Lecture Plan for Mathematics 4D/N
A detailed list of this years curriculum (pensum) can be found at https://wiki.math.ntnu.no/tma4130/2022h/exam
The following plan is preliminary and subject to change.
For the analytical parts of the lecture, we will mostly follow the book Advanced Engineering Mathematics by Erwin Kreyszig, 10th edition, John Wiley & Sons, 2011, and the chapter numbers in the table below refer to this textbook. The numerical parts are based on our own notes; we will publish them during the course of the semester.
The .ipynb files can be run by Jupyter Notebook. If Jupyter Notebook is not already installed, we recommend using the Anaconda distribution, a detailed installation guide for which can be found here. Moreover, you can find an introduction to Jupyter notebooks with python here (click here for a view-only version, if Jupyter Notebook is not installed yet).
In order to work with jupyter notebooks in Anaconda, follow the following steps:
- (Download and install Anaconda on your computer.)
- Download the jupyter notebook on your computer. We recommend to set up a dedicated working directory for Maths 4N/D.
- Start the Anaconda Navigator, and launch Jupyter Notebook. This should open a new window in your web-browser, from which you can navigate to your stored notebooks or open new ones.
If you want to have a nicer theme for your jupyter notebook, download the cascade stylesheet file tma4320.css and store it in the same directory as the jupyter notebooks.
| Week | Topic | Additional material | Literature | ||
|---|---|---|---|---|---|
| Markus | Douglas | Anne | |||
| Numerical mathematics | |||||
| 34 | Introduction and Numerical mathematics Example: chemical reactor Two-point boundary value problems Numerical differentiation | Annotations1 Notebook Annotations2 | Boundary value problems: pdf, ipynb | ||
| 35 | Polynomial interpolation Spline interpolation Numerical integration Simple and composite quadrature rules Adaptive integration | Annotations1 Notebook1 Annotations2 Notebook2 | Interpolation: pdf, ipynb (Secs 1, 3, and the direct approach in Sec 2; updated 07.11.) Numerical integration: pdf, ipynb |
||
| 36 | Python with numpy (only 4N) Rounding errors (only 4N) Multivariable calculus (only 4D) Numerical solution of nonlinear equations Fixed-point iterations | Notebook - Sep 05 | Notebook1 Annotations1 Annotations2 | Rounding errors: Notes Multivariable calculus:pdf Nonlinear equations: pdf, ipynb (updated 14.09) |
|
| 37 | Newton's method Newton's method in several variables | Newton method Newton for a system | Annotations1 Notebook1 | Nonlinear equations: pdf, ipynb (updated 14.09) | |
| Fourier analysis | |||||
| Periodic functions Fourier series Euler's formulas Convergence of Fourier series | Annotations2 | Section 11.1 in the book Sketch of Fourier series |
|||
| 38 | Changes of the period Half-range expansions Approximation with trigonometric polynomials Complex Fourier series | Annotations1 Annotations2 | Sections 11.2 and 11.4 in the book Half range expansions This note on complex Fourier series |
||
| 39 | Fourier transformation Properties of the Fourier transform Convolution Discrete Fourier Transform (DFT) | Sketch of Convolutions Data analysis with DFT Dataset for the above code1) | Annotations1 Annotations2 | DFT Slides DFT notebook | Section 11.9 in the book Discrete Fourier Transform (updated 10.10.) |
| Partial differential equations | |||||
| 40 | Partial differential equations (PDEs) Wave equation Separations of variables | Solutions of the wave equation | Annotations1 Annotations2 | vibrating_string.py | Sections 12.1, 12.2 Section 12.3 |
| 41 | Numerics for the wave equation d'Alembert's solution method Heat equation | Numerics for the wave equation D'Alembert's solution Heat equation | Annotations1 Annotations2 | Numerics of PDEs: pdf, ipynb (updated 27.10.) Section 12.4 Section 12.6 |
|
| 42 | Numerics of the heat equation Fourier methods for PDEs | Numerics for the heat equation | Annotations1 Annotations2 | Numerics of PDEs: pdf, ipynb (updated 27.10.) Section 12.7 |
|
| Laplace transform | |||||
| 43 | Laplace transform | Annotations1 Annotations2 | Sections 6.1, 6.2 | ||
| 44 | Laplace transform | Annotations1 Annotations2 Examples | Summary + RCL example (updated 02.11) | Sections 6.3-6.5 | |
| Numerics of ordinary differential equations | |||||
| 45 | Numerics of initial value problems | Annotations1 Annotations2 | Numerics of ODEs: pdf, ipynb, python code (updated 10.11) | ||
| 46 | Numerics of initial value problems | Annotations1 Annotations2 Adaptivity.ipynb | Numerics of ODEs, part 2: pdf, ipynb, python code (preliminary, updated 15.11.) | ||
| Summary and revision | |||||
| 47 | Revision | Summary2) | Overview Exercises (8/12) | Summary (4D)3) Rettelse fra forelesning: Presisjonsgrad av kvadraturformler er ikke pensum. | |
Notes
If you want to have a nicer theme for your jupyter notebook, download the cascade stylesheet file tma4320.css and store it in the same directory as the jupyter notebooks.
- Introduction to Jupyter with Python: ipynb, View-only-version of Introduction.ipynb
- Rounding errors: pdf (uploaded September 30, 2022)