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MAM045 Mathematics 24.0 ECTS credits | |
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TIMEPERIOD: I-IV LANGUAGE:English/Swedish EXAMINER H Kallioniemi Univ lekt PREREQUISITES COURSE AIM The aim of the course is to give the student basic knowledge and an acquaintance with central mathematical concepts, methods and logical structures in order to make Mathematics an efficient tool and to provide a good base for further studies in Mathematics, Science, Technology and Economics. CONTENTS Period 0 Preliminaries, review of courses from the Gymnasium (High School) Period 1 Calculus: Fundamentals of Mathematics, Limits, Continuity and Derivative. Period 2 Linear algebra: Geometric Vector Algebra, Matrix Algebra. Calculus: Integrals. Period 3 Linear Algebra: Linear Spaces Calculus: Differential Equations, Complex Numbers Period 4 Multivariable Calculus. Calculus: Fundamentals, the Systematic structure of Mathematics, Logic, Sets, Number Systems, Limits, Important Limits, Continuity, Differentiation, Rules, Differentials, Extreme Values, Solving Equations, Approximation with Polynomials, Taylor's Formula, Integrals, Definition and Properties, Methods of Integration, Applications. Improper Integrals. Complex numbers, Algebraic Equations, the Exponential Function. Differential equations. Ordinary differential equations. Models, Functions of Several Variables, Derivatives, Differentials, Taylor's Formula, Extrem Values, Multiple and Line Integrals, Vector Calculus and Geometric Applications. Linear algebra: Geometry, Vectors Vector Space, Linear Dependence, Basis, Change of Basis, Subspace, Inner Product, Orthogonality, Linear Transformations, Eigenvalues, Eigenvectors, Quadratic Forms, Systems of Linear Equations, Existence and Uniqueness. Numerical Methods: Solving Equations, Systems of Linear Equations and Differential, Numerical Integration. TEACHING Instruction is given in form of lectures, lessons and laboratory exercises. EXAMINATION A written examination is given at the end of each period. They are coded MAM039-047:1 - MAM039-047:4 and MAM115:1-4. Students who have studied the course earlier without passing the examination have to follow the last schedule for the course. A more precise description of the latest contents can be obtained from the department. The written examination covers both problem solving and theory. COURSE GRADE SCALE: 3, 4, 6 ITEMS/CREDITS | |
| Written exam | 3.60ECTS |
| Written exam | 7.50ECTS |
| Laboratory work | 0.60ECTS |
| Written exam | 6.00ECTS |
| Written exam | 6.30ECTS |
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COURSE LITTERATURE Adams Robert A: Calculus, A Complete Course. Addison-Wesley, third edition, 1995. Anton Howard/Rorres Chris: Elementary linear algebra. Applications version, Wiley, seventh edition, 1994. Vretblad Anders: Algebra och kombinatorik. Gleerups, 1992. Råde L./Westergren B.: BETA, Mathematics Handbook |
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