Unit 1: Limits and Continuity
Limits: Graph & Numeric
Limits: Analytic
Trigonometric Limits
The Squeeze Theorem
Continuous Functions
Finding Asymptotes Using Limits
Unit 2: Differentiation: Basic Derivatives
Average and Instantaneous Rate of Change
Definition of the Derivative
Equations of Tangent and Normal Lines
Continuity and Differentiability
Simple Rules of Differentiation
Derivative of Natural Logarithm
Derivative of Natural Exponential
Derivatives of Sine, Cosine, and Tangent
Product and Quotient Rules
Derivatives of Cosecant, Secant, and Cotangent
Unit 3: Differentiation: Composite, Implicit, and Inverse Functions
Chain Rule
Implicit Differentiation
Derivatives of Inverse Functions
Derivatives of Inverse Trigonometric Functions
Higher-Order Derivatives
Unit 4: Contextual Applications of Derivatives
Position, Velocity, Acceleration
Related Rates
Linear Approximation
L'Hospital's Rule
Unit 5: Analytical Applications of Derivatives
Rolle's Theorem and Mean Value Theorem
Increasing and Decreasing Functions
Extrema and Optimization
Concavity and the Second Derivative
Unit 6: Integration and Accumulation of Change
Riemann Sums
Antiderivatives and Basic Integration Rules
First Fundamental Theorem of Calculus
Definite Integrals
Second Fundamental Theorem of Calculus
Functions Defined by Integrals
Integration by Substitution
Integration by Parts
Integration by Partial Fractions
Improper Integrals and L'Hôpital's Rule
Unit 7: Differential Equations
Slope Fields and Euler's Method
Separable Differential Equations
Exponential Growth and Decay
Logistic Differential Equations
Unit 8: Applications of Integration
Average Value of a Function
Area Between Curves
Volume by Cross-Sections
Volume by Disks and Washers
Arc Length
Unit 9: Parametric Equations, Polar Coordinates, & Vector-Valued Functions
Parametric Equations
Velocity and Acceleration Vectors
Speed and Total Distance
Slope of Tangent Line and Concavity
Polar Equations
Derivatives of Polar Functions
Area of Polar Curves
Area Between Polar Curves
Unit 10: Infinite Sequences and Series
Sequences, Series, and Partial Sums
Geometric Series, p-Series, nth Term Test
Direct Comparison, Limit Comparison, Ratio Test
Integral Test, Alternating Series Test
Power Series/Radius and Interval of Convergence
Maclaurin Series
Lagrange Error Bound
Taylor Series