| TAIU10 |
Calculus, one variable, B.Sc. Course, 12 ECTS credits.
/Analys i en variabel/
For:
DI
EL
KA
MI
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Prel. scheduled
hours: 202
Rec. self-study hours: 118
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
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, derivatives, antiderivatives and integrals.
- Perform investigations of functions using derivatives, limits and the properties of basic functions and from this draw conclusions regarding the properties of the functions
- Use standard techniques to calculate antiderivatives and definite integrals.
- Express and calculate geometrical quantities like areas of plane regions, arc length, volumes of solids of revolution and areas of solids of revolution.
- Handle differential equations (first-order separable and first-order linear equations and constant-coefficient equations of higher order.) and integralequations.
- Explain Taylor�?Ts formula
- Use Taylorexpansions to approximate functions and investigate limits.
- Perform checks of results and calculations to verify that they are correct and reasonable
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Transform Methods, Discrete Mathematics, Numerical Algorthms
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Organisation:
The course is taken during the first semester of the first year. Teaching is done in lectures and problem classes. The examination consists of two written tests.
The course runs over the entire autumn semester.
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Course contents:
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. Induction. Functions of a real variable. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions. Primitive functions. Integration and geometrical applications, including area, curve length, areas of rotation and volumes of rotation. Improper integrals. Taylor's formula. Maclaurin expansions of elementary functions with applications to the calculation of limits. Linear ordinary differential equations of first and second order, separable equations.
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Course literature:
Forsling, Göran and Neymark Mats: Matematisk analys, en variabel. Liber 2011.
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Examination: |
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Written examination, part 1
Written examination, part 2
Written test
Written test
Written test
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6 ECTS
6 ECTS
0 ECTS
0 ECTS
0 ECTS
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Passed written test 1 and written test 2 gives a bonus on the first written examination (TEN1).
Approved written test 3 gives a bonus to the second written examination (TEN2). The right to count the bonuses from the tests is 12 months from the date of writing.
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: Magnus Berggren
Link to the course homepage at the department
Course Syllabus in Swedish
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