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