Multivariable Calculus 7,5 CreditsThe course focuses on the basic theory of functions of several variables.
Course ContentsThe course presents the basics of the Calculus in several variables.
The course focuses on the following topics:
- Curves and surfaces in implicit form and parameter form (in particular the quadrics)
- Basic set-theoretical concepts. Polar, cylindrical and spherical coordinates
- Functions of several variables, level curves and surfaces
- Limits and continuity, partial derivatives
- Gradient, differentiability, directional derivatives and linerization
- The chain rule, change of variables, the nabla differential operator, curl and divergence. Higher order partial derivatives, the Laplace and wave PDEs
- Second-order Taylor polynomial, classification of critical points and identification of local extremes
- Optimization on compact domains, optimization subject to constraints, Lagrange multipliers
- Double and triple integrals, Fubini evaluation, change of variables
- Basic calculus of vector-valued functions, line and surface integrals, conservative fields, potentials
- The Green's, Gauss' divergence and Stokes formulas.
PrerequisitesGeneral entry requirements and completed course Single Variable Calculus, 6 credits and Linear Algebra, 6 credits or Basic Calculus, 6 credits and Linear Algebra and Optimization, 9 credits
Level of Education: Undergraduate G1F
Course code/Ladok code: TFVK17
The course is conducted at: School of Engineering