Meets MnTC Goal Areas 2 and 4. The course content includes a study of vectors in the plane and space, differentiation and integration of vector-valued functions, and partial differentiation, multiple integrals, including line and surface, in rectangular, polar, cylindrical, spherical and other systems, and a study of Stokes' Theorem, Green's Theorem, and the Divergence Theorem.
- Interpret vector operations geometrically in two and three dimensions.
- Evaluate the limits of vector-valued functions.
- Perform dot products and cross products of two vectors.
- Differentiate and integrate vector-valued functions.
- Relate planes in space with parametric equations.
- Define the equations of surfaces in space.
- Evaluate the limits and continuity of multivariable functions.
- Differentiate multivariable functions.
- Develop directional derivatives and gradients.
- Investigate Lagrange Multipliers to solve problems with constraints.
- Produce triple integrals in rectangular, cylindrical, and spherical coordinates and other change of variable systems.
- Analyze vector fields, line, and surface integrals.
- Investigate Green's Theorem, Stokes Theorem and the divergence of a vector field.
2. Critical Thinking
4. Mathematics/Logical Reasoning
Degrees that use this course
Associate of Science (AS)