Calculus 2008/09 school year Unit A - Functions Unit A1 – Characteristics, Limits, Continuities A.1.1 - Function Characteristics increase/decrease/concavity/domain 2L A.1.2 - Continuities piecewise fcns 2L A.1.3 - Limits left/right/piecewise 2L A.1.4 - Rates of Change average/instantaneous 2L A.1.5 - Area Under Curves RAM, trapezoids 2L UNIT B - Differential Calculus Unit B1 - Derivatives & Differentiation Techniques B.1.1 - Limit Definition of a Derivative 2L B.1.2 - Derivatives of Products 1L B.1.3 - Derivatives of Rational Functions - The Quotient Rule 1L B.1.4 - Derivatives of Composite Functions - The Chain Rule 1L B.1.5 - Derivatives of Exponential Functions 1L B.1.6 - Derivatives of Logarithmic Functions 1L B.1.7 - Derivatives of Trigonometric Functions 2L Unit B2 - Derivatives and Graphical Analysis B.2.1 - Graphical Differentiation 2L B.2.2 - Increasing and Decreasing Functions 1L B.2.3 - Relative Extrema 1L B.2.4 - Absolute Extrema 1L B.2.5 - Higher Derivatives, Concavity 2L B.2.6 - Curve Sketching 2L Unit B3 - Applications of Derivatives B.3.1 - Applications of Extrema 3L B.3.2 - Implicit Differentiation 2L B.3.3 - Related Rates 2L B.3.4 - Differentials: Linear Approximations 1L B.3.5 - Newton-Raphson Approximations 2L Unit C - Integral Calculus Unit C1 - Basics of Integration C.1.1 - Antiderivatives 1L C.1.2 - Area & the Definite Integral 3L C.1.3 - The Fundamental Theorem of Calculus 4L Unit C2 - Techniques and Applications of Integration C.2.1 - Integration by Substitution 2L C.2.2 - Integration by Parts 2L C.2.3 - The Area Between 2 Curves 2L C.2.4 - Numerical Integration 1L C.2.5 - Average Value of a Function 1L C.2.6 - Volume 3L Unit C3 - Differential Equations C.3.1 - Differential Equations 1L C.3.2 - Separable Differential Equations 2L C.3.3 - Applications of Differential Equations 4L C.3.4 - Slope Fields 2L