| TATM73 | Calculus, several variables, 9 ECTS credits. /Analys B, flera variabler/ |
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Area of Education: Natural sciences Subject area: Mathematics |
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| Advancement level
(A-D): B
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| Aim: The course will give basic proficiency in several-variable calculus required for subsequent studies. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) TATM72 Calculus, one variable and one of TATM18 Linear Algebra, TATM13 Algebra III or TATM31 Algebra M. 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 or classes alone. |
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| Course contents: Improper integrals. Convergence. Absolute convergence. Numerical series. Convergence. Absolute convergence. Leibniz criterion. Power series. Radius of convergence. The space Rn. Fundamental notions from topology. Functions from Rn to R. Function graphs, level curves and level surfaces. Limit and continuity. Partial derivatives. Differentiability and differential. Change of variables in derivatives. Gradient, normal, tangent and tangent plane. Directional derivative. Taylors formula. Local and global extrema. Extremal problems with side conditions by means of Jacobians or Lagrange method of multipliers. Convex and concave functions and implicitly defined functions and implicit differentiation. Multiple integrals. Repeated integration. Change of variables. Area, volume, mass and center of gravity. Improper multiple integrals. The course will give proficiency in use of notions and relationships, e.g. ability in establishing convergence of series and improper integrals, finding limits, differentiation of functions with applications to change of variables in derivatives, geometric problems, local and global maxima and minima problems and differentiation of implicitly defined functions, evaluation of double and triple integrals with applications to area, volume and center of gravity problems. Applications will be given of mathematical models from various fields. |
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| Course literature: Persson, A, Böiers, L-C: Analys i flera variabler, Studentlitteratur, Lund 1988. Additional material published by the Department of Mathematics. |
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| Examination: | |||
| Written examination |
6 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Arne Enqvist Examiner: Link to the course homepage at the department Course Syllabus in Swedish |
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