Calculus 3

Welcome to Calculus 2! Dive deep into advanced calculus concepts and earn 4 college credits while mastering integrals, series, and more.

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Course Curriculum

1. Course Overview and Learning Outcomes
1. Introduction
1. Introduction to Sequences & Series
2. Quiz 1.1
1. VIDEOS
2. Sequences
3. Quiz 1.2
1. VIDEOS
2. Infinite Series
3. Quiz 1.3
1. VIDEOS
2. Geometric and Harmonic Series
3. Quiz 1.4
1. VIDEOS
2. Positive Term Series: Integral & P-Tests
3. Quiz 1.5
1. VIDEOS
2. Positive Term Series: Comparison Tests
3. Quiz 1.6
1. VIDEOS
2. Alternating Sign Series
3. Quiz 1.7
1. VIDEOS
2. Absolute Convergence and the Ratio Test
3. Quiz 1.8
1. VIDEOS
2. Power Series
3. Quiz 1.9
1. VIDEOS
2. Taylor and Maclaurin Series
3. Quiz 1.10
1. Fourier Series
2. Quiz 1.11
1. Chapter 1 Odd Answers
2. Summary
1. Introduction
1. Moving Beyond Two Dimensions
2. Quiz 2.1
1. VIDEOS
2. Vectors in the Plane
3. Quiz 2.2
1. VIDEOS
2. Rectangular Coordinates in Three Dimensions
3. Quiz 2.3
1. VIDEOS
2. Vectors in Three Dimensions
3. Quiz 2.4
1. VIDEOS
2. Dot Product
3. Quiz 2.5
1. VIDEOS
2. Cross Product
3. Quiz 2.6
1. VIDEOS
2. Lines and Planes in Three Dimensions
3. Quiz 2.7
1. Vector Reflections
2. Quiz 2.8
1. Chapter 2 Odd Answers
2. Summary
1. Introduction
1. VIDEOS
2. Vector-Valued Functions and Curves in Space
3. Quiz 3.1
1. VIDEOS
2. Derivatives & Antiderivatives of Vector-Valued Functions
3. Quiz 3.2
1. VIDEOS
2. Arc Length and Curvature of Space Curves
3. Quiz 3.3
1. VIDEOS
2. Cylindrical & Spherical Coordinate Systems in 3D
3. Quiz 3.4
1. Chapter 3 Odd Answers
2. Summary
1. Introduction
1. VIDEOS
2. Functions of Two or More Variables
3. Quiz 4.1
1. VIDEOS
2. Limits and Continuity
3. Quiz 4.2
1. VIDEOS
2. Partial Derivatives
3. Quiz 4.3
1. VIDEOS
2. Tangent Planes and Differentials
3. Quiz 4.4
1. VIDEOS
2. Directional Derivatives and the Gradient
3. Quiz 4.5
1. VIDEOS
2. Maximums and Minimums
3. Quiz 4.6
1. VIDEOS
2. Lagrange Multiplier Method
3. Quiz 4.7
1. VIDEOS
2. Chain Rule
3. Quiz 4.8
1. Chapter 4 Odd Answers
2. Summary
1. Introduction
1. VIDEOS
2. Introduction to Double Integrals
3. Quiz 5.1
1. VIDEOS
2. Double Integrals over Rectangular Domains
3. Quiz 5.2
1. VIDEOS
2. Double Integrals over General Domains
3. Quiz 5.3
1. VIDEOS
2. Double Integrals in Polar Coordinates
3. Quiz 5.4
1. Applications of Double Integrals
2. Quiz 5.5
1. Surface Area
2. Quiz 5.6
1. VIDEOS
2. Triple Integrals and Applications
3. Quiz 5.7
1. VIDEOS
2. Triple Integrals in Cylindrical and Spherical Coordinates
3. Quiz 5.8
1. VIDEOS
2. Changing Variables in Double and Triple Integrals
3. Quiz 5.9
1. Chapter 5 Odd Answers
2. Summary
1. Introduction
1. Introduction to Vector Calculus
2. Quiz 6.1
1. VIDEOS
2. Vector Fields
3. Quiz 6.2
1. VIDEOS
2. Divergence, Curl and Del in 2D
3. Quiz 6.3
1. VIDEOS
2. Line Integrals
3. Quiz 6.4
1. VIDEOS
2. Fundamental Theorem of Line Integrals and Potential Functions
3. Quiz 6.5
1. VIDEOS
2. Green's Theorem
3. Quiz 6.6
1. VIDEOS
2. Divergence and Curl in 3D
3. Quiz 6.7
1. VIDEOS
2. Parametric Surfaces
3. Quiz 6.8
1. VIDEOS
2. Surface Integrals
3. Quiz 6.9
1. VIDEOS
2. Stokes' Theorem
3. Quiz 6.10
1. VIDEOS
2. Gauss/Divergence Theorem
3. Quiz 6.11
1. Chapter 6 Odd Answers
2. Summary

About this course

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25% Quiz

25% Assignments

25% Final Exam

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Math 265: Calculus 2

CHAPTER 1: Comprehensive Overview of Series in Calculus: Power, Taylor, Maclaurin, and Fourier Series

