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Calculus in One and Several Variables, 6 credits

En- och flervariabelanalys, 6 hp

TATA91

Course starting semester

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Malgorzata Wesolowska

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 124 h

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6CMJU	Computer Science and Software Engineering, Master of Science in Engineering	4 (Spring 2021)	2	4	Swedish	Linköping, Valla	C
6CITE	Information Technology, Master of Science in Engineering	4 (Spring 2021)	2	4	Swedish	Linköping, Valla	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Master of Science in Information Technology
Master of Science in Computer Science and Software Engineering

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.

For the MSc programme in Information Technology, the course applies problem-based learning.

Examination

TEN1

Written exam

6 credits

U, 3, 4, 5

Grades

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

Other information

About teaching and examination language

The teaching language is presented in the Overview tab for each course. The examination language relates to the teaching language as follows:

If teaching language is Swedish, the course as a whole or in large parts, is taught in Swedish. Please note that although teaching language is Swedish, parts of the course could be given in English. Examination language is Swedish.
If teaching language is Swedish/English, the course as a whole will be taught in English if students without prior knowledge of the Swedish language participate. Examination language is Swedish or English (depending on teaching language).
If teaching language is English, the course as a whole is taught in English. Examination language is English.

Other

The course is conducted in a manner where both men's and women's experience and knowledge are made visible and developed.

The planning and implementation of a course should correspond to the course syllabus. The course evaluation should therefore be conducted with the course syllabus as a starting point.

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Malgorzata Wesolowska

Course website and other links

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

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 124 h

Course literature

Books

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

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

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

Books

Forsling, G. och Neymark, N., (2011) Matematisk analys, en variabel Liber

M. Neymark, (2016) Matematisk analys, flera variabler.

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
	2.3 System thinking
	2.4 Attitudes, thought, and learning
	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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