# Introductory Course in Calculus, 6 credits (TATA79)

Inledande matematisk analys, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

David Rule

### Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CDDD Computer Science and Engineering, M Sc in Engineering 1 (Autumn 2017) 2 2 Swedish Linköping o
6CITE Information Technology, M Sc in Engineering 1 (Autumn 2017) 2 2 Swedish Linköping o
6CMJU Computer Science and Software Engineering, M Sc in Engineering 3 (Autumn 2017) 2 2 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Computer Science and Engineering, M Sc in Engineering
• Information Technology, M Sc in Engineering
• Computer Science and Software Engineering, M Sc in Engineering

### 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.

### 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 and proofs by induction.
• 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 exercises 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

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

### Course literature

G. Forsling, M. Neymark: Matematisk analys, en variabel. Liber
Lecture notes produced by the Department of Mathematics
Material produced at the Department of Mathematics.

### Department

Matematiska institutionen

Jesper Thorén

David Rule

### Course website and other links

http://www.mai.liu.se/und/kurser/index-amne-tm.html

### Education components

Preliminary scheduled hours: 78 h
Recommended self-study hours: 82 h

### Course literature

##### Books
G. Forsling, M. Neymark, Matematisk analys, en variabel Liber
##### Articles

G. Forsling, M. Neymark: Matematisk analys, en variabel. Liber
Övningsmaterial producerat vid institutionen.

##### Compendiums

Lecture notes produced by the Department of Mathematics
Material produced at the Department of Mathematics.

### Books

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

### Articles

G. Forsling, M. Neymark: Matematisk analys, en variabel. Liber
Övningsmaterial producerat vid institutionen.

### Compendia

Lecture notes produced by the Department of Mathematics
Material produced at the Department of Mathematics.