Maths 265: Calculus II

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
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1. VIDEOS
2. Using Tables to Find Antiderivatives
3. Quiz 1.2
1. Introduction
1. VIDEOS
2. First Applications of Definite Integrals
3. Quiz 1.1
1. VIDEOS
2. Approximating Definite Integrals
3. Quiz 1.3
1. Introduction
1. Introduction to Applications
2. Quiz 2.1
1. VIDEOS
2. Volumes
3. Quiz 2.2
1. VIDEOS
2. Arc Lengths & Surface Areas
3. Quiz 2.3
1. VIDEOS
2. Moments & Centers of Mass
3. Quiz 2.4
1. VIDEOS
2. Additional Applications
3. Quiz 2.5
1. Summary
1. Introduction
1. VIDEOS
2. Introduction to Differential Equations
3. Quiz 3.1
1. VIDEOS
2. Differential Equation y'=f(x)
3. Quiz 3.2
1. VIDEOS
2. Separable Differential Equations
3. Quiz 3.3
1. VIDEOS
2. Exponential Growth, Decay & Cooling
3. Quiz 3.4
1. Summary
1. Introduction
1. Introduction Improper Integrals & Integration Techniques
2. Quiz 4.1
1. VIDEOS
2. Improper Integrals
3. Quiz 4.2
1. VIDEOS
2. Integration Review
3. Quiz 4.3
1. VIDEOS
2. Integration by Parts
3. Quiz 4.4
1. VIDEOS
2. Partial Fraction Decomposition
3. Quiz 4.5
1. VIDEOS
2. Trigonometric Substitution
3. Quiz 4.6
1. VIDEOS
2. Trigonometric Integrals
3. Quiz 4.7
1. Summary
1. Introduction
1. Introduction to Sequences & Series
2. Quiz 5.1
1. VIDEOS
2. Sequences
3. Quiz 5.2
1. VIDEOS
2. Infinite Series
3. Quiz 5.3
1. VIDEOS
2. Geometric and Harmonic Series
3. Quiz 5.4
1. VIDEOS
2. Positive Term Series: Integral & P-Tests
3. Quiz 5.5
1. VIDEOS
2. Positive Term Series: Comparison Tests
3. Quiz 5.6
1. VIDEOS
2. Alternating Sign Series
3. Quiz 5.7
1. VIDEOS
2. Absolute Convergence and the Ratio Test
3. Quiz 5.8
1. VIDEOS
2. Power Series
3. Quiz 5.9
1. VIDEOS
2. Taylor and Maclaurin Series
3. Quiz 5.10
1. Fourier Series
2. Quiz 5.11
1. Summary
1. Introduction
1. Moving Beyond Two Dimensions
2. Quiz 6.1
1. VIDEOS
2. Vectors in the Plane
3. Quiz 6.2
1. VIDEOS
2. Rectangular Coordinates in Three Dimensions
3. Quiz 6.3
1. VIDEOS
2. Vectors in Three Dimensions
3. Quiz 6.4
1. VIDEOS
2. Dot Product
3. Quiz 6.5
1. VIDEOS
2. Cross Product
3. Quiz 6.6
1. VIDEOS
2. Lines and Planes in Three Dimensions
3. Quiz 6.7
1. Vector Reflections
2. Quiz 6.8
1. Summary
1. Introduction
1. VIDEOS
2. Vector-Valued Functions and Curves in Space
3. Quiz 7.1
1. VIDEOS
2. Derivatives & Antiderivatives of Vector-Valued Functions
3. Quiz 7.2
1. VIDEOS
2. Arc Length and Curvature of Space Curves
3. Quiz 7.3
1. VIDEOS
2. Cylindrical & Spherical Coordinate Systems in 3D
3. Quiz 7.4
1. Summary
1. Introduction
1. VIDEOS
2. Functions of Two or More Variables
3. Quiz 8.1
1. VIDEOS
2. Limits and Continuity
3. Quiz 8.2
1. VIDEOS
2. Partial Derivatives
3. Quiz 8.3
1. VIDEOS
2. Tangent Planes and Differentials
3. Quiz 8.4
1. VIDEOS
2. Directional Derivatives and the Gradient
3. Quiz 8.5
1. VIDEOS
2. Maximums and Minimums
3. Quiz 8.6
1. VIDEOS
2. Lagrange Multiplier Method
3. Quiz 8.7
1. VIDEOS
2. Chain Rule
3. Quiz 8.8
1. Summary
1. Introduction
1. VIDEOS
2. Introduction to Double Integrals
3. Quiz 9.1
1. VIDEOS
2. Double Integrals over Rectangular Domains
3. Quiz 9.2
1. VIDEOS
2. Double Integrals over General Domains
3. Quiz 9.3
1. VIDEOS
2. Double Integrals in Polar Coordinates
3. Quiz 9.4
1. Applications of Double Integrals
2. Quiz 9.5
1. Surface Area
2. Quiz 9.6
1. VIDEOS
2. Triple Integrals and Applications
3. Quiz 9.7
1. VIDEOS
2. Triple Integrals in Cylindrical and Spherical Coordinates
3. Quiz 9.8
1. VIDEOS
2. Changing Variables in Double and Triple Integrals
3. Quiz 9.9
1. Summary
1. Introduction
1. Introduction to Vector Calculus
2. Quiz 10.1
1. VIDEOS
2. Vector Fields
3. Quiz 10.2
1. VIDEOS
2. Divergence, Curl and Del in 2D
3. Quiz 10.3
1. VIDEOS
2. Line Integrals
3. Quiz 10.4
1. VIDEOS
2. Fundamental Theorem of Line Integrals and Potential Functions
3. Quiz 10.5
1. VIDEOS
2. Green's Theorem
3. Quiz 10.6
1. VIDEOS
2. Divergence and Curl in 3D
3. Quiz 10.7
1. VIDEOS
2. Parametric Surfaces
3. Quiz 10.8
1. VIDEOS
2. Surface Integrals
3. Quiz 10.9
1. VIDEOS
2. Stokes' Theorem
3. Quiz 10.10
1. VIDEOS
2. Gauss/Divergence Theorem
3. Quiz 10.11
1. Summary
1. Introduction
1. VIDEOS
2. Polar Coordinates
3. Quiz 11.1
1. VIDEOS
2. Calculus with Polar Coordinates
3. QUIZ 11.2
1. VIDEOS
2. Parametric Equations
3. QUIZ 11.3
1. VIDEOS
2. Calculus with Parametric Equations
3. QUIZ 11.4
1. VIDEOS
2. Conic Sections
3. QUIZ 11.5
1. VIDEOS
2. Properties of the Conic Sections
3. QUIZ 11.6
1. Summary
1. Assignment
2. Rubric for Assignment
1. Final Exam Instructions
2. Final Exam

