A Complete Guide to Integral Calculus (Advanced Calculus)

How This Course Works

This course, A Complete Guide to Integral Calculus (Advanced Calculus), builds upon foundational calculus to dive deeply into the behavior and applications of functions in multiple dimensions. Focusing on integral calculus, it also provides an introduction to key vector calculus concepts that follow in the complete series, including major theorems like Green’s, Stokes’, and the Divergence Theorem. This course is essential for students in mathematics, physics, engineering, and other fields who want a practical and theoretical understanding of multivariable calculus tools for real-world problem-solving.

Who Should Take This Course?

This course is ideal for university students currently enrolled in Advanced Calculus, or those who have completed Calculus III and Linear Algebra. It’s also designed for anyone eager to explore multivariable calculus applications more deeply, especially in fields where calculus techniques are indispensable.

Course Overview

This course includes Integral Calculus, the first part of the complete Advanced Calculus series. You’ll have access to lecture videos, whiteboard notes, and problem sets with solutions. Topics covered here include:

Integral Calculus (Sections Included in This Course)

• Two-Variable Functions: Explore Jacobians in polar coordinates, variable changes in double integrals, and applications of double integrals.
• Gamma Function and Laplace Transform: Understand a key integral related to the Gamma function, the Gamma function itself, and the Laplace transform.
• Three-Variable Functions: Learn about Jacobians in cylindrical and spherical coordinates, transformations in triple integrals, and applications of triple integrals.
• Surface Area and Surface Integrals: Calculate surface areas and evaluate surface integrals in Cartesian, cylindrical, and spherical coordinates.

Vector Calculus, Integral Theorems, and Differential Calculus of Several Variables (Available in the Complete Course)

• Vector and Scalar Fields
• Line Integrals
• Flux, Circulation, and Vector Operators
• Integral Theorems
• Introduction to Partial Differential Equations
• Topics in Differential Calculus of Several Variables

Course Content

• Videos: Each topic is introduced and explained thoroughly, with step-by-step examples, making complex problems manageable.
• Notes: Downloadable lecture notes for each section to allow for offline review and reinforcement.
• Assignments: Practice problem sets with solutions so you can check your work after attempting each problem yourself.

Highlights of What’s Included

• Lifetime access to A Complete Guide to Integral Calculus (Advanced Calculus).
• Downloadable lecture videos and notes for anytime review.
• Two comprehensive problem sets with solutions to reinforce learning.
• An instructor committed to your success every step of the way.

See you inside the course!

– Gina Chou 🙂