Calculus in One Variable II, 6 credits

Envariabelanalys II, 6 hp

TNIU23

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Peter Holgersson

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 70 h
Recommended self-study hours: 90 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6KFTL Air Transportation and Logistics 6 (Spring 2017) 1 2 Swedish Norrköping E
6KLOG Civic Logistics 6 (Spring 2017) 1 2 Swedish Norrköping E
6IBYG Civil Engineering, B Sc in Engineering 2 (Spring 2017) 1 2 Swedish Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Civil Engineering, B Sc in Engineering
  • Civic Logistics
  • Air Transportation and Logistics

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 part 1

Intended learning outcomes

The student should after the course be able to:

  1. define, descirbe and combine basic analytical notions like indefinite- and definite integrals, Maclaurin- and Taylorpolynomials, differential equations,
  2. understand the content of most relevant theorems of analysis (like main theorem of analysis, main theorem of integral calculus, Taylor theorem),
  3. understand the ideas of proofs of some of these theorems,
  4. calculate integrals of various functions by an appropriate choice of integration method
  5. apply integral calculus for calculations of various geometric quantities (like area of figures or volume of three-dimensional objects) by choosing suitable methods,
  6. apply integral calculus for calculations of various features (like expecte value, standard deviation or quantiles) of one-dimensional continuous stochastic variables,
  7. approximate functions with Maclaurin- or Taylorpolynomials,
  8. handle some simple differential equations and apply them for mathematical modelling of simple systems.

Course content

Primitive functions and basic integration methods. Definite integrals and main theorem of analysis. Geomtric applications of integral calculus. Application of integrals in statistics: evaluations of expected value, standard deviation and quantiles for continous stochastic variables. Approximation of functions through Maclaurin- and Taylorexpansions. Differential equations: first order separable and linear differential equations and linear differential equations of second order.

Teaching and working methods

The course is given in a series of lectures and tutorials and is examined by a written exam TEN1. A bonus-point system based on an optional written test is applied.

Examination

KTR1Optional written test0 creditsU, G
TEN1Written examination6 creditsU, 3, 4, 5

Grades

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

Department

Institutionen för teknik och naturvetenskap

Director of Studies or equivalent

George Baravdish

Examiner

Peter Holgersson

Course website and other links

www.itn.liu.se/~krzma

Education components

Preliminary scheduled hours: 70 h
Recommended self-study hours: 90 h

Course literature

Göran Forsling, Mats Neymark, ”Matematisk analys. En variabel”. Förlaget: Liber AB, ISBN: 978-91-47-10023-1. Göran Forsling, ”Övningar i analys i en variabel”, Matematiska Institutionen, LiU, 2001.
Code Name Scope Grading scale
KTR1 Optional written test 0 credits U, G
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. 

Göran Forsling, Mats Neymark, ”Matematisk analys. En variabel”. Förlaget: Liber AB, ISBN: 978-91-47-10023-1. Göran Forsling, ”Övningar i analys i en variabel”, Matematiska Institutionen, LiU, 2001.

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
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)
X
X
TEN1

                            
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
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities
X
X

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
3.2 Communications
X

                            
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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