Course - Linear Methods - TMA4145
TMA4145 - Linear Methods
About
Examination arrangement
Examination arrangement: School exam
Grade: Letter grades
| Evaluation | Weighting | Duration | Grade deviation | Examination aids |
|---|---|---|---|---|
| School exam | 100/100 | 4 hours | D |
Course content
Linear and normed spaces. Completeness, Banach spaces and Banach's fixed point theorem. Picard's theorem. Linear transformations. Inner product spaces, projections, and Hilbert spaces. Orthogonal sequences and approximations. Linear functionals, dual space, and Riesz' representation theorem. Spectral theorem, Jordan canonical form, and matrix decompositions.
Learning outcome
1. Knowledge. The student has knowledge of central concepts in the theory of vector spaces, normed spaces and Hilbert spaces. In the theory of vector spaces the main objective is that the student understand the transition from Euclidean spaces to general vector spaces. This includes an understanding of isomorphisms and bases of finite dimensional vector spaces and the relationship between linear transformations and matrices. The student is familiar with principles of matrix factorization. In the theory of normed spaces a key objective is that the student understand the Banach fixed point theorem. This includes an understanding of convergence of sequences and continuous functions. The student masters the basic concepts from the theory of Hilbert spaces, including orthogonality, closest point and duality. The student understands the Riesz representation theorem.
2. Skills. The student is able to apply his or her knowledge of the theory of vector spaces, normed spaces and Hilbert spaces to solve concrete problems. A key skill is that the student is able to combine results and construct new proofs using the theory acquired in the course.
Learning methods and activities
Lectures and mandatory exercises.
Compulsory assignments
- Exercises
Further on evaluation
Retake of examination may be given as an oral examination. The retake exam is in August.
Recommended previous knowledge
The course is based on TMA4100/05/15/20 Mathematics 1/2/3/4K, or equivalent. Alternatively, the courses MA1101 Basic Calculus I, MA1102 Basic Calculus II, MA1103 Vector Calculus, MA1201 Linear Algebra and Geometry, MA1202 Linear Algebra with Applications.
Course materials
Will be announced at the start of the course.
Credit reductions
| Course code | Reduction | From | To |
|---|---|---|---|
| SIF5020 | 7.5 |
Version: 1
Credits:
7.5 SP
Study level: Third-year courses, level III
Term no.: 1
Teaching semester: AUTUMN 2024
Language of instruction: English
Location: Trondheim
- Mathematics
- Technological subjects
Department with academic responsibility
Department of Mathematical Sciences
Examination
Examination arrangement: School exam
- Term Status code Evaluation Weighting Examination aids Date Time Examination system Room *
- Autumn ORD School exam 100/100 D 2024-12-05 15:00 INSPERA
-
Room Building Number of candidates SL111 lyseblå sone Sluppenvegen 14 72 SL111 orange sone Sluppenvegen 14 60 - Summer UTS School exam 100/100 D INSPERA
-
Room Building Number of candidates
- * The location (room) for a written examination is published 3 days before examination date. If more than one room is listed, you will find your room at Studentweb.
For more information regarding registration for examination and examination procedures, see "Innsida - Exams"