# Where can I get advanced math problems

## Advanced math

### Content of the lecture

The event focuses on the following three problems:

- Find all the solutions to the equation f (
**x**) = 0. - Determine the global maximum and minimum places of a function y = f (
**x**) on a certain amount of S. - Solve the initial value problem of an ordinary first order differential equation.

The problem areas are economically motivated. The structure takes place with appropriate mathematical rigor and central proofs are also discussed and checked. In particular, numerical methods are discussed and the programs GeoGebra and Maple are presented and used.

The material covered in the lectures Mathematics 1 and Mathematics 2 (1st half) is required and assumed to be known.

### Organizational matters

**RegistrationPlease note that you have to register or de-register with me by September 5th, 2020.Courses**

The event is primarily held online (zoom).

You will receive the meeting ID and passcode after (non-binding) registration by email.

You will receive the meeting ID and passcode after (non-binding) registration by email.

It exists

*no*Compulsory attendance in the (online) courses.

**Exercise / housework**

It *got to* an exercise / term paper on the topics of the course can be worked on individually and submitted on time (in person or by email).

Download the term paper

Submission: by Monday, 09/28/2020 12:00 p.m. at the latest

I will correct your term paper until Monday, October 5th, 2020 and (if necessary) in the period from October 5th. - 09.10.2020 hold an individual (follow-up) meeting (direct or zoom) with you.

The exercise / term paper is graded (preliminary grade). The preliminary grade (with a weight of 1/3) and the examination grade (with a weight of 2/3) result in the final grade.

### Teaching aids

**Primary literature**: Lecture scripts**Supplementary literature**:

- Sydsaeter K., Hammond P., Seierstad A., Strom A .: Further Mathematics for Economic Analysis, Prentice Hall.
- Chiang, Alpha C .: Fundamental Methods of Mathematical Economics, McGraw-Hill International Editions.

**software**:

- GeoGebra is free dynamic math software for high school and college students. GeoGebra supports innovative learning in mathematics and statistics and can be downloaded from the homepage www.geogebra.org and installed (mostly problem-free) on your private computer (laptop, tablet or mobile phone).
- Maple is a powerful computer algebra system that can also be used for numerical calculations. You can obtain the program from the IT services of the University of Basel https://its.unibas.ch/ and install it on your private computer.

Of course, you can also bring your (small and charged) computer with you. Please note, however, that space in the lecture hall is limited.

### exam

**The exam will take place on Tuesday, October 13th, 2020 from 9:30 a.m. to 11:00 a.m. in seminar room S14 (WWZ).**

**General:**

At the end of the course there is a 1.5-hour exam, which is composed as follows:

- About 70% of the tasks are based on the content of the exercises (and on the (example) tasks that are included in the script or discussed during the lectures)
- About 30% of the tasks test the material of the lecture directly (definitions, understanding of the central concepts, central proofs and derivations)

**Approved resources:**

**electronic tools:**Only simple pocket calculators in accordance with the study regulations are allowed to take the exam.**non-electronic aids:**open book

### Problem 1

**Let y = f (x) be a function. Find all the solutions to the equation f (x) = 0.**

Download: Script 1

Geograde files: Fixed point iteration, Newton's method

Daytime | theme |
---|---|

Mon, 08/31/20, 9:15 am-11: 00 am (zoom) | Complex numbers |

Mon, 08/31/20, 1:15 p.m. - 3:00 p.m. (zoom) | Contractive mappings / Banach's fixed point theorem |

Tue, 09/01/20, 9:15 a.m. - 11 a.m. (zoom) | Banach's Fixed Point Theorem (proof and application) |

Tue, 09/01/20, 1:15 p.m. - 3:00 p.m. (zoom) | Numerical methods |

### Problem 2

*Let y = f (x) be a function and S a subset of IR ^{n}. Find the global maximum and minimum places of f on p.*

Download: Script 2

Geographical files:

Daytime | theme |
---|---|

Wed, 02.09.20, 9:15 a.m. - 11 a.m. (zoom) | IR^{n}, Functions, gradient, Hessian matrix, Taylor formula and local extreme points |

Wed, 09/02/20, 1:15 p.m. - 3:00 p.m. (zoom) | Lagrange method |

Thursday, September 3rd, 2020, 9:15 am-11: 00 am (zoom) | Lagrange method, Karush-Kuhn-Tucker method |

Thu, 03.09.20, 1:15 p.m. - 3:00 p.m. (zoom) | Karush-Kuhn-Tucker methods and numerical methods |

Fri, 04.09.20 | Social activity? |

### Problem 3

*Let y '= f (x, y) be an ordinary first-order differential equation with the initial condition y (x _{0}) = y_{0}. Find the solution to the initial value problem.*

Download: Script 3

Day | theme |
---|---|

Mon, 09/07/20, 9:15 a.m. - 11 a.m. (zoom) | Difference and differential equations: fundamentals |

Mon, 09/07/20, 1:15 p.m. - 3:00 p.m. (zoom) | Special classes of first order differential equations |

Tue, 08.09.20, 9:15 a.m. - 11 a.m. (zoom) | Linear differential equations |

Tue, 09/08/20, 1:15 p.m. - 3:00 p.m. (zoom) | Numerical methods |

Repetition | |

Wed, 08.09.20, 9:15 a.m. - 11 a.m. (zoom) | General open question time (all topics) |

Wed, 09/08/20, 1:15 p.m. - 3:00 p.m. (zoom) | General open question time (all topics) |

Thu, 09.09.20, 9:15 a.m. - 3:00 p.m. | Individual consultation hours (by appointment, directly at the WWZ or via Zoom) |

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