Videos to Accompany Thomas Calculus 11th Edition

Chapter 1: Functions

1.1 Part 1: Functions

1.1 Part 2: Graphs of Basic Functions

1.2 Part 1: Linear Functions, Slope, and Applications

1.2 Part 2: More on Functions

1.2 Part 3: Symmetry and Transformations

1.3 Part 1: Function Operations and Composition Shifting and Scaling Graphs

1.3 Part 2: Shifting and Scaling Graphs

1.5 and 1.6 Exponential Functions; Inverse Functions and Logarithms

Chapter 2: Limits and Continuity

2.2 Calculating Limits Using the Limit Laws

2.3 The Precise Definition of a Limit

2.4 One-Sided Limits and Limits at Infinity

2.5 Infinite Limits and Vertical Asymptotes

2.6 Continuity

2.7 Tangents and Derivatives

Chapter 3: Differentiation

3.1 The Derivative as a Function

3.2 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients

3.3 The Derivative as a Rate of Change

3.4 Derivatives of Trigonometric Functions

3.5 The Chain Rule and Parametric Equations

3.6 Implicit Differentiation

3.7 Derivatives of Inverse Functions and Logarithms

3.8 Inverse Trigonometric Functions

3.9 Related Rates

3.10 Linearization and Differentials

Chapter 4: Applications of Derivatives

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.5 Applied Optimization Problems

4.6 Indeterminate Forms and L'Hôpital's Rule

4.7 Newton's Method

Chapter 5: Integration

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Rule

5.6 Substitution and Area Between Curves

Chapter 6: Applications of Definite Integrals

6.1 and 6.3 Volumes by Slicing and Rotation About an Axis; Lengths of Plane Curves

6.2 Volumes by Cylindrical Shells

6.4 Moments and Centers of Mass

6.5 Areas of Surfaces of Revolution and the Theorems of Pappus

6.6 Work

6.7 Fluid Pressures and Forces

Chapter 7: Integrals and Transcendental Functions

7.1 The Logarithm Defined as an Integral

7.4 Hyperbolic Functions

Chapter 8: Techniques of Integration

8.2 Integration by Parts

8.4 Trigonometric Integrals

8.5 Trigonometric Substitutions

8.7 Numerical Integration

Chapter 9: Further Applications of Integration

9.1 Slope Fields and Separable Differential Equations

9.2 First-Order Linear Differential Equations

9.3 and 9.5 Euler's Method; Applications of First-Order Differential Equations

Chapter 11: Infinite Sequences and Series

11.1 and 11.2 Sequences; Infinite Series

11.7 and 11.8 and 11.9 Power Series; Taylor and Maclaurin Series; Convergence of Taylor Series; Error Estimates

Chapter 12: Vectors and the Geometry of Space

12.1 - 12.5 Three-Dimensional Coordinate Systems; Vectors (Part 1); The Dot Product (Part 1); The Cross Product; Lines and Planes in Space

12.2 and 12.3 Vectors (Part 2); The Dot Product (Part 2)

Chapter 13: Vector-Valued Functions and Motion in Space

13.1 Vector Functions

13.2 Modeling Projectile Motion

13.3 - 13.5 Arc Length and the Unit Tangent Vector T; Curvature and the Unit Normal Vector N; Torsion and the Unit Binormal Vector B

Chapter 14: Partial Derivatives

14.1 - 14.3 Functions of Several Variables; Limits and Continuity in Higher Dimensions; Partial Derivatives

14.4 - 14.6 The Chain Rule; Directional Derivatives and Gradient Vectors; Tangent Planes and Differentials

14.7 and 14.8 Extreme Values and Saddle Points; Lagrange Multipliers

Chapter 15: Multiple Integrals

15.1 Double Integrals

Chapter 16: Integration in Vector Fields

16.1 and 16.2 Line Integrals; Vector Fields, Work, Circulation, and Flux