TNDE21	Analysis and linear algebra, 15 ECTS-points /Analys och linjär algebra/ Advancement level: B
	Aim: To give the students ability to carry out calculations frequently encountered in technical applications. Modelling with derivatives, integrals and differential equations. Prerequisites: Fully obtained elementary mathematic course from the natural science program. Supplementary courses: TNDE23, TNIU54, TNIU56 Course organization: The first part of the course is preparatory, with compulsory exercises. Then follows the two main parts, consisting of a course in fundamental calculus and linear algebra. The teaching consists of lectures followed by lessons and computer exercises with problemsolving guided by a teacher. Course content: Preparatory course. Elementary algebra. Series and the sigma symbol. Binomial theorem. Simple algebraic equations. Powers. Logarithms. Trigonometry. Inequalities. Derivatives. Examination of simple functions. Vectors in the plane. Complex numbers. Part 1, Fundamental Calculus, 5 points. Real numbers, set of real numbers. Proofs by induction. Complex numbers. Functions of one real number: limits, sequences, continuity, differentiations, differentiation rules, monotone functions, elementary functions, antiderivatives, area, extreme values, mean-value theorem. Plane curves, tangent. Riemannintegral, the definite integral, methods of integration, the use of integrals. Part 2, Fundamental Calculus, continued, and Linear Algebra, 5 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. Linear Algebra: Geometric vectors, straight lines and planes. Matrixes. How to solve simultaneous linear equations using matrixes. Linear regression. Determinants. How to find and use the inverse to a square matrix. Linear, especially orthogonal, mapping using matrixes. Course literature: Calculus: will be announced later. Linear algebra: Tengstrand, A.; Lineär algebra med vektorgeometri.
TEN1	Written examination, 5 p.
TEN2	Written examination, 5 p.
TPR1	Written examination, 0 p.

Course language is swedish.