Foundation Course in Mathematics, 6 credits

Matematisk grundkurs, 6 hp

TATB03

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Jonas Bergman Ärlebäck

Director of studies or equivalent

Jesper Thorén

Education components

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

Possible deviation from course syllabus/programme syllabus

ECV = Elective / Compulsory / Voluntary

Course offered for		Semester	Period	Timetable module	Language	Campus	ECV
6ASIK	Asian Studies - Chinese	1 (Autumn 2022)		-	Swedish	Linköping	C
6ASIJ	Asian Studies - Japanese	1 (Autumn 2022)		-	Swedish	Linköping	C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

Asian Studies - China
Asian Studies - Japan

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

TEN3	Written examination	4.5 credits	U, 3, 4, 5
TEN2	Written examination	3 credits	U, 3, 4, 5
TEN1	Written examination	1.5 credits	U, 3, 4, 5
UPG1	Hand-in assignments	1.5 credits	U, G

Either TEN1 and TEN2, or the summary examination TEN3 is required. Grades are given based on the results from TEN1 and TEN2 or the result from TEN3. Attempts to improve grades are only allowed in TEN3.

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 could be given in Swedish, or partly in English. Examination language is Swedish, but parts of the examination can be in English.
If teaching language is “English”, the course as a whole is taught in English. Examination language is English.
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.

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.

If special circumstances prevail, the vice-chancellor may in a special decision specify the preconditions for temporary deviations from this course syllabus, and delegate the right to take such decisions.

Department

Matematiska institutionen

Course literature

Books

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

Other

Code	Name	Scope	Grading scale
TEN3	Written examination	4.5 credits	U, 3, 4, 5
TEN2	Written examination	3 credits	U, 3, 4, 5
TEN1	Written examination	1.5 credits	U, 3, 4, 5
UPG1	Hand-in assignments	1.5 credits	U, G

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

Books

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

Other

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	Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
	1.1 Knowledge of underlying mathematics and science (G1X level)	X	X	X	TEN3
	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	TEN3	Bevis, matematisk problemlösning, rimlighetskontroll
	2.2 Experimentation, investigation, and knowledge discovery		X	X	TEN3	Bevis, matematisk problemlösning
	2.3 System thinking
	2.4 Attitudes, thought, and learning		X	X	TEN3	Matematisk problemlösning, rimlighetskontroll
	2.5 Ethics, equity, and other responsibilities
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
	3.1 Teamwork
	3.2 Communications	X	X	X	TEN3 TEN2 TEN1 UPG1	Skriftlig matematisk kommunikation
	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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