About this course

245 lessons
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Math 265: Calculus 2

Ch 1.2: Advanced Techniques for Finding Antiderivatives Using Tables

Chapter 1: The Integral

Ch 1.1: Advanced Applications of Definite Integrals in Physics and Engineering

Ch 1.3: Advanced Techniques for Approximating Definite Integrals

Chapter 2: Comprehensive Overview of Definite Integrals: Concepts, Applications, and Approximation Methods

Ch 2.1: Introduction to Applications of Definite Integrals

Ch 2.2: Calculating Volumes of Solids Using Definite Integrals

Ch 2.3: Arc Length and Surface Area of Revolution in Calculus

Ch 2.4: Moments and Centers of Mass in Calculus

Ch 2.5: Advanced Applications of Integrals in Physical and Social Contexts

Summary of Chapter 2

Chapter 3: Introduction to Differential Equations: Solving, Applications, and Real-World Modeling

Ch 3.1: Introduction to Differential Equations and Their Applications

Ch 3.2: Solving Differential Equations and Direction Fields

Ch 3.3: Understanding and Solving Separable Differential Equations

Ch 3.4: Applications of Growth, Decay, and Cooling Models

Summary of Chapter 3

CHAPTER 4: Partial Fractions, Trigonometric Substitution, and Trigonometric Integrals

Ch 4.1: Introduction to Improper Integrals and Advanced Integration Techniques

Ch 4.2: Exploring Improper Integrals and Techniques for Evaluating Infinite and Unbounded Integrals

Ch 4.3: Reviewing Antiderivatives and Techniques for Complex Integration

Ch 4.4: Mastering Integration by Parts: Techniques, Examples, and Practice

Ch 4.5: Partial Fraction Decomposition: Techniques, Applications, and Practice

Ch 4.6: Trigonometric Substitution: Techniques, Examples, and Problem Solving

Ch 4.7: Integrals of Trigonometric Functions: Techniques, Identities, and Problem Solving

