Description
Units and Sub-Units
Unit 1 | Limits and Continuity
- 1.1 Introducing Calculus: Instantaneous Change — 20 Qs
- 1.2 Defining Limits & Notation — 20 Qs
- 1.3 Estimating Limits from Graphs — 20 Qs
- 1.4 Estimating Limits from Tables — 20 Qs
- 1.5 Limits via Algebraic Properties — 20 Qs
- 1.6 Limits via Algebraic Manipulation — 40 Qs
- 1.7 Selecting Procedures for Limits — 20 Qs
- 1.8 Squeeze Theorem — 20 Qs
- 1.9 Connecting Multiple Representations — 20 Qs
- 1.10 Types of Discontinuities — 20 Qs
- 1.11 Continuity at a Point — 20 Qs
- 1.12 Continuity on an Interval — 40 Qs
- 1.13 Removing Discontinuities — 20 Qs
- 1.14 Infinite Limits & Vertical Asymptotes — 20 Qs
- 1.15 Limits at Infinity & Horizontal Asymptotes — 50 Qs
- 1.16 Intermediate Value Theorem (IVT) — 20 Qs
Unit 2 | Differentiation: Definition & Fundamental Properties
- 2.1 Average vs. Instantaneous Rates of Change — 20 Qs
- 2.2 Defining the Derivative & Notation — 20 Qs
- 2.3 Estimating Derivatives at a Point — 20 Qs
- 2.4 Differentiability vs. Continuity — 50 Qs
- 2.5 Power Rule — 20 Qs
- 2.6 Constant, Sum/Difference, Constant Multiple Rules — 30 Qs
- 2.7 Derivatives of cos x, sin x, e^x, ln x — 20 Qs
- 2.8 Product Rule — 20 Qs
- 2.9 Quotient Rule — 20 Qs
- 2.10 Derivatives of tan, cot, sec, csc — 20 Qs
Unit 3 | Differentiation: Composite, Implicit, and Inverse Functions
- 3.1 Chain Rule — 80 Qs
- 3.2 Implicit Differentiation — 20 Qs
- 3.3 Derivatives of Inverse Functions — 20 Qs
- 3.4 Derivatives of Inverse Trig Functions — 20 Qs
- 3.5 Choosing Procedures for Derivatives — 20 Qs
- 3.6 Higher-Order Derivatives — 50 Qs
Unit 4 | Contextual Applications of Differentiation
- 4.1 Meaning of the Derivative in Context — 20 Qs
- 4.2 Motion: Position, Velocity, Acceleration — 20 Qs
- 4.3 Rates of Change in Non-Motion Contexts — 20 Qs
- 4.4 Intro to Related Rates — 20 Qs
- 4.5 Solving Related Rates — 20 Qs
- 4.6 Local Linearity & Linearization — 20 Qs
- 4.7 L’Hospital’s Rule — 30 Qs
Unit 5 | Analytical Applications of Differentiation
- 5.1 Mean Value Theorem — 50 Qs
- 5.2 EVT, Global vs. Local Extrema, Critical Points — 20 Qs
- 5.3 Intervals of Increase/Decrease — 20 Qs
- 5.4 First Derivative Test — 20 Qs
- 5.5 Candidates Test (Absolute Extrema) — 20 Qs
- 5.6 Concavity over Domains — 30 Qs
- 5.7 Second Derivative Test — 20 Qs
- 5.8 Sketching Functions & Derivatives — 20 Qs
- 5.9 Connecting f, f′, and f″ — 60 Qs
- 5.10 Intro to Optimization — 20 Qs
- 5.11 Solving Optimization Problems — 20 Qs
- 5.12 Behaviors of Implicit Relations — 20 Qs
Unit 6 | Integration and Accumulation of Change
- 6.1 Accumulations of Change — 20 Qs
- 6.2 Riemann Sum Approximations — 30 Qs
- 6.3 Riemann Sums, Σ-Notation, Definite Integral — 20 Qs
- 6.4 Fundamental Theorem of Calculus & Accumulation — 20 Qs
