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Calculus in one variable, 1, 6 ECTS credits.
/Envariabelanalys 1/
For:
D
DPU
EM
FyN
I
Ii
IT
KeBi
M
Mat
MED
TB
U
Y
Yi
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Prel. scheduled
hours: 66
Rec. self-study hours: 94
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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:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Foundation Course in Mathematics
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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Organisation:
Lectures and problem classes. The IT programme has a different organization,
due to the study programme syllabus.
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Course contents:
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.
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Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber.
A collection of problems edited by the Department of Mathematics.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Jesper Thorén
Examiner: 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)
Link to the course homepage at the department
Course Syllabus in Swedish
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