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Calculus in one variable, 2, 6 ECTS credits.
/Envariabelanalys 2/
For:
D
DPU
EM
FyN
I
Ii
IT
KeBi
M
Mat
MED
TB
Y
Yi
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Prel. scheduled
hours: 70
Rec. self-study hours: 90
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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
- quote and explain Taylor's formula and the concepts involved in numerical series and convergence of series
- derive expressions for, and compute, geometrical quantities such as plane area, arc length, and volume and surface area of solids of revolution
- solve ordinary differential equations (first order linear and separable equations, and higher order linear equations with constant coefficients) and integral equations
- use Taylor expansions to approximate functions by polynomials, compute limits and rational approximations, and to investigate local properties of functions
- carry out investigations of convergence of improper integrals, numerical series and power series
- use power series to calculate sums and to solve differential equations
- 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)
Calculus in one variable
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:
Calculus in several variables, Vector analysis, Complex analysis,
and Fourier analysis.
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Organisation:
Lectures and problem classes.
The IT programme has a different organisation, due to the study programme syllabus.
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Course contents:
Applications of integrals: plane area, arc length, volume and surface
area of solids of revolution and centre of mass. Taylor's and
Maclaurin's formulae: Maclaurin expansions of the elementary functions,
the Lagrange and Ordo forms of the remainder term, applications,
e.g. error estimates for approximations and computations of limits.
Ordinary differential equations: first order linear and separable
equations, integral equations, higher order linear equations with
constant coefficients. Improper integrals: investigation of convergence,
absolute convergence. Numerical series: investigation of convergence,
absolute convergence, Leibniz criterion.
Power series: radius of convergence, calculation of sums, solving differential equations
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Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber 2011.
Complementary material and 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: Lars Alexandersson (I,Ii), Johan Thim (D,IT,U,KB,TB), Ulf Janfalk (M,DPU,EMM), Tomas Sjödin (Y,Yi, MED,Mat,FyN,FRIST)
Link to the course homepage at the department
Course Syllabus in Swedish
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