- 6.5 Behavior of Accumulation Functions — 30 Qs
- 6.6 Properties of Definite Integrals — 60 Qs
- 6.7 FTC & Definite Integrals — 30 Qs
- 6.8 Antiderivatives & Indefinite Integrals — 50 Qs
- 6.9 Substitution — 50 Qs
- 6.10 Long Division & Completing the Square — 20 Qs
- 6.11 Integration by Parts (BC) — 20 Qs
- 6.12 Linear Partial Fractions (BC) — 20 Qs
- 6.13 Improper Integrals (BC) — 20 Qs
- 6.14 Selecting Antidifferentiation Techniques — 30 Qs
Unit 7 | Differential Equations
- 7.1 Modeling with Differential Equations — 20 Qs
- 7.2 Verifying Solutions — 20 Qs
- 7.3 Sketching Slope Fields — 20 Qs
- 7.4 Reasoning with Slope Fields — 20 Qs
- 7.5 Euler’s Method (BC) — 20 Qs
- 7.6 General Solutions via Separation — 20 Qs
- 7.7 Particular Solutions with Initial Conditions — 40 Qs
- 7.8 Exponential Models — 20 Qs
- 7.9 Logistic Models (BC) — 20 Qs
Unit 8 | Applications of Integration
- 8.1 Average Value of a Function — 20 Qs
- 8.2 Position, Velocity, Acceleration via Integrals — 40 Qs
- 8.3 Accumulation Functions in Context — 20 Qs
- 8.4 Area Between Curves (as functions of x) — 30 Qs
- 8.5 Area Between Curves (as functions of y) — 20 Qs
- 8.6 Areas with >2 Intersections — 20 Qs
- 8.7 Volumes: Cross-Sections (Squares/Rectangles) — 20 Qs
- 8.8 Volumes: Cross-Sections (Triangles/Semicircles) — 20 Qs
- 8.9 Volume: Disc Method about x- or y-Axis — 20 Qs
- 8.10 Volume: Disc Method about Other Axes — 20 Qs
- 8.11 Volume: Washer Method about x- or y-Axis — 20 Qs
- 8.12 Volume: Washer Method about Other Axes — 20 Qs
- 8.13 Arc Length & Distance Traveled (BC) — 20 Qs
Unit 9 | Parametric Equations, Polar Coordinates, and Vector-Valued Functions (BC)
- 9.1 Parametric Equations & d y/d x — 30 Qs
- 9.2 Second Derivatives (Parametric) — 20 Qs
- 9.3 Arc Length (Parametric) — 20 Qs
- 9.4 Vector-Valued Functions & Derivatives — 20 Qs
- 9.5 Integrating Vector-Valued Functions — 20 Qs
- 9.6 Motion with Parametric/Vector Functions — 50 Qs
- 9.7 Polar Coordinates & Differentiation — 50 Qs
- 9.8 Area of a Polar Region — 20 Qs
- 9.9 Area Between Two Polar Curves — 20 Qs
Unit 10 | Infinite Sequences and Series (BC)
- 10.1 Convergent vs. Divergent Series — 20 Qs
- 10.2 Geometric Series — 20 Qs
- 10.3 nth-Term Test for Divergence — 20 Qs
- 10.4 Integral Test — 20 Qs
- 10.5 Harmonic Series & p-Series — 20 Qs
- 10.6 Comparison Tests — 20 Qs
- 10.7 Alternating Series Test — 20 Qs
- 10.8 Ratio Test — 20 Qs
- 10.9 Absolute vs. Conditional Convergence — 20 Qs
- 10.10 Alternating Series Error Bound — 20 Qs
- 10.11 Taylor Polynomials — 20 Qs
- 10.12 Lagrange Error Bound — 20 Qs
- 10.13 Radius & Interval of Convergence — 20 Qs
- 10.14 Taylor/Maclaurin Series for Functions — 50 Qs
- 10.15 Representing Functions as Power Series — 20 Qs
