MATA181 Vector calculus 1 (5 cr)

Coordinates and vectors in 3-dimensional space, dot product, cross product. Equations of lines and planes, quadratic surfaces. Curves, differentiation and integration of vector valued functions of one variable. Limits and continuity for functions of two and three variables. Partial derivatives, tangent planes and approximation. Chain rule, gradient vector, directional derivatives. Extreme values, Lagrange multipliers.

After the course the student

• can use coordinates, vectors, dot products and cross products in geometric applications
• can express lines and planes using equations
• understands the concept of derivative for vector functions and its geometric interpretation
• can solve extreme value problems for vector functions

Calculus 1-2 (or Introduction to mathematical analysis 1-2). Calculus 3.

Adams: Calculus, Chapters 10-13.