# TMA4135 Mathematics 4D autumn 2018

Use the menu to find more information about the course.

## Messages

18.07 | 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) and an approved calculator. |
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18.01 | Here are finally the exam and solution: exam_fall18_tma4130_norsk.pdf, exam_fall18_tma4130_english.pdf, solutions_tma4130.pdf |

17.12 | The solutions of the exam will be available in before Thursday (at least). |

27.11 | The solutions for exercise set 12 are now available on Blackboard. |

22.11 | In order to be able to improve the course and the course material, we have made a questionnaire which can be found at https://kvass.svt.ntnu.no/TakeSurvey.aspx?SurveyID=l8M23l54. The more answers we get, the more valuable is the survey. So we urge all of you to spend two minutes to answer the questionnaire, and by that give your opinion about the course. |

21.11 | 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. |

19.11 | The solutions for exercise set 11 are now available on Blackboard. |

19.11 | The exercise sheet used in today lecture can be downloaded here. |

16.11 | The exercise set 12 is now available on the home-page and on Blackboard. |

12.11 | The solutions for exercise set 10 are now available on Blackboard. |

09.11 | The exercise set 11 is now available on the home-page and on Blackboard. |

07.11 | Exercise set 10 has been updated with an updated plot. |

05.11 | The solutions for exercise set 9 are now available in Blackboard. |

05.11 | We are a bit delayed, the topics this week will be adaptive ODE solvers and stiff ODEs. Numerical differentiation and PDEs starts next week. |

01.11 | The exercise set 10 is now available in Blackboard and on the home-page. |

29.10 | The solutions for exercise set 8 are now available in Blackboard. |

26.10 | The exercise set 9 is now available on the home-page and Blackboard. |

24.10 | The lecture Friday October 26 will be given by Tale Bakken Ulfsby. |

23.10 | Another typo in exercise set 8 has been corrected: in the first problem, third has been changed to second. |

22.10 | Old exams can now be found under "old exams" in the menu to the left. |

22.10 | The solutions for exercise set 7 are now available on Blackboard. |

21.10 | An updated version of exercise set 8 is out. Some typos in problem 1 and 2 have been corrected. |

18.10 | The exercise set 8 is now available on the home-page and on Blackboard. |

15.10 | The solutions for the extra exercise set are now available in Blackboard. |

12.10 | The exercise set 7 is now available on the home-page and Blackboard. |

08.10 | The solutions for exercise set 6 are now available on Blackboard. |

05.10 | IMPORTANT! Please check Blackboard for a notice regarding signing up for exercise groups if you have yet to do this. Those who have not signed up for a group will not have their submissions evaluated before doing so. |

01.10 | IMPORTANT! Check Blackboard for a notice on the extra exercise set ONLY for selected students. The extra exercises are only available on Blackboard. Please also note the deadline! This is the last chance to meet the requirement of at least 4 exercise sets approved from the first part of the course! |

01.10 | The solutions for the fifth exercise set are now available in Blackboard. |

27.09 | The sixth exercise set is now available on the home-page. |

24.09 | The solutions for the fourth exercise set are now available on Blackboard. |

20.09 | The fifth exercise set is now available on the home page and on Blackboard. |

18.09 | Suggested extra exercises (NOT to be handed in) are now available under the name "extra.pdf" under "Exercises". |

17.09 | The solutions for the third exercise set are now available in Blackboard. |

15.09 | An url to the previous year's home page can be found under "Lecture notes". There are notes on various topics of the course there in Norwegian. |

14.09 | The exercises have been updated with two stars marking the particularly difficult exercises. These are for students aiming for top grades in the course. Finally: per request, exercises will appear simultaneously on the home page and Blackboard. Thus exercise 4 will shortly be out on Blackboard. |

12.09 | Exercise set 4 is now available on the home page under "exercises". |

12.09 | The exercise group 1 has now an additional teaching assistant to reduce waiting time. |

11.09 | The third exercise set is now available in Blackboard. |

10.09 | The solutions for the second exercise set are now available under "exercises/øvinger" in Blackboard. |

06.09 | The third exercise set is now available on the home page under "Exercises". |

05.09 | Please note that exercise group 4 has changed room from S24 to S23 (they are next to each other). |

04.09 | An excerpt from the 9th edition of the book, on complex Fourier series can be found under "lecture notes". |

04.09 | The second exercise set is available in Blackboard. Please note that exercises will appear earlier on the home page than in Blackboard. Please note that there are still exercise classes even if the exercise set has not yet appeared on Blackboard! |

04.09 | The solutions to the first exercise set are available on Blackboard. |

04.09 | We will still use the use S3, no change of rooms for Sep. 17 Monday. |

29.08 | The second exercise set is now available on the home page. It will appear in Blackboard after the deadline for the first exercise set has been met. |

24.08 | the lecture room for Sep. 17 Monday (only that day) will change from S3 to S8. |

22.08 | The first exercise set is now available. Note that that submission is to be done in Blackboard. |

12.06 | Welcome to the course "Matematikk 4D" autumn 2018. The lecture will start on week 34, the exercises one week later. |

## Course Description

The official course description can be found here.

The course is divided into two parts:

#### Laplace transforms and Fourier analysis

On this part you will learn about Laplace transform (a smart way to transform differential equations into algebraic ones, that are more easy to solve). You will learn about Fourier series, a technique for expressing simple functions as a sum of sinus- and cosinus signals, as well as its extension, the Fourier transforms. These topics have applications in signal processing, image compression and a lot of other areas. We will also discuss functions of several variables, and how to solve partial differential equations, e.g. the heat equations, by Fourier series.

This part is lectured by Xu Wang, in English.

#### Numerical methods

Most of the mathematical equations and expressions encountered in real life applications can not be solved by pen and paper. Instead, we search for approximate solutions, found by the use of numerical algorithms and 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.

This part is lectured by Anne Kværnø, in Norwegian.

## Information about the lectures

### Lecturers

- Xu Wang; room 942 SB2; xu.wang@ntnu.no
- Anne Kværnø; room 1348 SB2; anne.kvarno@ntnu.no

### Office hours

Monday 10:30-11:45

### Head Teaching Assistant

Tai Nguyen; room 856 SB2; tai.t.h.nguyen@ntnu.no

### Lecture plan

- Monday 12:15-14:00 in S3 SB1
- Friday 10:15-12:00 in S2 SB1

For the exercise hours, see the timetable.

## Teaching material:

- Textbook:
*Advanced Engineering Mathematics*by Erwin Kreyszig, 10th edition, John Wiley & Sons, 2011. - Lecture notes
- Jupyter notebooks (will be made available when the numerics part of the course starts).

## Final exam

- December 14, 2018.