- Finding Limits Graphically
- Evaluating Limits by Direct Substitution
- Evaluating Limits by Factorization
- Evaluating Limits by Multiplying by the Conjugate
- Evaluating Limits by Simplifying a Complex Fraction
- Limits to Infinity and End Behavior
- Evaluating One-Sided Limits
- Discussing the Existence of a Limit
- Continuity over an Interval
- The Composite Function Theorem
- Finding the Delta Value Algebraically for a Given Epsilon
- The Intermediate Value Theorem
- Determining Horizontal and Vertical Asymptotes

- Average Rates of Change and Secant Lines
- Instantaneous Rate of Change
- The Rate of Change as a Derivative
- Derivatives Evaluated as Limits
- Determining Whether a Function Is Differentiable
- Finding Derivatives of Polynomial Functions
- Using the Product Rule to Find a Function Derivative
- Using the Quotient Rule to Find a Function Derivative
- Using the Chain Rule for the Derivatives of Single-Variable Functions
- First-Order Derivatives Using the Chain Rule
- Finding Higher-Order Derivatives Using the Chain Rule
- Derivatives of Trigonometric Functions
- Differentiation of the Natural Exponential Function
- Differentiation of the General Exponential Function
- Differentiation of Natural Logarithmic Functions
- Differentiation of General Logarithmic Functions
- Logarithmic Differentiation
- Finding a Tangent to the Graph of a Function
- Differentiating Implicitly Defined Functions
- Finding Higher-Order Derivatives Implicitly
- Tangent and Normal Lines of Implicit Functions
- Population Change and Change in Cost and Revenue
- Motion along a Line

- Related Rates
- Local Extrema and Critical Points
- First Derivative Test for Local Extrema
- Second Derivative Test for Local Extrema
- Monotonicity of a Function
- Locating Absolute Extrema
- Using Derivatives in Optimization Problems
- Concavity and Points of Inflection
- Applications of Derivatives: Sketching Graphs
- Consequences of Differentiability
- Linear Approximation
- Computing Differentials of a Function
- Applying L’Hôpital's Rule for Limits with 0/0 Output
- Applying L’Hôpital's Rule for Limits with ∞/∞ Output
- L’Hôpital's Rule
- Finding the Antiderivatives of Functions
- The Mean Value Theorem and Its Interpretation

- Expressing and Evaluating the Limit of a Riemann Sum
- Finding and Comparing the Approximated Area Evaluated by Riemann Sum
- Applying Right Endpoint Approximation to Find the Area under a Curve
- Applying Left Endpoint Approximation to Find the Area under a Curve
- Applying Midpoint Approximation to Find the Area under a Curve
- Finding the Indefinite Integrals of Functions
- Integration of Trigonometric Functions
- Integrate Functions Involving Exponential Functions
- Evaluating Integrals Involving Logarithmic Functions
- Evaluating the Definite Integrals of Polynomials Using the Power Rule
- Evaluating the Definite Integral
- Using Definite Integral Properties
- The Fundamental Theorem of Calculus
- Applying the Net Change Theorem
- Calculating the Average Value of a Function

- Integration by Parts for Indefinite Integrals
- Evaluating Indefinite Integrals by Substitution
- Evaluating Definite Integrals by Substitution
- Trigonometric Substitutions in Integrals
- Integration by Partial Fractions with Nonrepeated Linear Factors
- Integration by Partial Fractions with repeated Linear Factors
- Integration by Partial Fractions with Nonrepeated Irreducible Quadratic Factors
- Integration by Partial Fractions with Repeated Irreducible Quadratic Factors
- Integration by Partial Fractions of Improper Fractions
- Evaluating the Integral Using Partial Fraction Decomposition
- Integrating Products of Sines and Cosines of Different Angles
- Integrating Products of Powers of Sines and Cosines
- Integrating Products of Powers of Tangents (tan) and Secants (sec)

- Finding the Area between a Curve and the x-Axis
- Finding the Area of a Region between Two Curves
- Finding the Total Area Bounded by Alternating Functions
- Calculating Volumes of Solids of Revolution
- Finding Volume of a Solid by Rotating around x-Axis Using Disk Method
- Finding the Volume of a Solid by Rotating around the y-Axis Using the Disk Method
- Finding the Volume of a Solid by Rotating around the Horizontal Line Using the Washer Method
- Finding the Volume of a Solid of Revolution about the y-Axis Using the Washer Method
- Finding the Volume of a Solid by Rotating around a Vertical Line Using the Shell Method
- Finding Volume of a Solid by Rotating around a Horizontal Line Using the Shell Method
- Arc Length of a Curve y = ƒ(x)
- Average Value of a Function
- Exponential Growth Model
- Exponential Decay Model
- Rectilinear Motion as an Application of Integration

- Converting Points from Polar to Rectangular Coordinates
- Parametric Equations of Plane Curves
- Finding the Derivatives of Parametric Functions
- Finding the Slope of a Polar Curve
- Finding the Tangent and the Normal Equations of a Parametrically Defined Curve
- Finding the Length of a Polar Curve
- Finding the Arc Length of a Parametrically Defined Curve
- Differentiating Vector Valued Functions