# Calculus II, 6 credits (TNA004)

Analys II, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

Sixten Nilsson

### Director of studies or equivalent

George Baravdish
Course offered for Semester Period Timetable module Language Campus VOF
6CIEN Electronics Design Engineering, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping o
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping o
6CMEN Media Technology and Engineering, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• Electronics Design Engineering, M Sc in Engineering
• Communications, Transport and Infrastructure, M Sc in Engineering
• Media Technology and 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.

Analysis I

### Intended learning outcomes

To give basic proficiency in mathematical concepts, reasoning and relations contained in single-variable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to

• read and interpret mathematical text
• explain Taylors formula and the concepts series, power series and convergence of series.
• make comparisons metween sums and integrals
• use expressions for, and calculate, geometrical quantities such as plane areas, arc length, surface area, volumes of solids of revolution and areas of surfaces of revolution
• utilize ordinary differential equations (linear of first order: linear and separable and linear equations of higher order with constant coefficients, serie solutions) and integral equations
• use Taylors Theorem in approximating functions with polynomial, calculating limits and estimation errors and estimate local properties of functions.
• carry out convergence tests for improper integrals, series and power series and find derivatives and antiderivatives for power series
• carry out inspections of results and partial results, in order to verify that these are correct or reasonable.

### Course content

Applications of integrals - Improper integrals: definition and calculations, area, length of curves, volume of solids of revolution, area of surfaces of revolution. Generalised integrals. Estimation of sums. The formulas of Taylor and Maclaurin. The Maclaurin expansion of elementary functions. Applications, e.g. estimation of errors and finding limits. Ordinary differential equations. Equations of the first order: linear and separable equations. Integral equations. Linear equations of higher order with constant coefficients. Serie solutions. Applications will be given of mathematical models from various fields. Series.

### Teaching and working methods

Lectures and problem classes.

### Examination

 TEN1 Written exam U, 3, 4, 5 6 credits

### Grades

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

### Department

Institutionen för teknik och naturvetenskap

George Baravdish

Sixten Nilsson

### Course website and other links

http://www2.itn.liu.se/utbildning/kurs/

### Education components

Preliminary scheduled hours: 70 h
Recommended self-study hours: 90 h

### Course literature

Forsling, G. och Neymark, N.: Matematisk analys, en variabel. Liber. Problemsamling och kompletterande material utgivet av matematiska institutionen.
Forsling, G. och Neymark, N.: Matematisk analys, en variabel. Liber. Problemsamling och kompletterande material utgivet av matematiska institutionen.

### Download

 TEN1 Written exam U, 3, 4, 5 6 credits

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