MATH1C: MULTIVARI CALCULUS
A standard third semester Calculus course covering functions of several variables, vectors, surfaces, vector-valued functions, partial derivatives, multiple and line integrals, Green's Theorem, Stokes' Theorem, and the Divergence Theorem. PREREQUISITE: Mathematics 1B with a grade of 'C' or better.
- Identify, describe, and illustrate lines, planes, solids, cylinders, and quadric surfaces using three-dimensional coordinate systems.
- Formulate, analyze, and solve problems containing vectors and use parametric equations and vector functions to describe space curves.
- Apply differentiation and integration of vector functions to real world problems including arc length, curvature, velocity, and acceleration.
- Apply the concepts of domain, range, evaluation, limits, and continuity to functions of more than one variable.
- Formulate, analyze, and solve problems using partial derivatives including directional derivatives, gradient, and optimizations.
- Calculate double and triple integrals utilizing various three-dimensional coordinate systems and Jacobian transformations.
- Apply integration of mutilvariable functions to real-world problems including mass, moments, center of mass, surface area, and volume.
- Identify and sketch vector fields; find and sketch gradient fields.
- Calculate line integrals and apply the Fundamental Theorem of Line Integrals and Green's Theorem.
- Identify parametric surfaces; calculate surface integrals, and apply Stokes' Theorem and the Divergence Theorem.