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| TAIU10 | Calculus, B.Sc. course, 8 p (sw) /Analys i en variabel/ Advancement level: B | |
| 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. Prerequisites: Lycée mathematics (natural sciences or technical lines). Supplementary courses: TAIU 23 Transform Methods, TATM 95 Mathematics B. Sc. course, TATM 76 Calculus, TADI 20 Numerical algorithms.Course organization: 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. Course content: 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. Course literature: Preparatory material published by the Departement of Mathematics. Persson, A, Böiers, L-C: Analys i en variabel. Studentlitteratur, Lund 1990. Collection of problems published by the Departement of Mathematics. | ||
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