# Calculus, one variable, 6 credits (NMAA06)

Analys i en variabel, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

### Course type

Single subject and programme course

Magnus Berggren

### Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
Single subject course (Full-time, Day-time) Autumn 2017 1, 2 Swedish Linköping
6KKEM Chemistry - Molecular Design, Bachelor's Programme 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Chemistry - Molecular Design, Bachelor's Programme

### 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

That you as a student will learn to feel confident with the mathematical expressions, reasoning and relations from Single Variable Calculus and that it will teach you calculating and problem solving skills needed for your further studies. After a completed course you should be able to:

• Read and interpret mathematical texts
• Explain definitions and expressions like local extremes, limits, continuity, derivatives, primitive functions and integrals
• Explain and use central theorems like The Fundamental Theorem of Calculus, Mean-Value Theorems, The Intermediate-Value Theorem and The Max-Min Theorem.
• Use mathematical laws for limits of functions and derivatives.
• Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions

### Course content

• Preparatory course: Equations and systems of equations. Geometric and arithmetic sums. Inequalities. Binomial theorem. Exponential functions and logarithms. Polynomials. Trigonometry and trigonometric functions.
• Calculus: Real and complex numbers. Functions of a real variable. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions.

• ### Teaching and working methods

Teaching is done in lectures and problem classes.

### Examination

 TEN1 Written examination U, 3, 4, 5 6 credits KTR1 Written test U, 3, 4, 5 0 credits KTR2 Written test U, 3, 4, 5 0 credits
Passed written test 1 and written test 2 gives a bonus on the written examination (TEN1). The right to count the bonuses from the tests is 12 months from the date of writing.

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

### Other information

Supplentary courses: Mathematics, second course.

### Department

Matematiska institutionen

### Director of Studies or equivalent

Jesper Thorén

### Examiner

Magnus Berggren

### Course website and other links

http://www.mai.liu.se/kurser/

### Education components

Preliminary scheduled hours: 118 h
Recommended self-study hours: 42 h

### Course literature

Forsling, Göran och Neymark Mats: Matematisk analys, en variabel. Liber 2011.
Forsling, Göran och Neymark Mats: Matematisk analys, en variabel. Liber 2011.