-08 by Head of Programme (or corresponding).

Overview

  • Swedish nameTillämpad matematik
  • CodeTMA683
  • Credits7.5 Credits
  • OwnerTKKMT
  • Education cycleFirst-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language Swedish
  • Application code 53116
  • Maximum participants135
  • Open for exchange studentsNo
  • Only students with the course round in the programme overview.

Credit distribution

0115 Project 1.5 c
Grading: UG		 1.5 c
0215 Examination 6 c
Grading: TH		 6 c
  • 16 Jan 2025 am L
  • 14 Apr 2025 am J
  • 21 Aug 2025 pm J

In programmes

Examiner

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Eligibility

General entry requirements for bachelor's level (first cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

The same as for the programme that owns the course.
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

Analysis
  • Calculus (single and several variables): Complex numbers, series, trigonometry, Green's formula, Stokes's and Gauss theorems.
  • Integral calculus: Partial integration, partial devision of rational functions, numerical integration and multiple integrals.
  • Differential equations: Linear ordinary differential equation of first (scalar and system) and second order.
Linear Algebra
  • Linear system of equations
  • Matrix algebra
  • Linear spaces and eigenvalue problem.
Programming in MATLAB

Aim

The aim of this course is to study numerical, as well as analytical solutions for partial (and ordinary) differential equations (PDEs). To solve PDEs is one of the most modern mathematical tools applied in science and engineering.

Learning outcomes (after completion of the course the student should be able to)

After passing this course the student should be able to:
  • numerically solve partial and ordinary differential equations (such as (time dependent or stationary) heat equation, wave equation, convection-diffusion and reaction-diffusion equation) using the finite element method;
  • construct and implement numerical algorithms (in Matlab for instance);
  • use Laplace transform and inverse Laplace transform;
  • solve ordinary differential equations and integro-differential equations using Laplace transforms;
  • determine Fourier series for periodic functions, sine and cosine series for functions defined in an interval;
  • solve linear PDEs (such as the heat- and wave equations) using the method of separation of variables;
  • explain and in some cases prove the main theorems seen in the lectures.

Content

This course covers mathematical models in 1D (and 2D) for processes in science and engineering. These are phenomena described by (partial) differential equations. Typical examples are reaction, production, diffusion and convection processes.

The course has two parts. The focus of the first part is on numerical methods for differential equations, in particular the finite element method (FEM). The second part of the course deals with tools to find the exact solutions to particular differential equations. These tools are: Laplace transforms, Fourier series and separation of variables technique.

Organisation

The course consists of lectures, exercises and computer assignments.

Some (minor) parts  that will not be covered in the lectures are left to self-study. These moments are equally important and integrated part of the whole course.

Working with exercises and computer labs play an important role during the course and clarify the theoretical content from practical point views. The course consists of two parts: one part of 6 hp and another one of 1.5 hp. The 6 hp part is examined through a written examination. To pass the 1.5 hp part it is required passing the compuer-lab assignments (specified on the webpage of the course).

Literature

References and supplementary course material are posted on the course webpage.


Examination including compulsory elements

Written exam of problem solving nature with theoretical aspects (corresponds to 6 hp) and home and computer assignment: project (which are corresponding to 1,5 hp).

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

The course syllabus contains changes

  • Changes to course rounds:
    • 2024-05-14: Examinator Examinator changed from David Cohen (cohend) to Joakim Becker (becker) by Viceprefekt/adm
      [Course round 1]