# Foundation Course in Mathematics, 6 credits (TATA68)

Matematisk grundkurs, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

### Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CKEB Chemical Biology, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 3 Swedish Linköping o
6CTBI Engineering Biology, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 3 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Chemical Biology, M Sc in Engineering
• Engineering Biology, M Sc in Engineering

### Specific information

This course cannot be included in the same degree as the course TATM79.

### Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

### Prerequisites

Admission to the course requires, as well as general university entrance requirements, secondary school mathematics E (or equivalent).

### Intended learning outcomes

It is important that you acquire general mathematical accuracy and a stable foundation for your continued studies. After the course is completed you should be able to:

• read and comprehend mathematical texts.
• perform standard calculations with accuracy.
• handle calculations with algebraic expressions, inequalities and absolute values.
• solve polynomial equations and equations containing square roots.
• analyze how the concepts domain, range, injectivity and composition relate to particular functions.
• define and draw the graphs of the elementary functions: the natural logarithm, exponential-, power-, trigonometric- and inverse trigonometric functions.
• use and prove laws and formulas for the elementary functions.
• work with complex numbers in cartesian and polar form.
• define the complex exponential function and use and prove Euler's and deMoivre's formulas.
• solve problems concerning straight lines and circles in the plane.
• perform logical arguments
• work with geometric and arithmetic sums.
• check results and partial results in order to verify their correctness or reasonableness.

### Course content

Algebraic expessions, inequalities, modulus, complex numbers. Solving equations. Functions and graphs. Definitions and properties of the elementary functions: natural logarithm, exponential function, power function, trigonometric functions and complex exponential function, arcus functions. The Euler formulas. Basic principles of logic. Different types of proof techniques. Coordinate systems in the plane. Polar coordinates. Lines and circles. The complex plane. Complex numbers in polar form. Inverse trigonometric functions.

### Teaching and working methods

Problem classes, tutorials, and a few lectures.

### Examination

 UPG1 Hand-in assignments U, G 1.5 credits TEN3 Written examination U, 3, 4, 5 4.5 credits TEN2 Written examination U, 3, 4, 5 3 credits TEN1 Written examination U, 3, 4, 5 1.5 credits

It is possible to take either the smaller exams TEN1 and TEN2 or the larger TEN3. Grades are given on the total result on TEN1 and TEN2 or the result on TEN3. It is only possible to try to improve your grade on TEN3.

Four-grade scale, LiU, U, 3, 4, 5

### Department

Matematiska institutionen

Jesper Thorén

### Course website and other links

http://courses.mai.liu.se/Lists/html/index-amne-tm.html

### Education components

Preliminär schemalagd tid: 78 h

### Course literature

#### Kompletterande litteratur

##### Böcker
G. Forsling, M. Neymark, Matematisk analys, en variabel.

### Books

G. Forsling, M. Neymark, Matematisk analys, en variabel.

### Compendia

 UPG1 Hand-in assignments U, G 1.5 credits TEN3 Written examination U, 3, 4, 5 4.5 credits TEN2 Written examination U, 3, 4, 5 3 credits TEN1 Written examination U, 3, 4, 5 1.5 credits

It is possible to take either the smaller exams TEN1 and TEN2 or the larger TEN3. Grades are given on the total result on TEN1 and TEN2 or the result on TEN3. It is only possible to try to improve your grade on TEN3.

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

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