Foundation Course in Mathematics, 6 credits

Matematisk grundkurs, 6 hp

TATM79

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Fredrik Andersson (I,Ii), Mikael Langer (M,DPU,EMM), Johan Thim (Y,Yi,MED,Mat,FyN,FRIST)

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 78 h
Recommended self-study hours: 82 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
Single subject course (Half-time, Day-time) Autumn 2017 Swedish Linköping
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Chinese 1 (Autumn 2017) 0, 1 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, French 1 (Autumn 2017) 0, 1 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, German 1 (Autumn 2017) 0, 1 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Japanese 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering, Spanish 1 (Autumn 2017) 0, 1 4 Swedish Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping C
6CMED Biomedical Engineering, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping C
6CDPU Design and Product Development, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 3 Swedish Linköping C
6CEMM Energy - Environment - Management, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 1 (Autumn 2017) 0, 1 2 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 1 (Autumn 2017) 0, 1 2 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 1 (Autumn 2017) 0, 1 2 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 1 (Autumn 2017) 0, 1 2 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 1 (Autumn 2017) 0, 1 2 Swedish Linköping C
6CIII Industrial Engineering and Management, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 2 Swedish Linköping C
6KMAT Mathematics, Bachelor's Programme 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping C
6CMMM Mechanical Engineering, M Sc in Engineering 1 (Autumn 2017) 0, 1 -, 3 Swedish Linköping C
6KFYN Physics and Nanoscience, Bachelor's Programme 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Design and Product Development, M Sc in Engineering
  • Energy - Environment - Management, M Sc in Engineering
  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, M Sc in Engineering
  • Biomedical Engineering, M Sc in Engineering
  • Mechanical Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Physics and Nanoscience, Bachelor's Programme
  • Mathematics, Bachelor's Programme

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.

Intended learning outcomes

It is important that you acquire general mathematical accuracy and a stable foundation for your continued studies. After the course is completed you should be able to:

  • read and comprehend mathematical texts.
  • perform standard calculations with accuracy.
  • handle calculations with algebraic expressions, inequalities and absolute values.
  • solve polynomial equations and equations containing square roots.
  • analyze how the concepts domain, range, injectivity and composition relate to particular functions.
  • define and draw the graphs of the elementary functions: the natural logarithm, exponential-, power-, trigonometric- and inverse trigonometric functions.
  • use and prove laws and formulas for the elementary functions.
  • work with complex numbers in cartesian and polar form.
  • define the complex exponential function and use and prove Euler's and deMoivre's formulas.
  • solve problems concerning straight lines and circles in the plane.
  • perform logical arguments
  • work with geometric and arithmetic sums.
  • check results and partial results in order to verify their correctness or reasonableness.

Course content

Algebraic expessions, inequalities, modulus, complex numbers. Solving equations. Functions and graphs. Definitions and properties of the elementary functions: natural logarithm, exponential function, power function, trigonometric functions and complex exponential function, arcus functions. The Euler formulas. Basic principles of logic. Different types of proof techniques. Coordinate systems in the plane. Polar coordinates. Lines and circles. The complex plane. Complex numbers in polar form. Inverse trigonometric functions.

Teaching and working methods

Problem classes, tutorials, and a few lectures.

Examination

TEN5Examination1.5 creditsU, 3, 4, 5
TEN6Examination3 creditsU, 3, 4, 5
TEN7Examination4.5 creditsU, 3, 4, 5
UPG2Examination1.5 creditsU, G

Grades

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

Department

Matematiska institutionen

Director of Studies or equivalent

Jesper Thorén

Examiner

Fredrik Andersson (I,Ii), Mikael Langer (M,DPU,EMM), Johan Thim (Y,Yi,MED,Mat,FyN,FRIST)

Course website and other links

Education components

Preliminary scheduled hours: 78 h
Recommended self-study hours: 82 h

Course literature

Additional literature

Books

  • G. Forsling, M. Neymark, Matematisk analys, en variabel Liber

Other

Code Name Scope Grading scale
TEN5 Examination 1.5 credits U, 3, 4, 5
TEN6 Examination 3 credits U, 3, 4, 5
TEN7 Examination 4.5 credits U, 3, 4, 5
UPG2 Examination 1.5 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

G. Forsling, M. Neymark, Matematisk analys, en variabel Liber

Other

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
TEN5
TEN6
TEN7

                            
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
X
TEN5
TEN6
TEN7

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
X
TEN5
TEN6
TEN7

                            
2.5 Ethics, equity, and other responsibilities

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
3.2 Communications
X
X
X
UPG2

                            
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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