CALCULUS BC

APPLICATIONS OF INTEGRATION

  1. Areas Between Curves

  2. Volumes

  3. Volumes by Cylindrical Shells

  4. Work

  5. Average Value of a Function

TECHNIQUES OF INTEGRATION

  1. Integration by Parts

  2. Trigonometric Integrals

  3. Trigonometric Substitution

  4. Integration of Rational Functions by Partial Fractions

  5. Strategy for Integration

  6. Integration Using Tables and Computer Algebra Systems

  7. Approximate Integration

  8. Improper Integrals

FURTHER APPLICATIONS OF INTEGRATION

  1. Arc Length

  2. Area of a Surface of

  3. Applications to Physics and Engineering

  4. Applications to Economics and Biology

  5. Probability

DIFFERENTIAL EQUATIONS

  1. Modeling with Differential Equations

  2. Direction Fields and Euler’s Method

  3. Separable Equations

  4. Models for Population Growth

  5. Linear Equations

  6. Predator-Prey Systems

PARAMETRIC EQUATIONS AND POLAR COORDINATES

  1. Curves Defined by Parametric Equations

  2. Calculus with Parametric Curves

  3. Polar Coordinates

  4. Areas and Lengths in Polar Coordinates

  5. Conic Sections

  6. Conic Sections in Polar Coordinates

INFINITE SEQUENCES AND SERIES

  1. Sequences

  2. Series

  3. The Integral Test and Estimates of Sums

  4. The Comparison Tests

  5. Alternating Series

  6. Absolute Convergence and the Ratio and Root Tests

  7. Strategy for Testing Series

  8. Power Series

  9. Representations of Functions as Power Series

  10. Taylor and Maclaurin Series

  11. Applications of Taylor Polynomials

 FUNCTIONS AND MODELS

  1. Four Ways to Represent a Function

  2. Mathematical Models: A Catalog of Essential Functions

  3. New Functions from Old Functions

  4. Exponential Functions

  5. Inverse Functions and Logarithms

LIMITS AND DERIVATIVES

  1. The Tangent and Velocity Problems

  2. The Limit of a Function

  3. Calculating Limits Using the Limit Laws

  4. The Precise Definition of a Limit

  5. Continuity

  6. Limits at Infinity; Horizontal Asymptotes

  7. Derivatives and Rates of Change

  8. The Derivative as a Function

DIFFERENTIATION RULES

  1. Derivatives of Polynomials and Exponential Functions

  2. The Product and Quotient Rules

  3. Derivatives of Trigonometric Functions

  4. The Chain Rule

  5. Implicit Differentiation

  6. Derivatives of Logarithmic Functions

  7. Rates of Change in the Natural and Social Sciences

  8. Exponential Growth and DecayRelated Rates

  9. Linear Approximations and Differentials

  10. Hyperbolic Functions

APPLICATIONS OF DIFFERENTIATION

  1. Maximum and Minimum Values

  2. The Mean Value Theorem

  3. How Derivatives Affect the Shape of a Graph

  4. Indeterminate Forms and l’Hospital’s Rule

  5. Summary of Curve Sketching

  6. Graphing with Calculus and Calculators

  7. Optimization Problems

  8. Newton’s Method

  9. Antiderivatives

INTEGRALS

  1. Areas and Distances

  2. The Definite Integral

  3. The Fundamental Theorem of Calculus

  4. Indefinite Integrals and the Net Change Theorem

  5. The Substitution Rule