Calculus II, 6 credits

Analys II, 6 hp

TNA004

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Sixten Nilsson

Director of studies or equivalent

George Baravdish

Education components

Preliminary scheduled hours: 70 h
Recommended self-study hours: 90 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CKTS Communications, Transport and Infrastructure, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping, Norrköping C
6CIEN Electronics Design Engineering, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping, Norrköping C
6CMEN Media Technology and Engineering, M Sc in Engineering 2 (Spring 2017) 2 2 Swedish Norrköping, Norrköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Electronics Design Engineering, M Sc in Engineering
  • Communications, Transport and Infrastructure, M Sc in Engineering
  • Media Technology and Engineering, 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

Analysis I

Intended 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
  • explain Taylors formula and the concepts series, power series and convergence of series.
  • make comparisons metween sums and integrals
  • use expressions for, and calculate, geometrical quantities such as plane areas, arc length, surface area, volumes of solids of revolution and areas of surfaces of revolution
  • utilize ordinary differential equations (linear of first order: linear and separable and linear equations of higher order with constant coefficients, serie solutions) and integral equations
  • use Taylors Theorem in approximating functions with polynomial, calculating limits and estimation errors and estimate local properties of functions.
  • carry out convergence tests for improper integrals, series and power series and find derivatives and antiderivatives for power series
  • carry out inspections of results and partial results, in order to verify that these are correct or reasonable.

Course content

Applications of integrals - Improper integrals: definition and calculations, area, length of curves, volume of solids of revolution, area of surfaces of revolution. Generalised integrals. Estimation of sums. The formulas of Taylor and Maclaurin. The Maclaurin expansion of elementary functions. Applications, e.g. estimation of errors and finding limits. Ordinary differential equations. Equations of the first order: linear and separable equations. Integral equations. Linear equations of higher order with constant coefficients. Serie solutions. Applications will be given of mathematical models from various fields. Series.

Teaching and working methods

Lectures and problem classes.

Examination

TEN1Written exam6 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

Sixten Nilsson

Course website and other links

http://www2.itn.liu.se/utbildning/kurs/

Education components

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

Course literature

Forsling, G. och Neymark, N.: Matematisk analys, en variabel. Liber. Problemsamling och kompletterande material utgivet av matematiska institutionen.
Code Name Scope Grading scale
TEN1 Written exam 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. 

Student rights and obligations (login required)
Linköping University common rules and regulations (in Swedish)
Forsling, G. och Neymark, N.: Matematisk analys, en variabel. Liber. Problemsamling och kompletterande material utgivet av matematiska institutionen.

Download

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
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                            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)
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            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

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
 

                            		
                            
                                
X

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.3 System thinking
                            
                                
 

                            		
                            
                                
 

                            		
                            
                                
 

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.4 Attitudes, thought, and learning
                            
                                
 

                            		
                            
                                
X

                            		
                            
                                
X

                            		
                            
                            
                            
                                

                            		
                        

                        

                            
                            2.5 Ethics, equity, and other responsibilities
                            
                                
 

                            		
                            
                                
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                                3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
                            
                        

                    
                    
                        

                            
                            3.1 Teamwork
                            
                                
X

                            		
                            
                                
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                            3.2 Communications
                            
                                
X

                            		
                            
                                
X

                            		
                            
                                
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                            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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