Calculus III, 6 credits

Analys III, 6 hp

TNA006

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Olof Svensson

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6IBYG Civil Engineering, B Sc in Engineering 5 (Autumn 2017) 1 3 Swedish Norrköping E
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Norrköping C
6CIEN Electronics Design Engineering, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Norrköping C
6CMEN Media Technology and Engineering, M Sc in Engineering 3 (Autumn 2017) 1 3 Swedish Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

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

TEN1Written examination6 creditsU, 3, 4, 5
KTR1Written test0 creditsU, G

Grades

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

Director of Studies or equivalent

George Baravdish

Examiner

Olof Svensson

Course website and other links

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

Education components

Preliminary scheduled hours: 50 h
Recommended self-study hours: 110 h

Course literature

Additional literature

Books

  • Persson, A, Böiers, L-C, Analys i flera variabler
    Studentlitteratur.

Compendia


  • Problemsamling för kursen TNA006
Code Name Scope Grading scale
TEN1 Written examination 6 credits U, 3, 4, 5
KTR1 Written test 0 credits U, G

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. 

Additional literature

Books

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

Studentlitteratur.

Compendia

Problemsamling för kursen TNA006

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
TEN1

                            
1.2 Fundamental engineering knowledge (G1X level)
X

                            
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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