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Calculus in One Variable 1, 6 credits
Envariabelanalys 1, 6 hp
TATA41
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Axel Hultman (Y, Yi, MED, Mat, FyN, FRIST), Magnus Herberthson (I, Ii), Hans Lundmark (D, IT,U,KB,TB) och Mikael Langer (M,DPU, EMM)Director of studies or equivalent
Jesper ThorénEducation components
Preliminary scheduled hours: 66 hRecommended self-study hours: 94 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CKEB | Chemical Biology, M Sc in Engineering | 2 (Spring 2017) | 1 | 4 | Swedish | Linköping, Valla | C |
| 6CDDD | Computer Science and Engineering, M Sc in Engineering | 2 (Spring 2017) | 1 | 4 | Swedish | Linköping, Valla | C |
| 6CMJU | Computer Science and Software Engineering, M Sc in Engineering | 4 (Spring 2017) | 1 | 4 | Swedish | Linköping, Valla | C |
| 6CDPU | Design and Product Development, M Sc in Engineering | 2 (Spring 2017) | 1 | 3 | Swedish | Linköping, Valla | C |
| 6CEMM | Energy-Environment-Management M Sc in Engineering | 2 (Spring 2017) | 1 | 3 | Swedish | Linköping, Valla | C |
| 6CTBI | Engineering Biology, M Sc in Engineering | 2 (Spring 2017) | 1 | 4 | Swedish | Linköping, Valla | C |
| 6CITE | Information Technology, M Sc in Engineering | 2 (Spring 2017) | 1 | 4 | Swedish | Linköping, Valla | C |
| 6CMMM | Mechanical Engineering, M Sc in Engineering | 2 (Spring 2017) | 1 | 3 | Swedish | Linköping, Valla | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1XCourse offered for
- Industrial Engineering and Management - International, M Sc in Engineering
- Industrial Engineering and Management, M Sc in Engineering
- Biomedical 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
- Computer Science and Software Engineering, 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
- Mechanical Engineering, M Sc in Engineering
- Engineering Biology, 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
Foundation Course in MathematicsIntended 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
- qoute and explain definitions of concepts like local extremum, limit, continuity, derivative, antiderivative and integral
- qoute, explain and use central theorems such as the first and second fundamental theorem of calculus, the mean value theorems, the intermediate value theorem, the extreme value theorem
- use rules for limits, derivatives, antiderivatives and integrals
- carry out examinations of functions, e.g., using derivatives, limits and the properties of the elementary functions, and by that means draw conclusions concerning the properties of functions
- use standard techniques in order to determine antiderivatives and definite integrals
- make comparisons between sums and integrals
- 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
Functions of a real variable. Limits and continuity. Derivatives. Rules of differentiation. Derivatives of the elementary funtions. Properties of differentiable functions. Derivative and monotonicity. Graph sketching, tangents and normals, asymptotes. Local and global extrema. Derivatives of higher order. How to find antiderivatives. Partial integration, the method of substitution. Antiderivatives to rational functions, functions containing certain radicals and trigonometric functions. The Riemann integral: definition and properties.
Integration of continous functions. Connection between the definite integral and antiderivatives. Methods of integration. Definition and calculation of generalised integrals. Estimation of sums.
Teaching and working methods
Lectures and problem classes. The IT programme has a different organization,
due to the study programme syllabus.
Examination
| TEN1 | Written examination | 6 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Department
Matematiska institutionenDirector of Studies or equivalent
Jesper ThorénExaminer
Axel Hultman (Y, Yi, MED, Mat, FyN, FRIST), Magnus Herberthson (I, Ii), Hans Lundmark (D, IT,U,KB,TB) och Mikael Langer (M,DPU, EMM)Course website and other links
Education components
Preliminary scheduled hours: 66 hRecommended self-study hours: 94 h
Course literature
Additional literature
Books
- Forsling, G. och Neymark, N., Matematisk analys, en variabel Liber
Other
- Problemsamling utgiven av matematiska institutionen
| 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., Matematisk analys, en variabel Liber
Other
Problemsamling utgiven av matematiska institutionen
Note: The course matrix might contain more information in Swedish.
I = Introduce, U = Teach, A = Utilize
| I | U | A | Modules | Comment | ||
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| 1. DISCIPLINARY KNOWLEDGE AND REASONING | ||||||
| 1.1 Knowledge of underlying mathematics and science (G1X level) |
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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 |
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X
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X
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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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| 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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