TAIU25	Calculus and linear algebra, 18 ECTS-points /Analys och linjär algebra/ 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 96 Vector Analysis, TATM 33 Calculus. Course organization: The course is taken during the first three quarters of the first year, and is divided into two sub-courses. The first part deals with single variable analysis, the other with linear algebra. A mid-course test is taken halfway during part 1. Teaching is done in lectures and problem classes. 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. 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. Linear algebra: Geometric vectors. Straight lines. Planes. Scalar product and vector product. Matrices and determinants. Matrix inverse. Systems of linear equations. Overdetermined systems. Linear mappings. Eigenvalues and eigenvectors. Course literature: Preparatory material published by the Institute. Persson, A, Böiers, L-C: Analys i en variabel. Studentlitteratur, Lund 1990. Tengstrand, A: Linjär algebra för ingenjörsutbildningarna. Studentlitteratur, Lund, 1994. Collection of problems published by the Institute.
TEN1	Written examination, 8 p.
TEN2	Written examination, 4 p.
UPG1	Written examination, 0 p.

Course language is swedish.