| TATM72 | Calculus, One Variable, 10,5 ECTS credits. /Analys A/ |
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Prel. scheduled
hours: 128 |
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Area of Education: Science Subject area: Mathematics |
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| Advancement level
(A-D): B
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| Aim: The course will give basic proficiency in single-variable calculus required for subsequent studies. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Admission to the course requires, as well as general university entrance requirements, upper secondary school mathematics E (or equivalent). 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. The IT programme has a different organization, due to the study programme syllabus. |
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| Course contents: Factorization of polynomials. Inverse trigonometric functions. Functions of a real variable. Limits and continuity. Derivatives. Rules of differentiation. Properties of differentiable functions. Derivative and monotonicity. Graph sketching, tangents and normals, asymptotes. Local and global extrema. Derivatives of higher order. Convex and concave functions. How to find primitive functions. The Riemann integral. Definition and properties. Connection between the definite integral and primitive function. Methods of integration. Applications of integrals: 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. Applications will be given of mathematical models from various fields. |
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| Course literature: Persson, A, Böiers, L-C: Analys i en variabel, Studentlitteratur, Lund. Additional material published by the Department of Mathematics. |
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| Examination: | |||
| Written examination Written examination, optional Written examination, optional |
7 p 0 p 0 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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