Calculus, several variables, 6 credits

Flervariabelanalys, 6 hp

TATA83

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Joakim Arnlind

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CKEB	Chemical Biology, M Sc in Engineering	4 (Spring 2017)	1	1	Swedish	Linköping, Valla	C
6CTBI	Engineering Biology, M Sc in Engineering	4 (Spring 2017)	1	1	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Chemical Biology, M Sc in Engineering
Engineering Biology, 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

Linear Algebra, Calculus, one variable

Intended learning outcomes

The aim is that the student shall become familiar with the mathematical concepts, the reasoning, and the relations that constitute several variable calculus, and also to acquire computitional and problem solving skills, to the extent required for further studies. After completing the course, the student should be able to

explain basic concepts and theorems for calculus in several variables.
identify and apply relevant methods to solve problems in calculus in several variables.

Course content

The space R^n. Fundamental notions of topology. Functions from R^n to R^p. Function graphs, level curves and level surfaces. Limit and continuity. Partial derivatives. Differentiability. The chain rule. Gradient, normal, tangent and tangent plane. Directional derivative. Taylor's formula. Local and global extrema. Extremal problems on compact domains (parametrizing the boundary). Implicitly defined functions and implicit differentiation. Multiple integrals; iterated integration, change of variables. Area, volume, mass. Introduction to improper multiple integrals.

Teaching and working methods

Lectures and problem classes.

Examination

TEN1

Written examination

6 credits

U, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Joakim Arnlind

Course website and other links

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

Education components

Preliminary scheduled hours: 56 h
Recommended self-study hours: 104 h

Course literature

Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund 1988. Problemsamling och kompletterande material utgivet av matematiska institutionen.

Code	Name	Scope	Grading scale
TEN1	Written examination	6 credits	U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva.

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)

Course literature is preliminary.

Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund 1988. Problemsamling och kompletterande material utgivet av matematiska institutionen.

Download

Download course literature list as PDF

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize

		I	U	A	Modules
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	X	TEN1
	1.2 Fundamental engineering knowledge (G1X level)
	1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)
	1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)
	1.5 Insight into current research and development work
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
	2.1 Analytical reasoning and problem solving		X	X	TEN1
	2.2 Experimentation, investigation, and knowledge discovery			X
	2.3 System thinking
	2.4 Attitudes, thought, and learning		X	X	TEN1
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork
	3.2 Communications
	3.3 Communication in foreign languages
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
	4.1 External, societal, and environmental context
	4.2 Enterprise and business context
	4.3 Conceiving, system engineering and management
	4.4 Designing
	4.5 Implementing
	4.6 Operating
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
	5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development
	5.2 Economic conditions for knowledge development
	5.3 Identification of needs, structuring and planning of research or development projects
	5.4 Execution of research or development projects
	5.5 Presentation and evaluation of research or development projects

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