Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).
Overview
- Swedish nameLinjär algebra och analys fortsättning
- CodeMVE465
- 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 53126
- Maximum participants250
- 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 |
|---|---|---|---|---|---|---|---|
| 0115 Laboratory 1.5 c Grading: UG | 1.5 c | ||||||
| 0215 Examination 6 c Grading: TH | 6 c |
|
In programmes
- TKBIO - BIOENGINEERING, Year 1 (compulsory)
- TKKEF - CHEMICAL ENGINEERING WITH ENGINEERING PHYSICS, Year 1 (compulsory)
- TKKMT - CHEMICAL ENGINEERING, Year 1 (compulsory)
Examiner
- Alice Kozakevicius
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
Knowledge equivalent to the content in the course Single variable calculus and analytical geometry.Aim
The purpose of the course is to, together with the other math courses in the program, provide a general knowledge in the mathematics required in further studies as well as in the future professional career.Learning outcomes (after completion of the course the student should be able to)
- define the concept integral and account for its relation to differentiation
- apply and explain both analytical and numerical methods for calculating integrals
- explain the meaning of an ordinary differential equation and its directional field
- apply and explain analytical and numerical methods for solving ordinary differential equations
- account for the concepts of linear algebra given in this course.
- account for the connections between the different concepts and use these connections in problem solving
- use the software MATLAB in problem solving
Content
- Linear transformations, matrix representation
- Matrix algebra, matrix inverse and systems of linear equations
- The Euclidean vector space Rn, linear independence, subspaces of Rn, null space (kernel), column space (range), bases, change of basis, dimension, rank
- Eigenvalues, real and complex, eigenvectors, diagonalization
- Orthogonal projection, orthonormal basis, method of least squares, the spectral theorem
- Determinants
- Antiderivatives
- Riemann Sums and the definite integral, techniques of integration, integrals of rational functions and some other functions
- Improper integrals
- Application of integration: volumes by slicing, solids by revolution, arclengt and surface area
- Complex numbers, the fundamental theorem of algebra
- Ordinary differential equations: First-order equation in general, analytical solution of separable and linear equations. Second-order linear equations with constant coefficients, the equations of simple and damped harmonic motion
- Systems of first order linear differential equations with constant coefficients.
- Numerical methods for solving integrals and systems of ordinary differential equations. Implementation of the algorithms in MATLAB
- A joint project with chemistry department.
Organisation
Instruction is given in lectures and classes together with computer sessions using Matlab. More detailed information will be given on the course web page before start of the course. http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/kemiteknik http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/kemiteknik-med-fysik http://www.chalmers.se/math/SV/utbildning/grundutbildning-chalmers/arkitekt-och/bioteknikLiterature
Literature will be announced on the course web page before start of the course.Examination including compulsory elements
More detailed information of the examination will be given on the course web page before start of the course. Examples of assessments are:-selected exercises are to be presented to the teacher orally or in writing during the course
-other documentation of how the student's knowledge develops
-project work, individually or in group
-written or oral exam during and/or at the end of the course
-problems/exercises are to be solved with a computer and presented in writing and/or at the computer.
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.