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## Syllabus for

TMV225 - Introductory course in mathematics Inledande matematik

Owner: TKMAS
7,5 Credits
Grading: TH - Five, Four, Three, Fail
Education cycle: First-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

Teaching language: Swedish
Application code: 55157
Open for exchange students: No
Only students with the course round in the programme plan

 Module Credit distribution Examination dates Sp1 Sp2 Sp3 Sp4 Summer course No Sp 0108 Examination 7,5c Grading: TH 7,5c 29 Oct 2019 am SB_MU 09 Jan 2020 am SB_MU 26 Aug 2020 am J DIG

#### In programs

TKMAS MECHANICAL ENGINEERING, Year 1 (compulsory)

Anders Logg

#### Replaces

TMV155   Introductory course in mathematics

#### Eligibility:

In order to be eligible for a first cycle course the applicant needs to fulfil the general and specific entry requirements of the programme(s) that has the course included in the study programme.

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#### Aim

The purpose of the course is to strengthen, deepen and develop the
knowledge in secondary school mathematics and to thereby give a solid
ground for further studies in mathematics. The course will also
introduce the habit of using numerical computation in mathematics.

#### Learning outcomes (after completion of the course the student should be able to)

- fluently handle algebraic calculations and the elementary functions, both in problem solving and its theory.
- draw graphs and solve equations, both by hand and using MATLAB.
- solve systems of linear equations by hand and using MATLAB and master vector algebra in two and three dimensions.
- explain how functions can be approximated using polynomials and be represented as power series, and use this knowledge for problem solving. - know the concept of convergence for series of numbers. - write MATLAB programs that implement and illustrate the algorithms and functions that are studied.

#### Content

Algebraic calculations and the number systems. Fractions, rules for powers and power expansions. Basic trigonometry.

Analytic geometry.

Introduction to calculus: Real functions, graphs, limits, derivatives and the use of these concepts in basic modeling.

Deductive reasoning. Elementary set theory and fundamentals of logic. The general concept of a function.

The elementary functions: Polynomials, rational and power functions.
Inverse functions, exponentials, logarithms and inverse trigonometric functions. The derivative of the elementary functions.

Applications of differentiation: Extreme values, numerical methods for solving equations. Newton's method and other iterations.

Sequences and limits. Mathematical induction.

Systems of linear equations and matrices. Taylor's formula.  Series. The complex plane, rectangular and polar form. The complex exponential function.

#### Organisation

Instruction is given in lectures and classes. More detailed information will be given on the course web page before start of the course.

#### Literature

The main textbook will be announced on the course web page two weeks before the course begins.

N. Ericsson, S. Larsson, A. Logg, Beräkningsmatematik, kompendium, 2014.

#### Examination including compulsory elements

More detailed information of the examination will be given on the course web page before start of the course.
Examples of assessments are:
-selected exercises are to be presented to the teacher orally or in writing during the course,
-other documentation of how the student's knowledge develops,
-project work, individually or in group,
-written or oral exam during and/or at the end of the course.
-problems/exercises are to be solved with a computer and presented in writing and/or at the computer.

Published: Wed 26 Feb 2020.