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AP Calculus BC Course Outline Unit 1: Precalculus Review Unit 2: Limits and Continuity Unit 3: The Derivative A. Definition of the derivative B. Relationships between the graphs of f and f’ C. Differentiability 1. Local linearity 2. How f’ might fail to exist 3. Numeric derivatives using the calculator 4. Differentiability and continuity D. Derivatives of algebraic functions E. Velocity and other rates of change F. Derivative rules when combining functions G. Applications to velocity and acceleration H. Derivatives of trigonometric functions I. The chain rule J. Implicit derivatives 1. Differential method 2. y' method K. Derivatives of inverse trigonometric functions L. Derivatives of logarithmic and exponential functions Unit 4: Applications of the Derivative A. Extreme values 1. Local (relative) extrema 2. Global (absolute) extrema B. Using the derivative 1. Mean value theorem 2. Increasing and decreasing functions 3. Antiderivatives C. Analysis of graphs using the first and second derivatives 1. Critical values 2. First derivative test for extrema 3. Concavity and points of inflection 4. Second derivative test for extrema 5. Graphing f given f’ and/or f” D. Optimization problems E. Linearization models 1. linear approximations 2. Newton’s method (By hand and through the use of calculator program) 3. Differentials F. Related rates Unit 5: The Definite Integral A. Approximating areas 1. Riemann sums 2. Rectangular Approximation Methods (By hand and through the use of a calculator program) 3. Trapezoidal rule (By hand and through the use of a calculator program) B. Definite integrals and antiderivatives 1. Average Value Theorem 2. Mean Value Theorem 3. Definite integrals using the calculator C. The Fundamental Theorem of Calculus (part 1) D. The Fundamental Theorem of Calculus (part 2) Unit 6: Differential Equations and Mathematical Modeling A. B. C. D. E. Slope field’s and Euler’s Method (By hand and through the use of a calculator program) Differential equations Integration using u-substitution Integration by parts Separable differential equations 1. Growth and decay 2. Slope fields (By hand and through the use of a calculator program) 3. General differential equations Unit 7: Applications of Definite Integrals A. Integral as Net Change B. Areas in the plane 1. Area between curves 2. Area enclosed by intersecting curves 3. Areas with boundaries 4. Integrating with respect to “y” 5. Integrating using geometry formulas C. Volumes D. Volumes of solids with known cross sections. E. Volumes of solids of revolution F. Disk method G. Shell method Unit 8: Advanced Topics A. B. C. D. E. F. L’Hopital’s Rule Relative Rates of Growth Improper Integrals Partial Fractions and Integral Tables Arc Length Conic Sections Unit 9: Series A. sequences B. Power series (geometric series, representing a function, differentiation and integration of series) C. Taylor and MacLaurin series (general and ex, sin x and cos x) D. Manipulation of series E. Taylor polynomials and Lagrange error bound F. Radius of convergence (nth term test, comparison test, ratio test) G. Interval of convergence (integral test, p-series, alternating series) Unit 10: Polar, Parametric and Vectors A. B. C. D. E. F. Parametric Functions Vectors in the Plane Vector-valued Functions Modeling Projectile Motion Polar Coordinates and Polar graphs Calculus of Polar Curves