Summary of Chapter 4

CHAPTER 5: Comprehensive Overview of Series in Calculus: Power, Taylor, Maclaurin, and Fourier Series

Ch 5.1: Exploration of Sequences and Series in Contemporary Calculus

Ch 5.2: In-depth Exploration of Sequences: Convergence, Monotonicity, and Recurrence

Ch 5.3: Understanding and Analyzing Infinite Series in Calculus

Ch 5.4: Exploring Geometric and Harmonic Series in Calculus

Ch 5.5: Integral Test and P–Test for Series Convergence

Ch 5.6: Positive Term Series: Comparison Tests and Limit Comparison Tests

Ch 5.7: Alternating Series: Definition, Test, and Applications

Ch 5.8: Absolute Convergence, Conditional Convergence, and the Ratio Test

Ch 5.9: Power Series, Interval of Convergence, and Radius of Convergence

Ch 5.10: Taylor and Maclaurin Series: Theory, Applications, and Problem-Solving

Ch 5.11: Introduction to Fourier Series: Theory, Applications, and Computational Methods

Summary of Chapter 5

CHAPTER 6: Understanding Lines, Planes, and Vector Reflections in Three Dimensions

Ch 6.1: Introduction to Higher Dimensions in Calculus

Ch 6.2: Vectors in the Plane: Concepts, Operations, and Applications

Ch 6.3: Rectangular Coordinates in Three Dimensions: Concepts and Applications

Ch 6.4: Vectors in Three Dimensions: Concepts and Calculations

Ch 6.5: Dot Product and Its Applications in Vector Calculations

Ch 6.6: Cross Product and Its Applications in Vector Calculations

Ch 6.7: Lines and Planes in Three Dimensions: Equations, Intersections, and Distances

Ch 6.8: Vector Reflections: Understanding Reflections in 2D and 3D Space

Summary of Chapter 6

CHAPTER 7: Exploring Advanced Coordinate Systems: Arc Length, Curvature, and Coordinate Transformations

Ch 7.1: Understanding Vector-Valued Functions and Their Applications in 3D Space

Ch 7.2: Derivatives and Antiderivatives of Vector-Valued Functions in 3D Space

Ch 7.3: Arc Length and Curvature of Space Curves in Calculus

Ch 7.4: Understanding Cylindrical and Spherical Coordinate Systems in 3D Space

Summary of Chapter 7

CHAPTER 8 : Advanced Calculus: Applications of Derivatives in Multiple Variables

Ch 8.1: Functions of Several Variables: Definitions, Tables, and Graphical Representations

Ch 8.2: Limits and Continuity of Multivariable Functions: Definitions, Calculations, and Applications

Ch 8.3: Partial Derivatives: Definitions, Calculations, and Applications

Ch 8.4: Tangent Planes and Differentials: Concepts, Calculations, and Applications

Ch 8.5: Directional Derivatives and Gradient Vector: Advanced Concepts and Applications

Ch 8.6: Advanced Concepts in Finding Maximums and Minimums: Methods and Applications

Ch 8.7: Advanced Applications of Lagrange Multipliers in Optimization Problems

Ch 8.8: Advanced Chain Rule Applications for Functions of Several Variables

Summary of Chapter 8

CHAPTER 9: Advanced Techniques in Multivariable Calculus: Surface Areas, Triple Integrals, and Variable Transformations

Ch 9.1: Introduction to Double Integrals: Concepts, Approximations, and Applications

Ch 9.2: Double Integrals Over Rectangles: Theory, Computation, and Applications

Ch 9.3: Double Integrals Over General Regions: Theory, Methods, and Practical Applications

Ch 9.4: Double Integrals in Polar Coordinates: Concepts, Computations, and Applications

Ch 9.5: Applications of Double Integrals in Mass, Moments, and Center of Mass Calculations

Ch 9.6: Surface Areas Using Double Integrals

Ch 9.7: Triple Integrals and Their Applications

Ch 9.8: Triple Integrals in Cylindrical and Spherical Coordinates

Ch 9.9: Changing Variables in Double and Triple Integrals

Summary of Chapter 9

CHAPTER 10: Advanced Topics in Multivariable Calculus: Surface Integrals, Stokes' Theorem, and Gauss/Divergence Theorem

Ch 10.1: Understanding Vector Fields and Applications in Vector Calculus

Ch 10.2: Advanced Concepts in 2D and 3D Vector Fields