TNIU64	Analysis and linear algebra, 15 ECTS-points /Analys och linjär algebra/ Advancement level: B
	Aim: To give the students the ability to carry out calculations frequently encountered in technical applications. Modelling with derivatives, integrals and differential equations. Prerequisites: Fully obtained elementary mathematics course from the natural science program. Supplementary courses: TNDE 23, TNDE 63 Course organization: The course is divided into four parts. The first part of the course is preparatory with compulsory hand-in exercises. The three following main parts contain linear algebra and fundamental calculus. The course consists of lectures followed by tutorials and computer exercises with problem solving supervised by a teacher. Course content: Preparatory course. The basics of numbers and functions. Elementary equations. Part 1, Complex numbers and Linear Algebra, 3 points. Complex numbers: Different ways of writing a complex number. Equations. Linear Algebra: Geometric vectors, straight lines and planes. Matrixes. Systems of linear equations. Linear regression. Determinants. The inverse of a matrix. Linear, especially orthogonal, mappings using matrixes. Eigenvalues and eigenvectors. Part 2, Fundamental Calculus, 4 points. Real numbers, sets of real numbers. Realvalued functions of one real variable. Limits, sequences, continuity, differentiations, differentiation rules, monotone functions, elementary functions, extreme values, mean-value theorem, plane curves, tangent, optimization. Antiderivatives, area, the Riemannintegral, definite integrals, methods of integration, the use of integrals. Part 3, Fundamental Calculus, continued, 3 points. Taylor and Maclaurinseries: Maclaurin series for elementary functions, limits with Maclaurinseries. Ordinary differential equations: First order, separable and linear equations, second order linear equations, homogeneous linear equations with constant coefficients. Series: convergence test for series and improper integrals, power series. Course literature: Rodhe Staffan and Sollervall Håkan, Matematik för ingenjörer.
TEN1	Written exam on part 1, 3 p.
TEN2	Written exam on part 2, 4 p.
UPG1	, 3 p.

Course language is swedish.