Calculus Series . Math Thought Program

Calculus 3

Multivariable Calculus

Extends calculus to functions of several variables. Topics include partial derivatives, multiple integrals, vector calculus, line integrals, surface integrals, and the fundamental theorems of Green, Stokes, and Gauss.

This is where calculus becomes truly three-dimensional. You will learn to visualize and compute with surfaces, vector fields, and flux, giving you the mathematical tools for fluid dynamics, electromagnetism, and advanced engineering.

Prerequisite: Calculus 2 and AP Calculus BC

Self-Paced

Study Time: 6hr/wk

Take calculus into three dimensions.

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Video Lessons

32 Videos

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Topic Sections

10 Sections

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Avg Per Lesson

~20 Minutes

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Duration

Self-paced

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Practice Sets

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Certificate

On Completion

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What You Need First

Calculus Series . Math Thought Program

Calculus 2

A continuation of Calculus 1 covering advanced integration techniques, sequences and series, parametric equations, and polar coordinates.

Skills you will learn

Apply advanced integration techniques: substitution, integration by parts, partial fractions, trigonometric substitution
Evaluate improper integrals and determine convergence
Compute arc length and surface area of revolution
Determine convergence of infinite series using multiple tests
Construct Taylor and Maclaurin series representations

Why it matters

Calculus 2 concepts are used directly in Calculus 3
Problem-solving techniques carry forward to more advanced topics
Series and sequences appear in multivariable Taylor expansions
Integration techniques are needed for line and surface integrals

~ Calculus 2

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Calculus Series . Math Thought Program

AP Calculus BC

A brief review of inequalities, functions and plane analytic geometry; limits and continuity; the derivative and the differential; applications of dif...

Skills you will learn

Evaluate limits involving indeterminate forms using advanced techniques
Apply advanced integration techniques including substitution, integration by parts, and partial fractions
Work with sequences and series, including convergence tests and power series
Compute and interpret parametric equations
Analyze and compute in polar coordinates

Why it matters

HY IT MATTERS
Advanced integration techniques are essential for solving multivariable integrals in Calculus III
Series and convergence provide the foundation for approximation methods used across mathematics
Parametric and polar thinking prepares you to describe motion and geometry in multiple dimensions
Power series allow you to represent functions in ways that extend beyond standard formulas
Calculus III is not new mathematics, it is familiar ideas viewed through a higher-dimensional lens

~ AP Calculus BC

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Course Topics & Lessons

Lecture Series: Multivariable Calculus

32 lessons

01.1

Lecture: 3D Coordinates

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01.2

Lecture: Vector Basics

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01.3

Lecture: Lines in 3D

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01.4

Lecture: Intro to Vector Calculus

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01.5

Lecture: Multivariable Limits

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01.6

Lecture: Directional Derivatives

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01.7

Lecture: Double Integrals [Rectangular Regions]

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01.8

Lecture: Triple Integrals [Rectangular Coordinates]

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01.9

Lecture: Vector Calculus Fundamentals

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01.10

extra

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01.11

Lecture: 3D Graphing

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01.12

Lecture: Orthogonal Vectors [Part 01]

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01.13

Lecture: Fundamentals of Planes

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01.14

Lecture: Arclength & Curvature

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01.15

Lecture: Partial Derivatives

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01.16

Lecture: Multivariable Relative Extrema

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01.17

Lecture: Double Integrals [Generalized Regions]

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01.18

Lecture: Triple Integrals [Coordinates Systems]

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01.19

Lecture: Line Integrals [Part 01]

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01.20

Lecture: 3D Coordinate Systems

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01.21

Lecture: Orthogonal Vectors [Part 02]

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01.22

Lecture: Intro to Vector-Valued Functions

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01.23

Lecture: Components of Motion

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01.24

Lecture: Multivariable Chain Rule

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01.25

Lecture: Lagrange Multipliers [Part 01]

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01.26

Lecture: Double Integrals [Polar Coordinates]

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01.27

Lecture: Line Integrals & Conservative Vector Fields

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01.28

Lecture: Vector Projection

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01.29

Lecture: Tangent Planes

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01.30

Lecture: Lagrange Multipliers [Part 02]

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01.31

Lecture: Multivariable Substitution & The Jacobian

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01.32

Lecture: Green's Theorem & Other Related Theorems

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Course Materials

● Required 2 books

Course Textbook

Thomas Calculus: Early Transcendentals

Joel Hass, Christopher Heil, Przemyslaw Bogacki

2023 Pearson Education ISBN: 9780137728626

Course Textbook

MyLab Math eText

18-Weeks Pearson ISBN: 9780137559794

Instructor information will be available once you are enrolled.

Continue Your Journey

Differential Equations

Ordinary Differential Equations