**College Prep. Calculus**

**Topics**

*All topics listed below are presented to the students in a way that is consistent with the vision*

of the NCTM (National Council of Teachers of Mathematics)of the NCTM (National Council of Teachers of Mathematics)

**Preparation for calculus**-

**Graphs and Models**

**- Linear Models and Rates of Change**

**- Functions and their Graphs**

**- Fitting Models to Data**

**Limits and their Properties**

**- A Preview of Calculus**

**- Finding Limits Graphically and Numerically**

**- Evaluating Limits Analytically**

**- Continuity and One-Sided Limits**

**- Infinite Limits**

**Differentiation**

**- The Derivative and the Tangent Line Problem**

**- Basic Differentiation Rules and Rates of Change**

**- The Product and Quotient Rules**

**- Higher Order Dervatives**

**- The Chain Rule**

**- Implicit Differentiation**

**Applications and Differentiation**

**- Extrema on an Interval**

**- Rolle's Theorem and the Mean Value Theorem**

**- Increasing and Decreasing Functions**

**- First Derivative Test-- Increasing and Decreasing Functions**

*- Limits at Infinity*

*- Optimization Problems*

*- Newton's Method*

*- Differentials*

*Integration*

*- Antiderivatives and Indefinite Integrals*

*- Area*

*- Reimann Sums and Definite Integrals*

*- The Fundamental Theorem of Calculus*

*- Integration by Substitution*

*- Numerical Integration*

*Logarithmic, Exponential, and Other Transcendental Functions*

*- Differentiation of Natural Logarithmic Functions*

*- Integration of Natural Log Functions*

*- Inverse Functions*

*- Differentiation and Integration of Exponential Functions*

*- Bases other than e and Applications*

*- Differential equations: Growth & Decay*

*- Differential Equations: Separation of Variables*

*- Differentiation of Inverse Trig Functions*

*- Integration of Inverse Trig Functions*

*Applications of Integration*

*- Area of a Region Between Two Curves*

*- Volume: The Disk Method*

*- Volume : The Shell Method*

*- Arc Length and Surfaces of Revolution*

*- Work*

*Integration Techniques, L'Hopital's Rule, and Improper Integrals*

*- Basic Integration Rules*

*- Integration by Parts*

*- Trig Integrals*

*- Trigonometric Substitution*

*- Partial Fractions*

*- Improper Integrals*

*- L'Hopital's Rule*