| 1.1.1. | Integrating Algebraic Functions Using Substitution | |
| 1.1.2. | Integrating Linear Rational Functions Using Substitution | |
| 1.1.3. | Integration Using Substitution | |
| 1.1.4. | Calculating Definite Integrals Using Substitution | |
| 1.1.5. | Further Integration of Algebraic Functions Using Substitution | |
| 1.1.6. | Integrating Exponential Functions Using Linear Substitution | |
| 1.1.7. | Integrating Exponential Functions Using Substitution | |
| 1.1.8. | Integrating Trigonometric Functions Using Substitution | |
| 1.1.9. | Integrating Logarithmic Functions Using Substitution | |
| 1.1.10. | Integration by Substitution With Inverse Trigonometric Functions | |
| 1.1.11. | Integrating Hyperbolic Functions Using Substitution | |
| 1.1.12. | Integration by Substitution With Inverse Hyperbolic Functions | |
| 1.1.13. | Integration by Substitution With Inverse Reciprocal Hyperbolic Functions |
| 1.2.1. | Integrating Functions Using Polynomial Division | |
| 1.2.2. | Integrating Functions by Completing the Square | |
| 1.2.3. | Integration Using Hyperbolic Functions and Completing the Square | |
| 1.2.4. | Integration Using Inverse Reciprocal Hyperbolic Functions and Completing the Square |
| 1.3.1. | Integration Using Basic Trigonometric Identities | |
| 1.3.2. | Integration Using the Pythagorean Identities | |
| 1.3.3. | Integration Using the Double Angle Formulas |
| 1.4.1. | Integration Using Basic Hyperbolic Identities | |
| 1.4.2. | Integration Using the Hyperbolic Pythagorean Identities | |
| 1.4.3. | Integration Using the Hyperbolic Double Angle Formulas |
| 1.5.1. | Introduction to Integration by Parts | |
| 1.5.2. | Using Integration by Parts to Calculate Integrals With Logarithms | |
| 1.5.3. | Applying the Integration By Parts Formula Twice | |
| 1.5.4. | The Tabular Method of Integration by Parts | |
| 1.5.5. | Integration by Parts in Cyclic Cases |
| 1.6.1. | Expressing Rational Functions as Sums of Partial Fractions | |
| 1.6.2. | Expressing Rational Functions with Repeated Factors as Sums of Partial Fractions | |
| 1.6.3. | Expressing Rational Functions with Irreducible Quadratic Factors as Sums of Partial Fractions | |
| 1.6.4. | Integrating Rational Functions Using Partial Fractions | |
| 1.6.5. | Integrating Rational Functions with Repeated Factors | |
| 1.6.6. | Integrating Rational Functions with Irreducible Quadratic Factors |
| 1.7.1. | Improper Integrals | |
| 1.7.2. | Improper Integrals Involving Exponential Functions | |
| 1.7.3. | Improper Integrals Involving Arctangent | |
| 1.7.4. | Improper Integrals Over the Real Line | |
| 1.7.5. | Improper Integrals of the Second Kind | |
| 1.7.6. | Improper Integrals of the Second Kind: Discontinuities at Interior Points |
| 2.8.1. | Integrating Rates of Change | |
| 2.8.2. | Integrating Density Functions | |
| 2.8.3. | The Average Value of a Function | |
| 2.8.4. | The Area Between Curves Expressed as Functions of X | |
| 2.8.5. | The Area Between Curves Expressed as Functions of Y | |
| 2.8.6. | Finding Areas Between Curves that Intersect at More Than Two Points | |
| 2.8.7. | The Arc Length of a Smooth Planar Curve |
| 2.9.1. | Volumes of Solids with Square Cross Sections | |
| 2.9.2. | Volumes of Solids with Rectangular Cross Sections | |
| 2.9.3. | Volumes of Solids with Triangular Cross Sections | |
| 2.9.4. | Volumes of Solids with Circular Cross Sections |
