Important Files
| AB Files |
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| Course Schedules |
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| Projects |
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| Gateway Exams |
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| BC Files |
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| Course Schedules |
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| Projects |
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| Gateway Exams |
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Note: Topics that are BC-only are highlighted in yellow.
| Summer Homework |
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| Prerequisite Content (Problems and Solutions) |
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| Precalculus Review (Problems and Solutions) |
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| Chapter 1: Limits and Their Properties |
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| §1.2 Finding Limits Graphically and Numerically |
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| §1.3 Evaluating Limits Analytically |
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| §1.4 Continuity and One-Sided Limits |
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| §1.5 Infinite Limits |
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| §1.6 Limits at Infinity |
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| Chapter 2: Differentiation |
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| §2.1 The Derivative and the Tangent Line Problem |
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| §2.2 Basic Differentiation Rules and Rates of Change |
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| §2.3 Product and Quotient Rules and Higher-Order Derivatives |
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| §2.4a The Chain Rule |
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| §2.4b The Chain Rule |
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| §2.5 Implicit Differentiation |
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| §2.6 Derivatives of Inverse Functions |
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| §2.7 Related Rates |
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| Chapter 3: Applications of Differentiation |
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| §3.1 Extrema on an Interval |
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| §3.2 Rolle's Theorem and the Mean Value Theorem |
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| §3.3a Increasing and Decreasing Functions |
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| §3.3b The First Derivative Test |
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| §3.4a Concavity |
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| §3.4b The Second Derivative Test |
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| §3.5 A Summary of Curve Sketching |
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| §3.6 Optimization Problems |
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| Chapter 4: Integration |
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| §4.1 Antiderivatives and Indefinite Integration |
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| §4.3a Riemann Sums and Trapezoidal Approximations |
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| §4.3b Properties of Definite Integrals |
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| §4.4a The First Fundamental Theorem of Calculus |
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| §4.4b The Second Fundamental Theorem of Calculus |
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| §4.4c The Net Change Theorem |
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| §4.5 Integration by Substitution |
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| §4.6 The Natural Logarithmic Function: Integration |
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| §4.7 Inverse Trigonometric Functions: Integration |
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| Chapter 5: Differential Equations |
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| §5.1a Slope Fields |
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| §5.1b Euler's Method |
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| §5.3 Separation of Variables |
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| §5.4 The Logistic Equation |
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| Chapter 6: Applications of Integration |
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| §6.1 Area of a Region Between Two Curves |
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| §6.2a Volume: The Disk and Washer Methods |
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| §6.2b Volume: Solids with Known Cross Sections |
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| §6.4 Arc Length |
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| Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals |
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| §7.1 Basic Integration Rules |
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| §7.2 Integration by Parts |
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| §7.5 Partial Fractions |
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| §7.7 Indeterminate Forms and L'Hôpital's Rule |
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| §7.8 Improper Integrals |
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| Chapter 8: Taylor Polynomials and Infinite Series |
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| §8.1 Review of Sequences and Series |
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| §8.2 An Introduction to Taylor Polynomials |
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| §8.3 A Systematic Approach to Taylor Polynomials |
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| §8.4 Lagrange Remainder |
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| §8.6 Power Series and the Ratio Test |
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| §8.7a The Integral Test and p-Series |
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| §8.7b The Direct and Limit Comparison Tests |
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| §8.8a Alternating Series |
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| §8.8b Varying-Sign Series |
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| §8.10a Taylor Series |
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| §8.10b Manipulation of Known Taylor Series |
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| Chapter Text by B. Goldstein |
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| Chapter 9a: Polar Coordinates |
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| §9.4a Polar Coordinates and Polar Graphs |
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| §9.4b Polar Coordinates and Differentiation |
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| §9.5 Area in Polar Coordinates |
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| Chapter 9b: Parametric Equations and Vectors |
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| §9.2 Plane Curves and Parametric Equations |
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| §9.3 Parametric Equations and Calculus |
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| §9.7 Vector-Valued Functions |
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| §9.8 Velocity and Acceleration |
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The files below have not yet been updated for the 2018-2019 school year.
