Luleå University of Technology
home search contact us student
Course Catalog 1998/99


Mathematics

MAM048 Mathematics 27.0 ECTS credits

TIMEPERIOD:
I-V

LANGUAGE:English/Swedish

EXAMINER
G Brandell Univ lekt


PREREQUISITES


COURSE AIM
The aim of the course is to give the student a basic knowledge of and an acquaintance with central mathematical concepts, methods and logical structures in order to make mathematics an efficient tool and to provide a good foundation for further studies in mathematics, science, technology and economy.

CONTENTS
Period 0
Preliminaries, review of courses from upper secondary level (Swedish gymnasium).
Period 1
Calculus: Fundamentals of mathematics, limits, continuity and derivative.
Period 2
Linear algebra: Vector algebra, matrix algebra.
Calculus: Integrals.
Period 3
Linear algebra: Linear spaces.
Calculus: Differential equations, complex numbers.
Period 4
Functions of several variables.
Calculus: Fundamentals, the systematic structure of mathematics, logic, sets, number systems, limits, continuity, differentiation, differentials, extreme values, equations, approximation with polynomials, Taylors's formula, integrals, definition and properties, methods of integration, applications. Improper integrals.
Vector calculus: The concepts of vectorfields, gradient, divergence, curl. Theorems of Gauss and Stoke.
Complex numbers, algebraic equations, the exponential function, differential equations. Ordinary differential equations. Models, functions of several variables, derivatives, differentials, Taylors's formula, extreme values, multiple and line integrals, vector calculus and geometric applications.

Linear algebra: Geometry, vectors, linear spaces, linear dependence, basis, change of basis, subspace, inner product, orthogonality, linear transformations, eigenvalues, eigenvectors, quadratic forms, systems of linear equations, existence and uniqueness of solutions.

Numerical methods: Solution of equations, systems of linear equations and differential equations, 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 have codes MAM048:1-4.
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, 5

ITEMS/CREDITS

6.60ECTS
7.50ECTS
Laboratory work 0.60ECTS
Written exam 6.00ECTS
Written exam 6.30ECTS

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.
Råde L./Westergren B.: BETA, Mathematics Handbook.
Valid for school year 1998/99.
Current version this school year:http://www.luth.se/stuka

Web Editor: Karin.Lindholm@dc.luth.se

The University | Student | Research | Search | Contact us | In Swedish

LULEÅ UNIVERSITY OF TECHNOLOGY
University Campus, Porsön, 971 87 Luleå. Tel. +46 (0) 920-91 000, fax +46 (0) 920-91 399
Last edited 1998-12-16