# Course: Barron’s AP Calculus • 14th Edition

• 1 Functions
• A Definitions
• B Special Functions
• C Polynomial and Other Rational Functions
• D Trigonometric Functions
• E Exponential and Logarithmic Functions (BC Only)
• F Parametrically Defined Functions (BC Only)
• G Polar Functions
• 2 Limits and Continuity
• A Definitions and Examples
• B Asymptotes
• C Theorems on Limits
• D Limit of a Quotient of Polynomials
• E Other Basic Limits
• F Continuity
• 3 Differentiation
• A Definition of Derivative
• B Formulas
• C The Chain Rule; the Derivative of a Composite Function
• D Differentiability and Continuity
• E Estimating a Derivative
• E1 Numerically
• E2 Graphically (BC Only)
• F Derivatives of Parametrically Defined Functions
• G Implicit Differentiation
• H Derivative of the Inverse of a Function
• I The Mean Value Theorem
• J Indeterminate Forms and L’Hôpital’s Rule
• K Recognizing a Given Limit as a Derivative
• 4 Applications of Differential Calculus
• A Slope; Critical Points
• B Tangents to a Curve
• C Increasing and Decreasing Functions
• Case I Functions with Continuous Derivatives
• Case II Functions Whose Derivatives Have Discontinuities
• D Maximum, Minimum, Concavity, and Inflection Points: Definitions
• E Maximum, Minimum, and Inflection Points: Curve Sketching
• Case I Functions That Are Everywhere Differentiable
• Case II Functions Whose Derivatives May Not Exist Everywhere
• F Global Maximum or Minimum
• Case I Differentiable Functions
• Case II Functions That Are Not Everywhere Differentiable
• G Further Aids in Sketching
• H Optimization: Problems Involving Maxima and Minima
• I Relating a Function and Its Derivatives Graphically
• J Motion along a Line (BC Only)
• K Motion along a Curve: Velocity and Acceleration Vectors
• L Tangent-Line Approximations
• M Related Rates (BC Only)
• N Slope of a Polar Curve
• 5 Antidifferentiation
• A Antiderivatives
• B Basic Formulas (BC Only)
• C Integration by Partial Fractions (BC Only)
• D Integration by Parts
• E Applications of Antiderivatives; Differential Equations
• 6 Definite Integrals
• A Fundamental Theorem of Calculus (FTC); Evaluation of Definite Integral
• B Properties of Definite Integrals
• C Definition of Definite Integral as the Limit of a Riemann Sum
• D The Fundamental Theorem Again
• E Approximations of the Definite Integral; Riemann Sums
• E1 Using Rectangles
• E2 Using Trapezoids
• E3 Comparing Approximating Sums
• F Graphing a Function from Its Derivative; Another Look
• G Interpreting ln 𝑥 as an Area
• H Average Value
• 7 Applications of Integration to Geometry
• A Area
• A1 Area between Curves
• A2 Using Symmetry
• B Volume
• B1 Solids with Known Cross Sections
• B2 Solids of Revolution (BC Only)
• C Arc Length (BC Only)
• D Improper Integrals
• 8 Further Applications of Integration
• A Motion along a Straight Line (BC Only)
• B Motion along a Plane Curve
• C Other Applications of Riemann Sums
• D FTC: Definite Integral of a Rate Is Net Change
• 9 Differential Equations
• A Basic Definitions
• B Slope Fields (BC Only)
• C Euler’s Method
• D Solving First-Order Differential Equations Analytically
• E Exponential Growth and Decay
• Case I Exponential Growth
• Case II Restricted Growth (BC Only)
• Case III Logistic Growth
• 10 Sequences and Series
• A Sequences of Real Numbers (BC Only)
• B Infinite Series
• B1 Definitions
• B2 Theorems about Convergence or Divergence of Infinite Series
• B3 Tests for Convergence of Infinite Series
• B4 Tests for Convergence of Nonnegative Series
• B5 Alternating Series and Absolute Convergence (BC Only)
• C Power Series
• C1 Definitions; Convergence
• C2 Functions Defined by Power Series
• C3 Finding a Power Series for a Function: Taylor and Maclaurin Series
• C4 Approximating Functions with Taylor and Maclaurin Polynomials
• C5 Taylor’s Formula with Remainder; Lagrange Error Bound
• C6 Computations with Power Series (BC Only)
• C7 Power Series over Complex Numbers

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