TNG010	Multivariable Calculus, 9 ECTS-points /Flervariabelanalys/ Advancement level: B
	Aim: This course is a continuation of the first year course in single variable calculus. Consequently, the aims are similar: to give students an understanding of mathematical concepts and familiarity with mathematical methods of analysis. Here, these aims relate to the treatment of functions of several variables which arise in all branches of physics and engineering. Prerequisites: TNG001 Calculus in One Variable, TNG002 Linear Algebra Supplementary courses: TNG014 Theory of Integral Transforms, TNG013 Statistics and Probability Theory. Course organization: The course is given in the form of lectures, tutorials, and group study. Note. The course will be offered in English Course content: Functions of several variables. Limits and continuity of functions from R^n to R^m. Partial derivatives, the gradient, directional derivatives and differentials. The chain rule. Extreme values and Taylor's formula. vector-valued functions, the Jacobiam matrix and the Jacobian (determinant). Implicit functions. Optimization with and without constraints. Double and triple integrals. Iterated integrals. Change of variables. Applications. Space curves: arc length, curvature and torsion. Scalar and vector fields. The gradient, divergence and curl. Divergence theorem (Gauss' theorem), Green's formula and Stokes' theorem. Course literature: Adams, R.A.: Calculus. A Complete Course. Addison-Wesley, 1995.
TEN1	A written examination, 4 p.
UPG1	Compulsory assignment presentations and/or class tests, 2 p.

Course language is English.