Numbering approximately corresponds to James Stewart, Calculus, 6th ed. (Belmont, CA: Thompson, 2008).
Chapter 1: Functions
1.1 What is a function?
1.2 Types of functions
1.3 Transforming functions
Chapter 2: Limits
2.1 The Tangent Problem (the beginning of Differential Calculus)
2.2a What is a Limit?
2.2b Right and Left Hand Limits
2.3a Limit Laws
2.3b The Squeeze Theorem
2.4 The Precise Definition of a Limit
2.5 Limits and Continuity
Chapter 3: Derivatives
3.1 What is a Derivative?
3.2 The Power Rule (also Constant Rule, Sum Rule, Difference Rule)
3.3 The Product and Quotient Rule
3.4 Derivatives of Trig Functions
3.5 The Chain Rule
3.6 Implicit Differentiation
Chapter 4: Applications of Differentiation
4.1 Maximum and Minimum Values
4.2 The Mean Value Theorem
4.3 Derivative Tests
4.4 Infinite Limits
4.5 Summary of Sketching Graphs
4.6 Optimization Problems (including First Derivative Test, business functions)
4.7 Newton's Method
4.8 Antiderivatives
Chapter 5: Integral Calculus
5.1 The Area Problem (beginning of Integral Calculus)
5.2 The Definite Integral
5.3 The Fundamental Theorem of Calculus
5.4a Indefinite Integrals
5.4b Some Basic Indefinite Integral Formulas
5.4c Net Change Theorem
5.5a The Substitution Method (for indefinite integrals)
5.5b The Substitution Method (for definite integrals)
Chapter 6: Applications of Integration
6.1 Areas Between Curves
6.2 Volumes
6.3 Volume by Cylindrical Shell
6.4 Work (see also the physics video on work)
6.5 Average Value of a Function
Chapter 7: Inverse Functions
7.1 Introduction to Inverse Functions
Approach 1 to Logarithmic and Exponential Functions (from more intuitive perspective)
7.2a Review of Exponential Functions
7.2b Natural Exponential Function e^x
7.3 Logarithmic Functions (including natural log)
7.4a Derivatives of Natural Log Functions
7.2a Review of Exponential Functions
7.2b Natural Exponential Function e^x
7.3 Logarithmic Functions (including natural log)
7.4a Derivatives of Natural Log Functions
7.4c Logarithmic Differentiation (and e as a limit)
Approach 2 to Logarithmic and Exponential Functions (from more rigorous perspective)
Approach 2 to Logarithmic and Exponential Functions (from more rigorous perspective)
7.3a* Defining the Natural Exponential Function (e^x)
7.4b* Four Cases of Derivatives for Bases and Exponents (& proof of power rule)
7.4d* e as a Limit
7.5b Population Growth
7.5c Radioactive Decay
7.5d Newton's Law of Cooling
7.5e Continuously Compounded Interest
7.6 Inverse Trigonometric Functions
7.7 Hyperbolic Functions
7.8 Indeterminate Forms and L'Hospital's Rule
Chapter 8 Techniques of Integration
Chapter 8 Techniques of Integration
8.1a Integration by Parts (introduction)
8.2a Trigonometric Integrals (sine, cosine to an odd power)
8.2b Trigonometric Integrals (sine, cosine to even powers)
8.2c Trigonometric Integrals (secant to even powers with tangent)
8.2d Trigonometric Integrals (tangent to odd power with secant)
8.3a Trigonometric Substitution (using a-sin-theta)
8.3b Trigonometric Substitution (using a-tangent-theta)
8.3c Trigonometric Substitution (using a-sec-theta)
8.4a Integration by Partial Fractions (numerator larger)
8.4b Integration by Partial Fractions (denominator can reduce to linear factors)
8.4c Integration by Partial Fractions (denominator higher power)
8.4d Integration by Partial Fractions (completing the square in denominator)
8.5 Strategies for Integration
8.6 Integration using Formulas
8.7a Approximate Integration (using Left, Right Endpoints and Midpoints)
8.7b Approximate Integration (using the Trapezoidal and Simpson Rules)
8.8a Improper Integrals
8.8b Magnetic Potential u on Axis of Coil Equation
Chapter 9 Further Applications of Integration
9.1 Arc Length (7.4 in Essentials)
9.2 Area of a Surface of Revolution
9.3 Applications to Physics and Engineering
9.4 Applications to Economics and Biology
9.5 Probability
Chapter 10: Differential Equations
10.1 Modeling with Differential Equations
10.2a Slope and Distance Fields
10.2b Euler's Method
13.1 Three Dimensional Coordinate Systems
13.2 Vectors
13.3 The Dot Product (see also this physics version)
13.4 The Cross Product (see also this physics version)
Chapter 10: Differential Equations
10.1 Modeling with Differential Equations
10.2a Slope and Distance Fields
10.2b Euler's Method
Chapter 11: Parametric Equations and Polar Coordinates
11.1 Curves Defined by Parametric Equations
11.2 Calculus with Parametric Curves
11.3 Polar Coordinates
11.4 Areas and Lengths in Polar Coordinates
11.5 Conic Sections
11.6 Conic Sections in Polar Coordinates
Chapter 12: Infinite Sequences and Series (Chapter 8 in Essentials)
12.1 Sequences
12.2 Series
12.3 The Integral Test and Estimates of Sums
12.4 The Comparison Tests
12.5 Alternating Series
12.6 Absolute Convergence and the Ratio and Root Tests
12.7 Strategy for Testing Series
12.8 Power Series
12.9 Representations of Functions as Power Series
12.10 Taylor and Maclaurin Series
12.11 Applications of Taylor Polynomials
12.7
Chapter 13: Vectors and the Geometry of Space13.1 Three Dimensional Coordinate Systems
13.2 Vectors
13.3 The Dot Product (see also this physics version)
13.4 The Cross Product (see also this physics version)
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