MATA181 Vector calculus 1 (4 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 successful completion, the student 

• masters the use of coordinates, vectors, dot product and cross product in geometric applications 
• can express lines and planes in three dimensional space using equations 
• can calculate the partial and directional derivatives of a function of several variables, as well as the derivative of a vector-valued function of one variable 
• knows the chain rule for partial derivatives 
• can determine the tangent line of a curve and the tangent plane of a surface, and understands their use in approximation
• understands the geometric interpretation of the gradient 
• can determine the local extrema of a function of two variables
  
• can study the extreme values ​​of a function on a curve or surface using Lagrange's method

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

Adams: Calculus, Chapters 10-13.

Stewart: Calculus, Chapters 12-14