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donovan d ap calculus premium 12 practice tests 15ed 2019

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Textbook in PDF format Barron’s Essential Introduction The Courses Topic Outline for the AB and BC Calculus Exams The Examinations The Graphing Calculator: Using Your Graphing Calculator on the AP Exam Grading the Examinations This Review Book Flashcards Diagnostic tests Calculus AB Calculus BC Topical review and practice Functions Definitions Special Functions Polynomial and Other Rational Functions Trigonometric Functions Exponential and Logarithmic Functions Parametrically Defined Functions (BC Only) Polar Functions (BC Only) Practice Exercises Limits and Continuity Definitions and Examples Asymptotes Theorems on Limits Limit of a Quotient of Polynomials Other Basic Limits Continuity Practice Exercises Differentiation Definition of Derivative Formulas The Chain Rule; the Derivative of a Composite Function Differentiability and Continuity Estimating a Derivative E1. Numerically Graphically Derivatives of Parametrically Defined Functions (BC Only) Implicit Differentiation Derivative of the Inverse of a Function The Mean Value Theorem Indeterminate Forms and L’Hospital’s Rule Recognizing a Given Limit as a Derivative Practice Exercises Applications of Differential Calculus Slope; Critical Points Tangents to a Curve Increasing and Decreasing Functions Functions with Continuous Derivatives Functions Whose Derivatives Have Discontinuities Maximum, Minimum, Concavity, and Inflection Points: Definitions Maximum, Minimum, and Inflection Points: Curve Sketching Functions That Are Everywhere Differentiable Case II. Functions Whose Derivatives May Not Exist Everywhere Global Maximum or Minimum Case I. Differentiable Functions Functions That Are Not Everywhere Differentiable Further Aids in Sketching Optimization: Problems Involving Maxima and Minima Relating a Function and Its Derivatives Graphically Motion Along a Line Motion Along a Curve: Velocity and Acceleration Vectors (BC Only) Tangent-Line Approximations Related Rates Slope of a Polar Curve (BC Only) Practice Exercises Antidifferentiation Antiderivatives Basic Formulas Integration by Partial Fractions (BC Only) Integration by Parts (BC Only) Applications of Antiderivatives; Differential Equations Practice Exercises Definite Integrals Fundamental Theorem of Calculus (FTC); Evaluation of Definite Integral Properties of Definite Integrals Definition of Definite Integral as the Limit of a Riemann Sum The Fundamental Theorem Again Approximations of the Definite Integral; Riemann Sums Using Rectangles Using Trapezoids Comparing Approximating Sums Graphing a Function from Its Derivative; Another Look Interpreting ln x as an Area Average Value Practice Exercises Applications of Integration to Geometry Area Area Between Curves Using Symmetry Volume Solids with Known Cross Sections B2. Solids of Revolution Length of Curve (Arc Length) (BC Only) Improper Integrals (BC Only) Practice Exercises Further Applications of Integration Motion Along a Straight Line Motion Along a Plane Curve (BC Only) Other Applications of Riemann Sums FTC: Definite Integral of a Rate Is Net Change Practice Exercises Differential Equations Basic Definitions Slope Fields Euler’s Method (BC Only) Solving First-Order Differential Equations Analytically Exponential Growth and Decay Case I: Exponential Growth Case II: Restricted Growth Case III: Logistic Growth (BC Only) Practice Exercises Sequences and Series (BC Only) Sequences of Real Numbers Infinite Series B1. Definitions Theorems About Convergence or Divergence of Infinite Series Tests for Convergence of Infinite Series Tests for Convergence of Nonnegative Series Alternating Series and Absolute Convergence Power Series Definitions Convergence Functions Defined by Power Series Finding a Power Series for a Function: Taylor and Maclaurin Series Approximating Functions with Taylor and Maclaurin Polynomials Taylor’s Formula with Remainder Lagrange Error Bound Computations with Power Series Power Series over Complex Numbers Practice Exercises Miscellaneous Multiple-Choice Practice Questions Miscellaneous Free-Response Practice Exercises AB Practice examinations BC Practice examinations Appendix: Formulas and Theorems for Reference Index

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