| TAIU10 | Calculus, B.Sc. Course, 12 ECTS credits. /Analys i en variabel/ |
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Prel. scheduled
hours: 154 |
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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 student will: - become familiar with the mathematical concepts and methods which are basic to scientific and technical subjects - achieve a good ability to follow and carry out mathematical and logical reasoning - have the proficiency in calculating and in problem solving which is necessary for further technical and scientific studies. |
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| Prerequisites: (valid for students admitted to programmes within which the course is offered) Lycée mathematics (natural sciences or technical lines). 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: TAIU23 Transform Methods, TAIU30 Mathematics B.Sc. Course, TADI01 Diskrete Mathematics, TADI20 Numerical Algorthms |
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| Organisation: The course is taken during the first semester of the first year. Teaching is done in lectures and problem classes. The examination consists of two written tests. |
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| Course contents: Preparatory course: Equations and systems of equations. Geometric and arithmetic series. Inequalities. Exponential functions and logarithms. Trigonometric functions. Elementary geometry. Derivative and the study of functions. Calculus: Real and complex numbers. Binomial theorem. Induction. Functions of a real variable. Polynomials. Elementary functions. Sequences, limits. Derivatives and continuity. Rules for differentiation. Properties of continuous functions. Study of functions. Numerical solution of equations. Primitive functions. Integration and geometrical applications, including area, curve length, areas of rotation and volumes of rotation. Improper integrals and numerical series. Taylor's formula. Maclaurin expansions of elementary functions with applications to the calculation of limits. Linear ordinary differential equations of first and second order, separable equations. |
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| Course literature: Preparatory material published by the Departement of Mathematics. Persson, A, Böiers, L-C: Analys i en variabel. Studentlitteratur, Lund 2001. Collection of problems published by the Departement of Mathematics. |
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| Examination: | |||
| Written examination, part 1 Written examination, part 2 |
4 p 4 p |
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Course language is Swedish. Department offering the course: MAI. Director of Studies: Arne Enqvist Examiner: Magnus Berggren Link to the course homepage at the department Course Syllabus in Swedish |
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