Calculus, one variable, 6 credits

Analys i en variabel, 6 hp

NMAA06

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Magnus Berggren

Director of studies or equivalent

Jesper Thorén

Education components

Preliminary scheduled hours: 118 h
Recommended self-study hours: 42 h
Possible deviation from course syllabus/programme syllabus
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
Single subject course (Full-time, Day-time) Autumn 2017 1, 2 -, - Swedish Linköping, Valla
6KKEM Chemistry - Molecular Design, Bachelor's Programme 1 (Autumn 2017) 0, 1 -, 4 Swedish Linköping, Valla C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Chemistry - Molecular Design, Bachelor's Programme

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.

Intended learning outcomes

That you as a student will learn to feel confident with the mathematical expressions, reasoning and relations from Single Variable Calculus and that it will teach you calculating and problem solving skills needed for your further studies. After a completed course you should be able to:

  • Read and interpret mathematical texts
  • Explain definitions and expressions like local extremes, limits, continuity, derivatives, primitive functions and integrals
  • Explain and use central theorems like The Fundamental Theorem of Calculus, Mean-Value Theorems, The Intermediate-Value Theorem and The Max-Min Theorem.
  • Use mathematical laws for limits of functions and derivatives.
  • Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions

Course content

  • Preparatory course: Equations and systems of equations. Geometric and arithmetic sums. Inequalities. Binomial theorem. Exponential functions and logarithms. Polynomials. Trigonometry and trigonometric functions.
  • Calculus: Real and complex numbers. Functions of a real variable. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions.

    Teaching and working methods

    Teaching is done in lectures and problem classes.

    Examination

    KTR2Written test0 creditsU, 3, 4, 5
    KTR1Written test0 creditsU, 3, 4, 5
    TEN1Written examination6 creditsU, 3, 4, 5
    Passed written test 1 and written test 2 gives a bonus on the written examination (TEN1). The right to count the bonuses from the tests is 12 months from the date of writing.

    Grades

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

    Other information

    Supplentary courses: Mathematics, second course.

    Department

    Matematiska institutionen

    Director of Studies or equivalent

    Jesper Thorén

    Examiner

    Magnus Berggren

    Course website and other links

    http://www.mai.liu.se/kurser/

    Education components

    Preliminary scheduled hours: 118 h
    Recommended self-study hours: 42 h

    Course literature

    Forsling, Göran och Neymark Mats: Matematisk analys, en variabel. Liber 2011.
    • Code Name Scope Grading scale
    KTR2 Written test 0 credits U, 3, 4, 5
    KTR1 Written test 0 credits U, 3, 4, 5
    TEN1 Written examination 6 credits U, 3, 4, 5
    Passed written test 1 and written test 2 gives a bonus on the written examination (TEN1). The right to count the bonuses from the tests is 12 months from the date of writing.

    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, Göran och Neymark Mats: Matematisk analys, en variabel. Liber 2011.

    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
    X
    TEN1
    		 
    
                                		
                        
    
                        
    
                            
                            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
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.2 Experimentation, investigation, and knowledge discovery
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.3 System thinking
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.4 Attitudes, thought, and learning
                            
                                
     
    
                                		
                            
                                
    X
    
                                		
                            
                                
    X
    
                                		
                            
                                  
    TEN1
    
                                		
                            
                                
    
                                		
                        
    
                        
    
                            
                            2.5 Ethics, equity, and other responsibilities
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
                    
                        
    
                            
                                3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
                            
                        
    
                        
                    
                        
    
                            
                            3.1 Teamwork
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                                
     
    
                                		
                            
                            
                            
                                
    
                                		
                        
    
                        
    
                            
                            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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