# Calculus in One and Several Variables, 6 credits (TATA91)

En- och flervariabelanalys, 6 hp

### Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

Göran Forsling

### Director of studies or equivalent

Jesper Thorén
Course offered for Semester Period Timetable module Language Campus VOF
6CMJU Computer Science and Software Engineering, M Sc in Engineering 4 (Spring 2019) 2 4 Swedish Linköping o

### Main field of study

Mathematics, Applied Mathematics

First cycle

G1X

### Course offered for

• 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.

### Prerequisites

Calculus in one variable 1, Linear Algebra

### Intended learning outcomes

Gain familiarity with mathematical concepts, reasoning and relationships in calculus in one and several variables, and gain the calculation and problem solving skills needed for further studies. After completing this course you should be able to

• cite, explain and use the definitions and theorems of the course’s key concepts

• solve problems and verify that results are correct or resonable

### Course content

Taylor's and Maclaurin's formulae: Maclaurin expansions of the elementary functions, the Ordo form of the remainder term with applications, e.g. computations of limits. Ordinary differential equations: first order linear and separable equations, higher order linear equations with constant coefficients. Improper integrals: investigation of convergence, absolute convergence. Numerical series: investigation of convergence, absolute convergence, Leibniz criterion. The space R ^ n: basic topological concepts, functions from R ^ n to R ^ p, function surfaces,level surfaces and level curves. Differential calculus: partial derivatives, the chain rule, partial differential equations, gradient, normal, tangent, tangent plane and directional

### Teaching and working methods

The course consists of lectures and classes.

### Examination

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

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

### Department

Matematiska institutionen

Jesper Thorén

Göran Forsling

### Course website and other links

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

### Education components

Preliminär schemalagd tid: 36 h

### Course literature

##### Böcker
Forsling, G. och Neymark, N., (2011) Matematisk analys, en variabel LiberM. Neymark, (2016) Matematisk analys, flera variabler.

### Books

Forsling, G. och Neymark, N., (2011) Matematisk analys, en variabel Liber
M. Neymark, (2016) Matematisk analys, flera variabler.