| Chapter 2: Differentiation |
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| §2.5 Implicit Differentiation |
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| §2.6 Derivatives of Inverse Functions |
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| §2.7 Related Rates |
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| Chapter 2 Homework (Problems and Solutions) |
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| Chapter 3: Applications of Differentiation |
Notes |
Vids |
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| §3.1 Extrema on an Interval |
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| §3.2 Rolle's Theorem and the Mean Value Theorem |
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| §3.3a Increasing and Decreasing Functions |
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| §3.3b The First Derivative Test |
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| §3.4a Concavity |
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| §3.4b The Second Derivative Test |
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| §3.5 A Summary of Curve Sketching |
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| §3.6 Optimization Problems |
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| Chapter 3 Homework (Problems and Solutions) |
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| Chapter 4: Integration |
Notes |
Vids |
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| §4.1 Antiderivatives and Indefinite Integration |
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| §4.3 Riemann Sums and Definite Integrals |
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| §4.4a The First Fundamental Theorem of Calculus |
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| §4.4b The Second Fundamental Theorem of Calculus |
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| §4.4c The Net Change Theorem |
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| §4.5 Integration by Substitution |
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| §4.6 The Natural Logarithmic Function: Integration |
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| §4.7 Inverse Trigonometric Functions: Integration |
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| Chapter 4 Homework (Problems and Solutions) |
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| Chapter 5: Differential Equations |
Notes |
Vids |
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| §5.1a Slope Fields |
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| §5.1b Euler's Method |
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| §5.3 Separation of Variables |
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| §5.4 The Logistic Equation |
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| Chapter 5 Homework (Problems and Solutions) |
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| Chapter 6: Applications of Integration |
Notes |
Vids |
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| §6.1 Area of a Region Between Two Curves |
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| §6.2a Volume: The Disk and Washer Methods |
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| §6.2b Volume: Solids with Known Cross Sections |
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| §6.4 Arc Length |
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| Chapter 6 Homework (Problems and Solutions) |
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| Chapter 7: Integration Techniques, L'Hôpital's Rule, and Improper Integrals |
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Vids |
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| §7.1 Basic Integration Rules |
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| §7.2 Integration by Parts |
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| §7.5 Partial Fractions |
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| §7.7 Indeterminate Forms and L'Hôpital's Rule |
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| §7.8 Improper Integrals |
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| Chapter 7 Homework (Problems and Solutions) |
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| Chapter 8: Taylor Polynomials and Infinite Series |
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Vids |
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| §8.1 Review of Sequences and Series |
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| §8.2 An Introduction to Taylor Polynomials |
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| §8.3 A Systematic Approach to Taylor Polynomials |
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| §8.4 Lagrange Remainder |
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| §8.6 Power Series and the Ratio Test |
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| §8.7a Positive-Term Series |
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| §8.7b Positive-Term Series |
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| §8.8a Varying-Sign Series |
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| §8.8b Varying-Sign Series |
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| §8.10a Taylor Series |
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| §8.10b Taylor Series |
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| Chapter 8 Homework (Textbook, Problems, and Solutions) |
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| Chapter 9a: Polar Coordinates |
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| §9.4a Polar Coordinates and Polar Graphs (Desmos Activity) |
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| §9.4b Polar Coordinates and Differentiation |
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| §9.5 Area in Polar Coordinates |
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| Chapter 9a Homework (Problems and Solutions) |
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| Chapter 9b: Parametric Equations and Vectors |
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| §9.2 Plane Curves and Parametric Equations |
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| §9.3 Parametric Equations and Calculus |
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| §9.7 Vector-Valued Functions |
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| §9.8 Velocity and Acceleration |
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| Chapter 9b Homework (Problems and Solutions) |
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