# MA1103 Flerdimensjonal analyse

Kursbeskrivelse finnes i studiehåndboka.

The course will be taught in English.

Here you can find a possible solution to the exam from 07. juni 2016.

Enjoy the summer!

## Meldinger

**Friday, 03.06. 9:00-10:30 (room: EL3)**: We can discuss parameterizations and surface integrals. Please prepare also Exam 05/2015.

**Monday, 06.06. 9:00-10:30 (room: S1)**: Please prepare Exam 08/2015.

**Office hours (SBII 1148)**:

Thursday, 02.06. 9:00-12:00

Friday, 03.06. 10:30-12:00

Monday, 06.06. 10:30-12:00

During May, you can contact Mathias Nikolai Arnesen if you have any problems/questions.

04/5 | There was a small misprint on the list of formulas for 2016. In the line integral there was a dot missing. A new version is uploaded. |
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19/4 | The Referansegruppe has to write a final report on the course. Please send them an email if you want your feedback to be included. |

19/4 | Note that you can find the lists of formulas, which come together with the exam, under Faginformasjon. |

19/4 | Here you can find a short summary of the content of the course. |

18/4 | There is an Ekstra Øving (Øving 13) online (it's the last years exam). For those of you who are missing the 8th approved Øving, this is a chance to fill up. The fixed deadline for all for submitting Øving 13 is Monday, the 25th of April. |

15/4 | We will do a Kahoot-Quiz on Tuesday (19.04.). If you want to participate you need a device with internet connection. |

05/4 | There was a mistake in Øving 10, Exercise 10. The problem is removed and replaced by an optional exercise. A new version is uploaded. |

15/3 | There is a misprint on Øving 9, Exercise 5. There is a 1/(4*pi*pi) in front of the integral missing. A new version is uploaded. |

11/3 | Next Tuesday, that is the 15th of March, the lecture has to end at 15:45. Therefore, I suggest to have only a 5-10 minutes break. |

08/3 | There was actually a mistake in the lecture! I am very sorry for that! In the Change of variables formula it has to be the absolute value of the determinant! We will discuss this on Friday! |

07/3 | There is a misprint on Øving 8, Exercise 1. Since the curl is only defined for n=3, the statement has to be shown only for the case n=3 and not for general n! |

01/3 | Please note that the "Repetitions" are always available under Pensum og Tempoplan at least one day before the upcoming lecture. |

23/2 | Here is a link to a webpage giving an interpretation of the divergence and (if you click a bit through) the curl. Maybe you find this webpage also useful for other concepts we are discussing. |

18/2 | I got the info, that Theorem 7.3.4 in the linear algebra book Elementary Linear Algebra was actually not covered during the course. If you like, you can also refer to Lemma 2 of Chapter 3 (p.174) in our book Vector Calculus, where it is shown that the positive definiteness of a symmetric matrix implies the positive definiteness of the associated quadratic form (in 2 dimensions). |

15/2 | There is a misprint on Øving 5, Exercise 9 c). Within the second bracket it is supposed to be (x+ct) instead of (x+xt). A new version is uploaded. |

11/2 | Here is a nice illustration/animation of how to interpret mixed derivatives. Another example might be: Consider a function f(t,x) describing the temperature at position x and time t. f_t(t,x) is then the rate of change of temperature and f_{tx}(t,x) tells you how the rate of change of temperature changes if the position x varies. Think about what f_{xt}(t,x) would mean and note that f_{xt}=f_{tx} (by Thm 3.1). |

11/2 | There was a question in the last lecture concerning the remainder of the Taylor polynomial. Since the answer reaches to Taylor series's, which you will learn about in MA1102, I won't get too much into details in class, but let me say a few words here: If the function is smooth enough, the remainder will always go to zero if x goes to x_0! However, one might consider the Taylor polynomials T_n and ask what happens if n goes to infinity? This leads to Taylor series's. Here, one needs to tackle the question of whether the Taylor series converges? For which values of x does it converge and if it converges, to which function? All these questions are not trivial and there is an example of a function which is not the zero-function, but all Taylor polynomials at point x_0=0 are zero and the Taylor series converges for all values x (and is zero). That is, we have a function, whose Taylor series converges for all x, but it does not converge to the original function. You can find all that is said also here. Please let me know if there is something left that you wish to discuss. |

26/1 | There is a misprint in ØVING 2/EXERCISE 6 and EXERCISE 8b)! It is supposed to be "3(xx+yy)log(xx+yy)" in Exercise 6 and one of them should be a "union" in Exercise 8b)! A new version is uploaded. |

25/1 | Here you can find a book on Vector Calculus, which is in Norwegian and might be helpful as an additional resource. |

19/1 | There has been a misprint on Øving 2. In Exercise 2 there should be "2z" instead of "2y". It is already corrected in the file. |

14/1 | Gruppeinndelingen er nå klar: gruppeinndeling. Send e-post til mathias [dot] arnesen [at] math [dot] ntnu [dot] no hvis tildelt tid ikke passer. Dette gjelder særlig de som ikke tilhører noen av de store studieprogrammene i faget (BMAT, BFY, ÅMATSTAT og MLREAL), da tidspunktene for øvingstimene ble valgt hovedsaklig ut fra timeplanen til disse programmene. |

11/1 | Velkommen til MA1103, vårsemesteret 2016. Nettsida vil bli kontinuerlig oppdatert med informasjon. Første forelesning blir i morgen Tirsdag 12 Januar. |