* * * Updated for 2020-2021 school year * * *
Course Syllabus and Standards
Important Files
Important Links for Videos
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Course Schedules |
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Gateway Exams |
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BC Files |
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Course Schedules |
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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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Summer Homework (Letter and Instructions) |
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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 and Solutions 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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