Ace Advanced Calculus in 10.5 Hours (The Complete Course)
Master Multivariable Calculus with Vector Calculus, Integral Theorems, and PDEs
Updated on Jun, 2025
Language - English
Teaching and Academics ,Math,Calculus
Lectures -105
Resources -30
Duration -10 hours
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Course Description
How This Course Works
Welcome to Ace Advanced Calculus in 10.5 Hours (The Complete Course)! This is a complete course that extends foundational calculus, studying the behavior and applications of functions in multiple dimensions. You will learn four main topics: Integral Calculus, Vector Calculus, Integral Theorems (including Green's, Stokes', and the Divergence Theorem), and an Introduction to Partial Differential Equations. In any case, you're going to be a math, physics, engineering, or other technical major: this course gives you powerful theoretical understanding and practical tools for facing real-world problems.
Who Should Take This Course?
This course is ideal for:
University students enrolled in Advanced Calculus or those who have completed Calculus III and Linear Algebra.
Learners and professionals aiming to deepen their understanding of applications of multivariable calculus in their practices.
Anyone interested in learning the advanced calculus topics for academic or professional development.
Course Overview
Get a rich learning experience with lecture videos, detailed notes and practice problem-sets with their solutions.
Topics include:
Integral Calculus
Two-Variable Functions : Jacobians in polar coordinates, variable transformations in double integrals and their applications.
Gamma Function and Laplace Transform: Insights into key integrals and the Laplace transform.
Three Variable Functions: Jacobians in cylindrical and spherical coordinates, change of variables in triple integrals and applications.
Surface Area and Surface Integrals: Computing in Cartesian, cylindrical, and spherical coordinates.
Vector Calculus
Vector and Scalar Fields: Understand properties and differences between vector and scalar fields and importance in modeling phenomena such as fluid flow, temperature distribution, electric fields, etc.
Line Integrals: Learn how to compute line integrals over scalar and vector fields, important to determine work done by forces and other practical applications in physics and engineering.
Flux, Circulation, Vector Operators
Understand the concepts of flux and circulation in vector fields and become acquainted with key operators such as gradient, divergence, and curl.
Integral Theorems
Divergence (Gauss') Theorem: Applications, including Gauss' Law and fields following inverse-square laws.
Green's Theorem: Flux, scalar, and circulation versions, including applications to work, evaluating integrals, and calculating areas.
Stokes’ Theorem: Plane-specific applications and conservative fields.
Introduction to Partial Differential Equations
Fundamental concepts and derivations using the Divergence Theorem for:
Fluid flow
Heat diffusion
Electromagnetic theory (Maxwell's equations)
Course Content
Videos: Clear, step-by-step explanations to make complex problems manageable.
Notes: Downloadable lecture notes for each section to support offline review.
Assignments: Five practice problem sets with detailed solutions to solidify your understanding.
Highlights of What's Included
Lifetime access to Ace Advanced Calculus in 10.5 Hours (The Complete Course).
Videos and notes are downloadable so that you can learn anytime.
Five complete problem sets with solutions so that you practice actively.
Instructor committed to guiding you through every step.
See You Inside the Course!
– Gina Chou
Goals
- Apply double and triple integrals in multiple coordinates
Change variable for evaluation into polar, cylindrical, spherical coordinate systems
Compute areas and volume, with various other multivariable applications, of the Calculus
Determine the nature of vector and scalar fields
Find work and circulation via the line integral
Apply Gradient, Divergence, and Curl operators
Prove Green's, Stokes', and the Divergence Theorem
Use the integral theorems for solutions to physical applications
Develop the PDE model starting from physics.
Fluid flow of models, Diffusion of Heat, and Electro-magnetic Field. Solutions are given with exercise questions. Gain mastery over problem solutions of Calculus.
Prerequisites
- Proficiency in Single-Variable Calculus (Calculus 1 and 2): A solid understanding of differentiation and integration for single-variable functions, including the Fundamental Theorem of Calculus, techniques of integration, and applications of single-variable integrals.
- Introductory Multivariable Calculus Knowledge (Calculus 3): Familiarity with partial derivatives, double and triple integrals, and basic coordinate transformations (e.g., Cartesian to polar).
- Basic Linear Algebra Skills: Understanding of vectors and matrices, which is helpful for transformations and working with Jacobians.
Curriculum
Check out the detailed breakdown of what’s inside the course
Introduction
3 Lectures
-
Overview
03:02
03:02
-
Welcome and How It Works
03:14
03:14
-
Maximizing Your Learning Experience
I. Integral Calculus: Two-Variable Functions
7 Lectures
I. Integral Calculus: Gamma Function and Laplace Transform
7 Lectures
I. Integral Calculus: Three-Variable Functions
15 Lectures
I. Integral Calculus: Surface Area and Surface Integral
11 Lectures
II. Vector Calculus: Vector and Scalar Fields
7 Lectures
II. Vector Calculus: Line Integrals
8 Lectures
II. Vector Calculus: Flux, Circulation, and Vector Operators
12 Lectures
III. Integral Theorems
25 Lectures
IV. Introduction to Partial Differential Equations
8 Lectures
Conclusion
2 Lectures
Instructor Details
Gina Chou
During my undergraduate years, I always looked forward to exams because I was well-prepared and found them rewarding. I know this isn’t the case for everyone, so I'm here to share my knowledge and help make your university journey a bit easier!
A bit about me:
I earned my BSc in Atmospheric Science and Physics, with a minor in Mathematics, from McGill University in 2018. I then completed my MSc in 2019 and my PhD in 2024, both in Physics at the University of Toronto. My research focuses on the impact of wind observations on global predictability, Arctic climate, and weather processes.
Since my second year of undergrad, I’ve gained extensive tutoring experience, working with students at Liberty Tutoring, supporting high school and university students through SUS Peer Tutoring and Saturday Programs, and working with private students both in person and online. I also served as a teaching assistant for math and physics courses at both the undergraduate and graduate levels from 2017 to 2024.
I look forward to seeing you in class!
Gina C.
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