| 2.10.1. | Volumes of Revolution Using the Disc Method: Rotation About the Coordinate Axes | |
| 2.10.2. | Volumes of Revolution Using the Disc Method: Rotation About Other Axes | |
| 2.10.3. | Volumes of Revolution Using the Washer Method: Rotation About the Coordinate Axes | |
| 2.10.4. | Volumes of Revolution Using the Washer Method: Rotation About Other Axes | |
| 2.10.5. | The Shell Method: Rotating a Region About the X-Axis | |
| 2.10.6. | The Shell Method: Rotating a Region Between Two Curves About the X-Axis | |
| 2.10.7. | The Shell Method: Rotation About the Y-Axis |
| 2.11.1. | Surface Areas of Revolution: Rotation About the X-Axis | |
| 2.11.2. | Surface Areas of Revolution: Rotation About the Y-Axis | |
| 2.11.3. | Calculating Surface Areas of Revolution for Parametric Curves |
| 2.12.1. | Calculating Velocity Using Integration | |
| 2.12.2. | Determining Characteristics of Moving Objects Using Integration | |
| 2.12.3. | Calculating the Position Function of a Particle Using Integration | |
| 2.12.4. | Calculating the Displacement of a Particle Using Integration | |
| 2.12.5. | Calculating the Total Distance Traveled by a Particle | |
| 2.12.6. | Average Position, Velocity, and Acceleration |
| 3.13.1. | Defining and Differentiating Parametric Equations | |
| 3.13.2. | Calculating Tangent and Normal Lines with Parametric Equations | |
| 3.13.3. | Second Derivatives of Parametric Equations | |
| 3.13.4. | Finding the Arc Lengths of Curves Given by Parametric Equations | |
| 3.13.5. | Calculating Areas Bounded by Parametric Functions | |
| 3.13.6. | Further Calculating Areas Bounded by Parametric Functions |
| 3.14.1. | Defining and Differentiating Vector-Valued Functions | |
| 3.14.2. | Integrating Vector-Valued Functions |
| 3.15.1. | Calculating Velocity for Plane Motion Using Differentiation | |
| 3.15.2. | Calculating Acceleration for Plane Motion Using Differentiation | |
| 3.15.3. | Finding Velocity Vectors in Two Dimensions Using Integration | |
| 3.15.4. | Finding Displacement Vectors in Two Dimensions Using Integration | |
| 3.15.5. | Applying Newton's Second Law in the Coordinate Plane |
| 3.16.1. | Differentiating Curves Given in Polar Form | |
| 3.16.2. | Further Differentiation of Curves Given in Polar Form | |
| 3.16.3. | Horizontal and Vertical Tangents to Polar Curves | |
| 3.16.4. | Horizontal and Vertical Tangents to Polar Curves in Non-Differentiable Cases | |
| 3.16.5. | Tangent and Normal Lines to Polar Curves | |
| 3.16.6. | Finding the Area of a Polar Region | |
| 3.16.7. | Finding the Limits of Integration For a Given Polar Region | |
| 3.16.8. | The Total Area Bounded by a Single Polar Curve | |
| 3.16.9. | The Area Bounded by Two Polar Curves | |
| 3.16.10. | The Arc Length of a Polar Curve |
| 4.17.1. | Limits of Sequences | |
| 4.17.2. | Convergence of Geometric Sequences | |
| 4.17.3. | Further Convergence of Geometric Sequences | |
| 4.17.4. | Limits of Sequences With Factorials | |
| 4.17.5. | Determining Limits of Sequences Using Relative Magnitudes | |
| 4.17.6. | Further Determining Limits of Sequences Using Relative Magnitudes |
| 4.18.1. | Monotonic Sequences | |
| 4.18.2. | Identifying Monotonic Sequences Using Differentiation | |
| 4.18.3. | Identifying Monotonic Sequences Using Ratios |
| 4.19.1. | Infinite Series and Partial Sums | |
| 4.19.2. | Convergent and Divergent Infinite Series | |
