TMA 4115 Parallel MTFYMA Spring 2016
This page contains information on the parallel TMA 4115 MTFYMA. For general information applying to all parallels of TMA 4115 see the main page of the course.
Teaching in this parallel will be in english language (beklager, men jeg snakker bare litt norsk…). However, there are video recordings of lectures from Spring 2012 in Norwegian (see main page for more information).
Notice that the curriculum of the lectures has slightly changed since 2012. Hence the recordings are slightly dated, leave out some material now part of the course and deal instead with some topics not contained in the current lecture.
Announcements
Schedule of the lectures:
Mondays 10:15-12:00 in KJL1
Wednesdays 14:15-16:00 in KJL2
Here you can download the slides used in the lecture. In general, I will try to make the slides available before the lecture (so you can bring them if you want to take notes).
| Date | Slides (Short content description) | Comments |
| 11.01 | Introduction | |
| 13.01 | Complex numbers, polar representation | |
| 18.01 | Operations on complex numbers, roots, functions | |
| 20.01 | Complex functions and complex polynomials, First examples of Second order differential equations | Complex functions and polynomials are not covered in video lectures (only covers complex exponential function) |
| 25.01 | Example: Spring continued, Existence and uniqueness of solutions | |
| 27.01 | Linear differential equations, initial value problems | |
| | Constant coefficients, (simple) harmonic motion revisited | Second part of the slides used in the lecture |
| 01.02 | Method of undetermined coefficients | Slides about forced harmonic motion moved to next lecture |
| 03.02 | Inhomogeneous equations, forced harmonic motion, variation of constants | |
| 08.02 | Linear Equations and their solutions | |
| 10.02 | Linear Equations and vectors | |
| 15.02 | Linear Equations, vector equations and matrix equations | |
| | Example: Linear Equations arising from linear networks | Slides concerning the linear network describing a roundabout |
| 17.02 | Matrix equations, Linear (In-)depence of vectors | |
| 22.02 | Tests for linear independence, Matrix transformations | |
| 29.02 | Matrix algebra in particular: products of matrices) | |
| 02.03 | Invertible matrices, the invertible Matrix theorem, LU factorisation, Determinants | LU factorisation is not covered in the video lectures. Instead the video lectures cover Cramers rule and the "adjugate matrix" of a matrix (this is no longer part of the current lecture). |
| 07.03 | Determinants, abstract vector spaces | |
| 09.03 | (Abstract) vector spaces, subspaces and linear transformations | |
| 14.03 | Basis and coordinate functions | |
| 16.03 | Coordinate functions, Markov chains | |
| 30.03 | Markov chains, eigenvectors | |
| 04.04 | Eigenvectors and eigenvalues, Diagonalisation of matrices | |
| 06.04 | No slides | lecture dealt with systems of linear differential equations |
| 11.04 | Length and orthogonality of vectors | |
| 13.04 | Orthogonal complements, orthogonal projections and the Gram-Schmidt algorithm | In the textbook in Chapter 6.3 also QR-factorisations of matrices are discussed. We did not cover this in the lecture (it is also not part of the video lectures). |
| 18.04 | Applications of the Gram-Schmidt algorithm, least square problems | |
| 20.04 | Least square problems, symmetric and orthogonal matrices, Spectral Theorem | |
| 25.04 | No slides (only repetition in the lecture) | We did only begin a discussion of quadratic forms (chapter 7.2) so most of this material is not relevant for the exam. |
In the first chapter of the lecture we discuss complex numbers.
To explore complex numbers, you should try the Mathlets for complex numbers offered by MIT. A link to these Mathlets can be found on the left in the menu.
Antoine Julien has created a flowchart which summarizes the general strategy for solving a linear system.
Referansegruppe
The reference group for this parallel consists of the following students
| Alexandra Log | alexandra [døt] log (æt) hotmail (dåt) com |
| Ragnhild Roaldsnes | ragnhilr96 (æt) hotmail (dåt) com |
| Oda Solesvik Oppedal | odasop (æt) stud [døt] ntnu (dåt) com |
Please contact them if you have suggestions concerning the lecture the reference group should discuss.
(If you are not a robot then it should not be hard to turn the above addresses into real email addresses)