Calculus

2008/2009 School Year

Course Outline

Fall Semester:

Unit 1: Limits and Their Properties

Topics Covered: Finding Limits Graphically and Numerically, Evaluating Limits Analytically, Continuity and One-Sided Limits, Infinite Limits and Vertical Asymptotes

Unit 2: Differentiation

Topics Covered: Defining the Derivative, Rules of Differentiation, Differentiation of Algebraic Functions, Differentiation of Transcendental Functions, Implicit Differentiation, Rates of Change & Higher-Order Derivatives, Related Rates

Unit 3: Applications of Differentiation

Topics Covered: Extrema, Rolle’s Theorem and the Mean Value Theorem, Increasing and Decreasing Functions and the First Derivative Test, Concavity and the Second Derivative Test, Limits at Infinity, Differentials/Linear Approximations

Unit 4 Part 1: Integration

Topics Covered: Antiderivatives, Differential Equations, Position, Velocity, and Acceleration

Spring Semester:

Unit 4 Part 2: Integration

Topics Covered: Summation, Upper, Lower, Midpoint, and Riemann Sums, Definite Integrals, the Fundamental Theorems of Calculus, Integration by Substitution, The Mean Value Theorem for Integrals, the Trapezoidal Rule

Unit 5: Integration of Transcendental Functions and Applications of Integration

Topics Covered: Integration of Transcendental Functions, Separable Differential Equations, Slope Fields, Area Between Two Curves, Volume of Solids of Revolution and Solids of Known Cross-Section

AP Exam: May 6, 2009