Calculus III, 6 credits (TNA006)

Analys III, 6 hp

Main field of study

Mathematics Applied Mathematics

First cycle

Programme course

Olof Svensson

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 3 (Autumn 2017) 1 3 Swedish Norrköping o
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Norrköping o
6CMEN Media Technology and Engineering, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Norrköping o
6IBYG Civil Engineering, B Sc in Engineering 5 (Autumn 2017) 1 3 Swedish Norrköping v

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
• Civil Engineering, B 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 I-II and Linear algebra, or similar courses.

Intended learning outcomes

This course is a continuation of the first year course in single variable calculus. Consequently, the aims are similar: to give students an understanding of mathematical concepts and familiarity with mathematical methods of analysis. Here, these aims relate to the treatment of functions of several variables which arise in all branches of physics and engineering. Students will be expected to be able to do the following after completing this course:

• handle multivariable functions, e.g. to be able to determine limits,
• decide if a function is continuous and differentiable, determine partial derivatives and use the chain rule for transforming and solving partial differential equations
• solve global and local maximum and minimum problems, with and without constaints.
• quote and explain definitions of concepts like limit, contiuity, partial derivative, differentiability, gradient, tangent plane, multiple integrals.
• explain and use central theorems like the implicit function theorem, calculate double and triple integrals, derive expressions for area and volumes using multiple integrals.

Course content

Functions of several variables. Limits and continuity. Partial derivative,
the gradient, directional derivative and differential. Tangent plane and
linearization. The chain rule. Taylor's formula. Vector-valued functions,
the Jacobian matrix and the Jacobian. Implicit differentiation and implicit
functions. Local and global maxima and minima. Finding of maxima and minima
with and without constraints. Double and triple integrals. Iterated integrals.
Change of variables. Space curves.

Teaching and working methods

The course is given in the form of lectures, tutorials, tests and a final
examination.

Examination

 KTR1 Written test U, G 0 credits TEN1 Written examination U, 3, 4, 5 6 credits

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

Other information

Supplementary courses: Vector analysis, Applied transform theory, Optimization, Statistics and Probability Theory.

Department

Institutionen för teknik och naturvetenskap

George Baravdish

Examiner

Olof Svensson

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

Education components

Preliminär schemalagd tid: 50 h

Course literature

Kompletterande litteratur

Böcker
Persson, A, Böiers, L-C, Analys i flera variabler

Studentlitteratur.

Kompendier

Problemsamling för kursen TNA006

Books

Persson, A, Böiers, L-C, Analys i flera variabler

Studentlitteratur.

Compendia

Problemsamling för kursen TNA006