Calculus in One and Several Variables, 6 credits

En- och flervariabelanalys, 6 hp

TATA91

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Göran Forsling

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 36 h
Recommended self-study hours: 124 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CMJU Computer Science and Software Engineering, M Sc in Engineering 4 (Spring 2019) 2 4 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

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

TEN1Written exam6 creditsU, 3, 4, 5

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Göran Forsling

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

Books

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

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

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
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

                            
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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