Multivariable Calculus II: Integral Calculus

Master Integrals, Theorems, and Beyond: In this advanced course, you’ll dive deeper into multivariable calculus with a focus on integral calculus in multiple dimensions. Start with double integrals over rectangles and irregular regions, leveraging polar coordinates for applications like surface area, then advance to triple integrals in cylindrical and spherical coordinates. You’ll also apply the change of variables technique to simplify complex integrations across various coordinate systems and explore vector fields, line integrals, Green’s Theorem, curl, divergence, and parametric surface calculus. The course ends with surface integrals, leading to Stokes’ Theorem and the Divergence Theorem—powerful tools in mathematics and physics.

Why Take This Course? Using a computer algebra system (CAS), you’ll visualize problems and enhance your understanding through collaborative projects and real-world applications. Ideal for aspiring mathematicians, physicists, or engineers, this course prepares you to tackle complex, multi-dimensional problems with confidence and precision.

Successful completion of Multivariable Calculus I: Vector & Differential Calculus, and the equivalent of a university year of single-variable calculus with integration techniques, including trigonometric substitution, integration by parts, and partial fractions. Completion of the AP Calculus BC curriculum with a score of 4 or 5 on the AP Exam would be considered adequate preparation.

Students in GOA courses will need reliable access to a computer with webcam/microphone connections, an email address (preferably school-based), a Web-conferencing app (GOA courses use Zoom), and a Word processing app (GOA courses use Google’s G Suite). When necessary, alternative arrangements may be made. Some courses require additional materials which can be found here.

NCAA-approved course

UC-approved course