Ch 1.1: Exploration of Sequences and Series in Contemporary Calculus

Ch 1.2: In-depth Exploration of Sequences: Convergence, Monotonicity, and Recurrence

Ch 1.3: Understanding and Analyzing Infinite Series in Calculus

Ch 1.4: Exploring Geometric and Harmonic Series in Calculus

Ch 1.5: Integral Test and P–Test for Series Convergence

Ch 1.6: Positive Term Series: Comparison Tests and Limit Comparison Tests

Ch 1.7: Alternating Series: Definition, Test, and Applications

Ch 1.8: Absolute Convergence, Conditional Convergence, and the Ratio Test

Ch 1.9: Power Series, Interval of Convergence, and Radius of Convergence

Ch 1.10: Taylor and Maclaurin Series: Theory, Applications, and Problem-Solving

Ch 1.11: Introduction to Fourier Series: Theory, Applications, and Computational Methods

Summary of Chapter 1

CHAPTER 2: Understanding Lines, Planes, and Vector Reflections in Three Dimensions

Ch 2.1: Introduction to Higher Dimensions in Calculus

Ch 2.2: Vectors in the Plane: Concepts, Operations, and Applications

Ch 2.3: Rectangular Coordinates in Three Dimensions: Concepts and Applications

Ch 2.4: Vectors in Three Dimensions: Concepts and Calculations

Ch 2.5: Dot Product and Its Applications in Vector Calculations

Ch 2.6: Cross Product and Its Applications in Vector Calculations

Ch 2.7: Lines and Planes in Three Dimensions: Equations, Intersections, and Distances

Ch 2.8: Vector Reflections: Understanding Reflections in 2D and 3D Space

Summary of Chapter 2

CHAPTER 3: Exploring Advanced Coordinate Systems: Arc Length, Curvature, and Coordinate Transformations

Ch 3.1: Understanding Vector-Valued Functions and Their Applications in 3D Space

Ch 3.2: Derivatives and Antiderivatives of Vector-Valued Functions in 3D Space

Ch 3.3: Arc Length and Curvature of Space Curves in Calculus

Ch 3.4: Understanding Cylindrical and Spherical Coordinate Systems in 3D Space

Summary of Chapter 3

CHAPTER 4 : Advanced Calculus: Applications of Derivatives in Multiple Variables

Ch 4.1: Functions of Several Variables: Definitions, Tables, and Graphical Representations

Ch 4.2: Limits and Continuity of Multivariable Functions: Definitions, Calculations, and Applications

Ch 4.3: Partial Derivatives: Definitions, Calculations, and Applications

Ch 4.4: Tangent Planes and Differentials: Concepts, Calculations, and Applications

Ch 4.5: Directional Derivatives and Gradient Vector: Advanced Concepts and Applications

Ch 4.6: Advanced Concepts in Finding Maximums and Minimums: Methods and Applications

Ch 4.7: Advanced Applications of Lagrange Multipliers in Optimization Problems

Ch 4.8: Advanced Chain Rule Applications for Functions of Several Variables

Summary of Chapter 4

CHAPTER 5: Advanced Techniques in Multivariable Calculus: Surface Areas, Triple Integrals, and Variable Transformations

Ch 5.1: Introduction to Double Integrals: Concepts, Approximations, and Applications

Ch 5.2: Double Integrals Over Rectangles: Theory, Computation, and Applications

Ch 5.3: Double Integrals Over General Regions: Theory, Methods, and Practical Applications

Ch 5.4: Double Integrals in Polar Coordinates: Concepts, Computations, and Applications

Ch 5.5: Applications of Double Integrals in Mass, Moments, and Center of Mass Calculations

Ch 5.6: Surface Areas Using Double Integrals

Ch 5.7: Triple Integrals and Their Applications

Ch 5.8: Triple Integrals in Cylindrical and Spherical Coordinates

Ch 5.9: Changing Variables in Double and Triple Integrals

Summary of Chapter 5

CHAPTER 6: Advanced Topics in Multivariable Calculus: Surface Integrals, Stokes' Theorem, and Gauss/Divergence Theorem

Ch 6.1: Understanding Vector Fields and Applications in Vector Calculus

Ch 6.2: Advanced Concepts in 2D and 3D Vector Fields

Ch 6.3: Exploring the Del Operator, Divergence, and Curl in 2D Vector Fields

Ch 6.4: Applications of Line Integrals in Calculus

Ch 6.5: The Fundamental Theorem of Line Integrals and Potential Functions

Ch 6.6: Green’s Theorem and Its Applications in Vector Calculus

Ch 6.7: Understanding Divergence and Curl in 3D Vector Fields

Ch 6.8: Exploring Parametric Surfaces and Surface Area in 3D Calculus

Ch 6.9: Surface Integrals in 3D Calculus: Concepts and Applications

Ch 6.10: Exploring Stokes' Theorem and Its Applications in 3D Calculus

Ch 6.11: Understanding the Gauss/Divergence Theorem in 3D Calculus

Summary of Chapter 6

About this course

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