| TNA004 |
Calculus II, 6 ECTS credits.
/Analys II/
For:
ED
KTS
MT
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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
- 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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Analysis I
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.
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Course contents:
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.
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Course literature:
Forsling, G. and Neymark, N.: Matematisk analys, en variabel. Liber.
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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: ITN.
Director of Studies: George Baravdish
Examiner: Sixten Nilsson
Link to the course homepage at the department
Course Syllabus in Swedish
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