## Resources for Math 19: Calculus & Analytical Geometry I

Important Notes:

• The following list of topics does not cover the entire Math 19 syllabus; there is no material here on the Intermediate Value Theorem, Rolle's Theorem, the Mean Value Theorem, or the Integral Mean Value Theorem. Also, the the material here on trigonometric functions is intended for non-science majors.
• Trigonometric functions are discussed separately (and briefly) in an on-line text intended for non-math majors (see below), so there is no coverage of trig funtions in the other topic resources.
• Exponential functions are and logarithms are included in this list below -- you may not encounter these until Math 20. We have also included material on integration by parts.

 Homework Problems (Waner's sections only) Here is a complete set of homework problems and answers: (Waner's section)

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: Click Here Extra On-Line Topics: New Functions from Old: Scaled and Shifted Functions Using and Deriving Algebraic Properties of Logarithms Fitting Functions to Data: Linear and Exponential Regression 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
 Topic Summary: Click Here True-False Quiz: Click Here
Topic 7: Trigonometric Functions and Calculus
Modeling with the Sine Function, The Six Trigonometric Functions, Derivatives of Trigonometric Functions, Integrals of Trigonometric Functions
 Complete Text is On-Line! Click Here