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Ace Advanced Calculus in 10.5 Hours (The Complete Course)
48 students
What you'll learn
- Evaluate double and triple integrals using various coordinate systems
- Transform integrals into polar, cylindrical, and spherical coordinates
- Compute areas, volumes, and other quantities using multivariable calculus
- Understand the properties of vector and scalar fields
- Calculate line integrals for work and circulation in vector fields
- Apply vector operators like gradient, divergence, and curl
- Master Green’s, Stokes’, and the Divergence Theorem
- Solve real-world problems using integral theorems
- Derive partial differential equations from physical principles
- Model fluid flow, heat diffusion, and electromagnetic fields
- Reinforce learning through practice problems with solutions
- Build confidence in solving complex calculus problems
Explore related topics
Course content
11 sections • 100 lectures • 10h 20m total length
Requirements
- 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.
Description
How This Course Works
Welcome to Ace Advanced Calculus in 10.5 Hours (The Complete Course)! This comprehensive course expands on foundational calculus, exploring the behavior and applications of functions in multiple dimensions. You'll delve into four main topics: Integral Calculus, Vector Calculus, Integral Theorems (including Green’s, Stokes’, and the Divergence Theorem), and an Introduction to Partial Differential Equations. Whether you're pursuing a degree in mathematics, physics, engineering, or another technical field, this course equips you with both theoretical insights and practical tools for tackling real-world problems.
Who Should Take This Course?
This course is perfect for:
University students enrolled in Advanced Calculus or those who have completed Calculus III and Linear Algebra.
Learners and professionals seeking a deeper understanding of multivariable calculus applications in their fields.
Anyone eager to master advanced calculus concepts for academic or professional growth.
Course Overview
Access a rich learning experience featuring lecture videos, detailed notes, and practice problem sets with 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, transformations in triple integrals, and practical applications.
Surface Area and Surface Integrals: Calculations in Cartesian, cylindrical, and spherical coordinates.
Vector Calculus
Vector and Scalar Fields: Explore the properties and differences between vector and scalar fields, and understand their significance in modeling physical phenomena like fluid flow, temperature distribution, and electric fields.
Line Integrals: Learn to compute line integrals over scalar and vector fields, essential for evaluating work done by forces and other real-world applications in physics and engineering.
Flux, Circulation, and Vector Operators: Understand the concepts of flux and circulation in vector fields, and master 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).
Downloadable videos and notes for anytime learning.
Five comprehensive problem sets with solutions for active practice.
An instructor committed to guiding you every step of the way.
See You Inside the Course!
– Gina Chou
Who this course is for:
- Undergraduate and graduate students in mathematics, physics, engineering, and related fields.
- Seek a deeper understanding of integral calculus concepts and techniques for multi-variable functions.
- Wish to develop skills in using advanced calculus tools like Jacobians, Gamma functions, and Laplace transforms to simplify and solve complex integrals.
- Aim to apply integral calculus to real-world problems in areas such as fluid dynamics, electromagnetism, and probability theory.