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.

Topic 1: Functions & Graphs Coordinates and Graphs, Functions and their Graphs, Linear Functions Linear Models, Quadratic Functions and Models, Solving Equations Using Graphing Calculators or Computers

Topic Summary: Click Here True-False Quiz: Click Here Topic Review Exercises: Click Here On-Line Tools & Mac Software: On-Line Graphing Utility (an advanced Java graphing utility with trace, zoom and many other features) On-Line Evaluation of Functions (Creates a table of values for any function you specify) On-Line Regression (equations of exact and best-fit lines, parabolas and cubics) Download Graphing Software

Topic 2: Exponential & Logarithmic Functions Exponential Functions and Applications , Continuous Growth and Decay and the Number e, Logarithmic Functions, Applications of Logarithms

Topic Summary: Click Here True-False Quiz: Click Here Topic Review Exercises: Click Here (has exercises on exponential and linear functions, but not logarithmic functions as yet) On-Line Tools & Mac Software: On-Line Graphing Utility (an advanced Java graphing utility with trace, zoom and many other features) On-Line Evaluation of Functions (Creates a table of values for any function you specify) On-Line Regression (equations of exact and best-fit exponential functions) Download Graphing Software

Topic 3: 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 On-Line Tutorials: (with animated graphics!) Rates of Change and the Derivative Geometric Interpretation of the Derivative Limits and Continuity Derivatives of Powers and Polynomials True-False Quiz: Click Here Topic Review Exercises: Click Here (includes questions on Topic 4 below) On-Line Tools & Mac Software: On-Line Graphing Utility (an advanced Java graphing utility with trace, zoom and many other features) On-Line Evaluation of Functions (Use this to evaluate difference quotients) Download Graphing Software (Use the zoom feature to estimate derivatives)

Topic 4: 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!) True-False Quiz: Click Here Topic Review Exercises: Click Here

Topic 5: 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 Topic Review Exercises: Click Here (Applied maxima & minima exercises) On-Line Tools & Mac Software: On-Line Graphing Utility (an advanced Java graphing utility with trace, zoom and many other features) On-Line Evaluation of Functions (Useful in curve sketching) Download Graphing Software

Topic 6: 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 Topic Review Exercises: Click Here

Topic 7: 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 6: 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 Topic Review Exercises: Click Here

Topic 8: 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

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