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