COURSE SYLLABUS

Mathematics 7.5 credits

Matematik M
First cycle, M0013M
Version
Course syllabus valid: Autumn 2021 Sp 1 - Present
The version indicates the term and period for which this course syllabus is valid. The most recent version of the course syllabus is shown first.

 Education level First cycle Grade scale G U 3 4 5 Subject Mathematics Subject group (SCB) Mathematics

Entry requirements

In order to meet the general entry requirements for first cycle studies you must have successfully completed upper secondary education and documented skills in English language and Courses M0029M-M0031M or corresponding.

Selection

The selection is based on 1-165 credits.

Course Aim
After the course the student shall
• be able to use key concepts for functions of several variables: limit, continuity, partial derivative, the chain rule, directional derivative, gradient and Taylor polynom
• be able to find stationary points and classify them, determine the maximum and minimum values of continuous functions on closed bounded domains and be able to use the Lagrange multiplicator method.
• be able to compute multiple integrals by interated integration and do suitable change of variables when it is needed.
• be to compute and interpret line- and surface integrals
•  Be able to apply and interpret important concepts within vector calculus: Vector field, divergence, curl, Green’s theorem, divergence theorem and Stokes’ theorem.
• be able to find the Fourier series corresponding to a periodic function and be able to find odd and even half range expansions of a given function.
• Be able to derive som important partial differential equations (PDE) from known physical laws: wave equation, heat equation and Poisson’s equation.
• be able to use the method of separation of variables to solve the above mentioned PDE for some simple geometries.
• Be able to identify and solve problems which can be analyzed with the methods from the course and present the solutions in a logical and correct way and so that they are easy to follow.

An overall aim is that the student after the course besides being able to use the concepts and methods in the course also must be able to do the corresponding calculations with high accuracy, i.e. the final result should be correct.

Contents
- Calculus in several variables: functions of several variables, partial differentiation, Taylor series, extreme values, multiple integration, line integrals, surface integrals, vector analysis (the divergence theorem and Stoke’s theorem). - Partial differential equations (PDE): Well known PDE (e.g. the wave equation, the heat equation, Laplace equation...) will be presented and discussed from an engineering point of view. Solution of PDE by separation of variables.

Realization
Each course occasion´s language and form is stated and appear on the course page on Luleå University of Technology's website.
Lectures and lessons.

Examination
If there is a decision on special educational support, in accordance with the Guideline Student's rights and obligations at Luleå University of Technology, an adapted or alternative form of examination can be provided.
You have to pass a written exam. Grading scale: 3 4 5

Transition terms
The course M0013M is equal to MAM235.

Examiner
Peter Wall

Transition terms
The course M0013M is equal to MAM235

Literature. Valid from Autumn 2007 Sp 1 (May change until 10 weeks before course start)
Kreyszig E: Advanced Engineering Mathematics, latest edition.

Course offered by
Department of Engineering Sciences and Mathematics

Modules