# TMA4130 Mathematics 4N autumn 2018

## Messages

 18.07.2019 Note: regarding the retake exam, you are allowed to use the same tools as in the first exam, i.e., one yellow, stamped A5 sheet with own handwritten formulas and notes (on both sides). Here is the exam and solution: exam_fall18_tma4130_norsk.pdf, exam_fall18_tma4130_english.pdf, solutions_tma4130.pdf IMPORTANT! The time and place for a questions-session before the exam has been decided. The place is S2 in central building 1 and the time is 11th and 12th of December both days from 10:00 to 12:00. The exam information has been updated with extra exercises for the numerics part Here is a link to a chapter on complex Fourier series. Extra office hours will be offered on Monday, Dec. 10 (9:00-10:30) and Wed. 12 (9:00-10:30). Please send me a short email (before Dec. 8) if you plan to come to my office. Exercise set 8 has been updated (fixed some typos in exercise 1 and 2) The lectures in week 39 will be given by Tale Bakken Ulfsby (Mon. 8:00-10:00 and Thr. 12:00-14:00) and Prof. Anne Kværnø (Mon. 10:00-12:00 and Wed. 10:00-12:00). Prof. X. Wang has prepared short lecture notes covering the material of the first seven weeks of the parallel course Mat 4D ( "Laplace transform, Fourier transform and differential equations"). Exercise set 2 is now available. Exercise set 1 is now available. Welcome to the course "Matematikk 4N" autumn 2018. The lecture will start on week 34, the exercises one week later.

## Official Course Description

The course description can be found here.

The lectures will be given in English.

The course is divided into two parts:

#### Part I: Laplace transforms and Fourier analysis

This part introduces you to the Laplace transform (a smart way to transform differential equations into algebraic ones, that might be easier to solve). After Laplace transforms you will learn about Fourier series, which express simple functions as sums of sinus- and cosinus signals, and their extension, the Fourier transforms. These topics have applications in signal processing, image compression and many other areas in applied mathematics and the mathematical sciences. We will also discuss functions of several variables, and how to solve partial differential equations (PDEs), e.g., the heat equations, by Fourier series.

#### Part II: Numerical methods

Most of the mathematical equations and expressions encountered in real life applications can not be solved exactly using pen and paper. Instead, we search for approximate solutions, using numerical algorithms implemented on computers. In this course, we will look at numerical algorithms for solving nonlinear algebraic as well as ordinary and partial differential equations. We will also study how functions can be approximated by polynomials, and how this can be used to find approximations to integrals. Implementation and testing are indispensable elements when studying numerical methods. The lecture material in this part of the course is given as Jupyter notebooks, which are interactive web based notes containing both mathematical text and executable python code.

### Lecturer

Kurusch Ebrahimi-Fard, Sentralbygg II, office 1342

### Office hours

Monday, 10:30-11:45

### Lecture plan

• Monday, 8:15 - 10:00, S2, GL-SB1
• Monday, 12:15 - 14:00, F1, GL-ITS
• Wednesday, 10:15 - 12:00, F1, GL-ITS
• Thursday, 12:15 - 14:00, A2, GL-EG

For the exercise hours, see the timetable.

## Textbook

• Advanced Engineering Mathematics by Erwin Kreyszig, 10th edition, John Wiley & Sons, 2011.
• Notes and handouts (to appear)
• Jupyter notebooks (to appear)

## Final exam

• December 14, 2018.