Multivariable Calculus, 5 cr

Core content

• Real valued functions of several variables: Graphs and contour plots of functions of two variables. Limits and continuity, first and higher order partial derivatives, directed derivative and gradient.
• Vector-valued functions of several variables: Derivative matrix and the chain rule.
• Extreme values of a function: Local and global maxima and minima.
• Integrals of functions of two and three variables: Computing in vertically and horizontally simple domains, computing using polar, cylinder and spherical coordinates.

Complementary knowledge

• Linear approximation and differentiability
• Hessian matrix, Taylor's formula
• Constrained extremal values and Lagrange's method.
• Center of mass, improper integrals.
• Using Matlab as a tool in solving the exercise problems.

Specialist knowledge

• A ball, open and closed sets
  
• General change of variables, mean value theorem and average of a function