Course syllabus adopted 2021-01-15 by Head of Programme (or corresponding).
Overview
- Swedish nameMatematisk analys, fortsättning
- CodeTMA976
- Credits6 Credits
- OwnerTKTFY
- Education cycleFirst-cycle
- Main field of studyMathematics, Engineering Physics
- DepartmentMATHEMATICAL SCIENCES
- GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Course round 1
- Teaching language Swedish
- Application code 57138
- Open for exchange studentsNo
- Only students with the course round in the programme overview.
Credit distribution
Module | Sp1 | Sp2 | Sp3 | Sp4 | Summer | Not Sp | Examination dates |
|---|---|---|---|---|---|---|---|
| 0105 Examination 6 c Grading: TH | 6 c |
|
In programmes
- TKTEM - ENGINEERING MATHEMATICS, Year 1 (compulsory)
- TKTFY - ENGINEERING PHYSICS, Year 1 (compulsory)
Examiner
Michael Björklund- Professor, Analysis and Probability Theory, Mathematical Sciences
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.
Aim
The course provides basic knowledge of the fundamental theories within mathematical physics
Learning outcomes (after completion of the course the student should be able to)
Understand the basic concepts and definitions in mathematical analysis
To be able to prove the basic theorems in mathematical analysis in one variable
To be able to formulate and solve linear/separable differential equations
To be able to expand analytic functions in Taylor series
To be able to analyze the asymptotics of certain sequences (for instance coming from linear difference equations and iterations schemes)
To be able to establish convergence/divergence of series using various tests/criteria.
To be able to establish convergence/divergence of power series.
To apply the notions of pointwise and uniform convergence for function series
To compute limits of functions in several variables
To be able to produce proofs independently.
To be able to solve problems which involve two or more of the above.
Content
Ordinary differential equations: linear equations of the first order, separable equations, linear differential equations of arbitrary order with constant coefficients, systems of equations, some special types such as Euler's differential equation. Mathematical models giving rise to differential equations. Numerical solution of differential equations. Taylor's formula, computation of limits, l'Hospital's rules. Difference equations. Sequences, series, power series, convergence criteria, solution of differential equations by means of power series. Uniform convergence of function sequences and function series. The vector space Rn, polar and spherical coordinates, some topological concepts.
Organisation
Lectures and exercises.
Literature
A. Persson, L.-C. Böiers: Analys i en variabel, Studentlitteratur, Lund. A. Persson, L.-C. Böiers: Analys i flera variabler, Studentlitteratur, Lund. Övningar till Analys i en variabel, Matematiska institutionen, Lunds tekniska högskola. Övningar till Analys i flera variabler, Matematiska institutionen, Lunds tekniska högskola. F. Eriksson, E. Larsson, G. Wahde: Matematisk analys med tillämpningar, del 3. OTHER LITERATURE L. Råde, B. Westergren: BETA - Mathematics Handbook, Studentlitteratur, Lund.
Examination including compulsory elements
A written examination.
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.