## Resources for Math 10 and 10E: Basic Calculus

Note: Different sections of Math 10 and 10E may cover different topics selected from the following list, and not necessarily in the order given. Choose your topic and then select the resource you want.

### Topic 1: Functions & Graphs

Coordinates and Graphs, Functions and their Graphs, Linear Functions, Linear Models, Quadratic Functions and Models, Exponential Functions and Applications , Continuous Growth and Decay and the Number e, Logarithmic Functions, Applications of Logarithms, Linear Regression

 Topic Summary: Linear Functions & Models Non-Linear Functions & Models Extra On-Line Topics: New Functions from Old: Scaled and Shifted Functions Fitting Functions to Data: Linear and Exponential Regression Using and Deriving Algebraic Properties of Logarithms Trigonometric Functions and Calculus True-False Quiz: Click Here Review Exercises: Click Here On-Line Tools & Mac Software: On-Line Graphing & Evaluation of Functions(Creates a table of values and graph for any function you specify) On-Line Graphing Utility(an advanced Java graphing utility with trace, zoom and many other features) On-Line Regression(equations of exact and best-fit lines, parabolas and cubics) Download Graphing Software

### Topic 2: Introduction to the Derivative

Rates of Change and the Derivative, Geometric Interpretation of the Derivative, Limits, Continuity, Differentiability, Derivatives of Powers and Polynomials, Marginal Analysis

 Topic Summary: Click Here Extra On-Line Topics: Sketching the Graph of the Derivative Proof of the Power Rule Continuity and Differentiability On-Line Tutorials: (with animated graphics!) Average Rate of Change The Derivative as Rate of Change: A Numerical Approach The Derivative as Slope: A Geometric Approach The Derivative as a Function: An Algebraic Approach Limits and Continuity: Numerical & Graphical Approaches Limits and Continuity: Algebraic Approach True-False Quiz: Click Here Review Exercises: Click Here On-Line Tools & Mac Software: On-Line Graphing & Evaluation of Functions(Creates a table of values and graph for any function you specify) On-Line Graphing Utility(an advanced Java graphing utility with trace, zoom and many other features) Download Graphing Software(Use the zoom feature to estimate derivatives)

### Topic 3: Techniques of Differentiation

The Product and Quotient Rule, The Chain Rule, Derivatives of Logarithmic and Exponential Functions, Implicit Differentiation, Linear Approximation and Error Estimation

 Topic Summary: Click Here On-Line Tutorials: Product and Quotient Rules The Chain Rule Derivatives of Logarithmic and Exponential Functions (with tables you can print out!) On-Line Text for Derivatives of Trig Functions True-False Quiz: Click Here Review Exercises: Click Here

### Topic 4: Applications of the Derivative

Maxima and Minima
Applications of Maxima and Minima, The Second Derivative: Acceleration and Concavity, Curve Sketching, Related Rates, Elasticity of Demand

 Topic Summary: Click Here True-False Quiz: Click Here On-Line Tutorial: Related Rates Review Exercises: Click Here (Applied maxima & minima exercises) On-Line Tools & Mac Software: On-Line Graphing & Evaluation of Functions(useful in curve sketching) On-Line Graphing Utility(an advanced Java graphing utility with trace, zoom and many other features) Download Graphing Software

### Topic 5: The Integral

The Indefinite Integral, Substitution, Applications of the Indefinite Integral, Geometric Definition of the Definite Integral, Algebraic Definition of the Definite Integral, The Fundamental Theorem of Calculus, Numerical Integration

 Topic Summary: Click Here On-Line Tutorials: The Indefinite Integral Substitution True-False Quiz: Click Here Review Exercises: Click Here Extra On-Line Topics: Numerical Integration On-Line Tools: Numerical Integration Utility(For left- and right Riemann Sums, Trapezoid Rule, and Simplson's Rule)

### Topic 6: Further Techniques and Applications of the Integral

Integration by Parts, Integration Using Tables, Area Between Two Curves and Applications, Averages and Moving Averages, Improper Integrals and Applications