Course - Mathematics 3 - Linear algebra - TMA4115
Mathematics 3 - Linear algebra
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About the course
Course content
Complex numbers and the complex exponential function. Second order linear differential equations. Systems of linear equations, Gauss-Jordan elimination, reduced echelon form, matrix algebra, determinants. Vector spaces, subspaces, linear dependence and independence. Inner products, orthogonality, orthogonal projections, Gram-Schmidt orthogonalization, and the method of least squares. Eigenvalues and eigenvectors, diagonalization, symmetric matrices and quadratic forms. First order systems of differential equations.
Learning outcome
1. Knowledge. The student is able to recognize, understand and apply concepts and methods from linear algebra in Euclidean spaces and systems of differential equations.
2. Skills. The student is able to apply his or her knowledge of linear algebra and systems of differential equations to formulate and solve problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.
Learning methods and activities
Lectures and compulsory exercises. Parts of this course can be taught in English.
Compulsory assignments
- Exercises
Further on evaluation
Grade based on written final written examination. Retake of examination may be given as an oral examination. The retake exam is in August.
Recommended previous knowledge
TMA4100 Calculus 1 or equivalent.
Course materials
Will be announced at the beginning of the semester.
Credit reductions
| Course code | Reduction | From |
|---|---|---|
| SIF5010 | 7.5 sp | |
| MA1201 | 3 sp | Autumn 2009 |
| MA1202 | 3 sp | Autumn 2009 |
| TMA4110 | 7.5 sp | Autumn 2006 |
| MA0003 | 1.5 sp | Autumn 2009 |
| MA6201 | 3 sp | Autumn 2012 |
| TMA4101 | 3.7 sp | Autumn 2020 |
| TMA4106 | 3.7 sp | Autumn 2020 |
Subject areas
- Technological subjects