| 4.19.3. | Properties of Infinite Series | |
| 4.19.4. | Telescoping Series |
| 4.20.1. | Finding the Sum of an Infinite Geometric Series | |
| 4.20.2. | Writing an Infinite Geometric Series in Sigma Notation | |
| 4.20.3. | Finding the Sum of an Infinite Geometric Series Expressed in Sigma Notation | |
| 4.20.4. | Convergence of Geometric Series | |
| 4.20.5. | Repeating Decimals as Infinite Geometric Series |
| 4.21.1. | The Nth Term Test for Divergence | |
| 4.21.2. | The Integral Test | |
| 4.21.3. | The Remainder Estimate for the Integral Test | |
| 4.21.4. | Harmonic Series and p-Series | |
| 4.21.5. | The Comparison Test | |
| 4.21.6. | The Limit Comparison Test | |
| 4.21.7. | The Alternating Series Test | |
| 4.21.8. | The Ratio Test | |
| 4.21.9. | The Root Test | |
| 4.21.10. | Absolute and Conditional Convergence | |
| 4.21.11. | The Alternating Series Error Bound | |
| 4.21.12. | Determining Convergence Parameters for Infinite Series | |
| 4.21.13. | Selecting Procedures for Analyzing Infinite Series |
| 4.22.1. | Second-Degree Taylor Polynomials | |
| 4.22.2. | Analyzing Second-Degree Taylor Polynomials | |
| 4.22.3. | Third-Degree Taylor Polynomials | |
| 4.22.4. | Higher-Degree Taylor Polynomials | |
| 4.22.5. | The Lagrange Error Bound |
| 4.23.1. | Radius of Convergence of Power Series Centered at the Origin | |
| 4.23.2. | Radius of Convergence of Power Series | |
| 4.23.3. | Maclaurin Series | |
| 4.23.4. | Taylor Series | |
| 4.23.5. | Representing Functions as Power Series | |
| 4.23.6. | Recognizing Standard Maclaurin Series | |
| 4.23.7. | Recognizing Standard Maclaurin Series for Trigonometric Functions | |
| 4.23.8. | Differentiating Taylor Series | |
| 4.23.9. | Approximating Integrals Using Taylor Series |
| 5.24.1. | Introduction to Differential Equations | |
| 5.24.2. | Verifying Solutions of Differential Equations | |
| 5.24.3. | Solving Differential Equations Using Direct Integration | |
| 5.24.4. | Solving First-Order ODEs Using Separation of Variables | |
| 5.24.5. | Solving Initial Value Problems Using Separation of Variables | |
| 5.24.6. | Modeling With Differential Equations | |
| 5.24.7. | Further Modeling With Differential Equations |
| 5.25.1. | Qualitative Analysis of Differential Equations | |
| 5.25.2. | Equilibrium Solutions of Differential Equations |
| 5.26.1. | Exponential Growth and Decay Models With Differential Equations | |
| 5.26.2. | Exponential Growth and Decay Models With Differential Equations: Calculating Unknown Times and Initial Values | |
| 5.26.3. | Exponential Growth and Decay Models With Differential Equations: Half-Life Problems |
| 5.27.1. | Logistic Growth Models With Differential Equations | |
| 5.27.2. | Qualitative Analysis of the Logistic Growth Equation | |
| 5.27.3. | Solving the Logistic Growth Equation |
| 5.28.1. | Slope Fields for Directly Integrable Differential Equations | |
| 5.28.2. | Slope Fields for Autonomous Differential Equations | |
| 5.28.3. | Slope Fields for Nonautonomous Differential Equations | |
| 5.28.4. | Analyzing Slope Fields for Directly Integrable Differential Equations | |
| 5.28.5. | Analyzing Slope Fields for Autonomous Differential Equations | |
| 5.28.6. | Analyzing Slope Fields for Nonautonomous Differential Equations |
| 5.29.1. | Euler's Method: Calculating One Step | |
| 5.29.2. | Euler's Method: Calculating Multiple Steps |
