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Calculus in One Variable 2, 6 credits
Envariabelanalys 2, 6 hp
TATA42
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Mats Aigner (I,Ii), Johan Thim (D,IT,U,KB,TB), Ulf Janfalk (M,DPU,EMM), Tomas Sjödin (Y,Yi, MED,Mat,FyN,FRIST)Director of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 70 hRecommended self-study hours: 90 h
ECV = Elective / Compulsory / Voluntary
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1XCourse offered for
- Industrial Engineering and Management, M Sc in Engineering
- Computer Science and Engineering, M Sc in Engineering
- Design and Product Development, M Sc in Engineering
- Energy-Environment-Management M Sc in Engineering
- Information Technology, M Sc in Engineering
- Chemical Biology, M Sc in Engineering
- Biomedical Engineering, M Sc in Engineering
- Mechanical Engineering, M Sc in Engineering
- Engineering Biology, M Sc in Engineering
- Applied Physics and Electrical Engineering, M Sc in Engineering
- Physics, Bachelor´s Programme
- Mathematics, Bachelor´s Programme
- Industrial Engineering and Management - International, M Sc in Engineering
- Applied Physics and Electrical Engineering - International, 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 variableIntended learning outcomes
To give basic proficiency in mathematical concepts, reasoning and relations contained in single-variable calculus. To provide the skills in calculus and problem solving required for subsequent studies. After a completed course, the student should be able to
- read and interpret mathematical text
- quote and explain Taylor's formula and the concepts involved in numerical series and convergence of series
- derive expressions for, and compute, geometrical quantities such as plane area, arc length, and volume and surface area of solids of revolution
- solve ordinary differential equations (first order linear and separable equations, and higher order linear equations with constant coefficients) and integral equations
- use Taylor expansions to approximate functions by polynomials, compute limits and rational approximations, and to investigate local properties of functions
- carry out investigations of convergence of improper integrals, numerical series and power series
- use power series to calculate sums and to solve differential equations
- perform routine calculations with confidence
- carry out inspections of results and partial results, in order to verify that these are correct or reasonable.
Course content
Applications of integrals: plane area, arc length, volume and surface
area of solids of revolution and centre of mass. Taylor's and
Maclaurin's formulae: Maclaurin expansions of the elementary functions,
the Lagrange and Ordo forms of the remainder term, applications,
e.g. error estimates for approximations and computations of limits.
Ordinary differential equations: first order linear and separable
equations, integral equations, higher order linear equations with
constant coefficients. Improper integrals: investigation of convergence,
absolute convergence. Numerical series: investigation of convergence,
absolute convergence, Leibniz criterion.
Power series: radius of convergence, calculation of sums, solving differential equations
Teaching and working methods
Lectures and problem classes.
The IT programme has a different organisation, due to the study programme syllabus.
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
Supplementary courses: Calculus in several variables, Vector analysis, Complex analysis, and Fourier analysis.
Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Mats Aigner (I,Ii), Johan Thim (D,IT,U,KB,TB), Ulf Janfalk (M,DPU,EMM), Tomas Sjödin (Y,Yi, MED,Mat,FyN,FRIST)Course website and other links
http://www.mai.liu.se/und/kurser/index-amne-tm.htmlEducation components
Preliminary scheduled hours: 70 hRecommended self-study hours: 90 h
Course literature
Additional literature
Books
- Forsling, G. och Neymark, N., (2011) Matematisk analys, en variabel Liber
Compendia
Complementary material and a collection of problems edited by the Department of Mathematics.
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
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
Forsling, G. och Neymark, N., (2011) Matematisk analys, en variabel Liber
Compendia
Complementary material and a collection of problems edited by the Department of Mathematics.
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
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
|
X
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X
|
TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
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X
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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| 3.2 Communications |
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X
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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