Multivariable calculus — vectors, partial derivatives, multiple integrals, and the great integral theorems.
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97% Completion RateCourse completion rate
28–30 DaysAverage course completion
Save $650+vs. average community college cost
Self-Paced · Final Exam · ACE & NCCRS Recommended
What You'll Learn
A full semester of calculus iii — completed at your own pace, with no deadlines or fixed class times.
Learning Outcomes
What You'll Be Able to Do
✓Perform vector operations in 2D and 3D space — including dot product, cross product, and projections — and apply them to geometric problems involving lines, planes, and quadric surfaces
✓Analyze vector-valued functions using calculus to compute derivatives, integrals, arc length, curvature, and model motion in space
✓Compute and interpret partial derivatives, gradients, and directional derivatives for multivariable functions, and apply the chain rule and linear approximation
✓Solve constrained and unconstrained optimization problems for multivariable functions using critical point analysis and Lagrange multipliers
Course Curriculum
Your path through the course
Work through each lesson at your own pace and build your understanding step by step.
✓
Evaluate double and triple integrals in Cartesian, polar, cylindrical, and spherical coordinates, and apply them to compute area, volume, mass, and center of mass
✓Compute line integrals of scalar and vector fields, apply the Fundamental Theorem for Line Integrals, and use Green's Theorem to relate line and double integrals
✓Evaluate surface integrals over parametric and explicit surfaces, compute flux integrals, and apply Stokes' Theorem and the Divergence Theorem
