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Understanding that technology can be both a valuable tool and as an active companion in the learning of calculus, Weimer has produced a textbook that students-those majoring in business, management, economics, and the social, life and physical sciences-will appreciate for the way it helps guide them into the 21st century. Students are introduced to functions and associated preliminary algebraic material, and then are presented with basic concepts of differential calculus. The organization and careful introduction of material is designed to help even poorly prepared students succeed. This text is ideal for professors who wish to integrate DERIVE® or the TI-92 graphing calculator into the applied calculus course.
1. FUNCTIONS Introduction to Functions / Graphs of Functions / Constructing New Functions from Old Functions / Linear Functions / Polynomial, Rational, and Power Functions / Exponential Functions / Logarithmic Functions 2. THE DERIVATIVE Slope of a Curve / Rates of Change / Limits and Continuity / The Derivative 3. GRAPHS AND APPLICATIONS OF THE DERIVATIVE Characteristics of Graphs / Asymptotes / Extreme Points / Concavity, Inflection Points, and Curve Sketching / Applications Invoking Optimization / Differentials 4. THE DERIVATIVE: MORE PROPERTIES The Generalized Power Property / The Product Property / The Quotient Property / Implicit Differentiation 5. DERIVATIVES OF LOGARITHMIC AND EXPONENTIAL FUNCTIONS The Chain Rule and the Calculus of Logarithmic and Exponential Functions / Growth and Decay Applications / Applications to Business and Economics: Elasticity of Cost and Demand 6. THE INTEGRAL The Antiderivative / Applications of the Indefinite Integral / The Definite Integral / Integration: A Process of Accumulation / Area of a Region and Applications 7. ADDITIONAL INTEGRATION TOPICS The Method of Substitution / Integration by Parts / Separable Differential Equations / Improper Integrals / Discrete Probability / Continuous Probability Distributions 8. CALCULUS OF SEVERAL VARIABLES Functions of Several Variables / Partial Derivatives / Optimizing Functions of Several Variables / Lagrange Multipliers / Double Integration / Applications of the Double Integration /APPENDIX A: IMPORTANT DERIVE® COMMANDS FOR IBM-PC's OR PC COMPATIBLES / APPENDIX B: DERIVE® FOR WINDOWS, VERSION 4.02 / APPENDIX C: TI-92 / ANSWERS TO ODD-NUMBERED EXERCISES / INDEX