Calculus: Applications and Technology - Softcover

Tomastik, Edmond C.

Softcover

ISBN 10: 0030215595 ISBN 13: 9780030215599

Publisher: Cengage Learning, 1980

Synopsis

By always bringing graphical and numerical, as well as algebraic viewpoints each topic, this work presents a conceptual understanding of the calculus that is useful in accommodating diverse applications.

About this title

Review

1. FUNCTIONS. Graphers Versus Calculus. Functions. Mathematical Models. Exponential Models. Combinations of Functions. Logarithms. 2. MODELING WITH LEAST SQUARES. Method of Least Squares. Quadratic Regression. Cubic, Quartic, and Power Regression. Exponential and Logarithmic Regression. Logistic Regression. Selecting the Best Model. 3. THE DERIVATIVE. Introduction to Calculus. Limits. Rates of Change. The Derivative. Local Linearity. 4. RULES FOR THE DERIVATIVE. Derivatives of Powers, Exponents, and Sums. Derivatives of Products and Quotients. The Chain Rule. Derivatives of Exponential and Logarithmic Functions. Elasticity of Demand. Management of Renewable Natural Resources. 5. CURVE SKETCHING AND OPTIMIZATION. The First Derivative. The Second Derivative. Limits at Infinity. Additional Curve Sketching. Absolute Extrema. Optimization and Modeling. The Logistic Model. Implicit Differentiation and Related Rates. 6. INTEGRATION. Antiderivatives. Substitution. Distance Traveled. The Definite Integral. The Fundamental Theorem of Calculus. Area Between Two Curves. Additional Applications of the Integral. 7. ADDITIONAL TOPICS IN INTEGRATION. Integration by Parts. Integration Using Tables. Numerical Integration. Improper Integrals. 8. FUNCTIONS OF SEVERAL VARIABLES. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Total Differentials and Approximations. Double Integrals. OPTIONAL CD-ROM CHAPTERS. 9. THE TRIGONOMETRIC FUNCTIONS. Angles. The Sine and Cosine. Differentiation of the Sine and Cosine Functions. Integrals of the Sine and Cosine Functions. Other Trigonometric Functions. 10. TAYLOR POLYNOMIALS AND INFINITE SERIES. Taylor Polynomials. Errors in Taylor Polynomial Approximation. Infinite Sequences. Infinite Series. The Integral and Comparison Tests. The Ratio Test and Absolute Convergence. Taylor Series. 11. PROBABILITY AND CALCULUS. Discrete Probability. Continuous Probability Density Functions. Expected Value and Variance. The Normal Distribution. 12. DIFFERENTIAL EQUATIONS. Differential Equations. Separation of Variables. Approximate Solutions to Differential Equations. Qualitative Analysis. Harvesting a Renewable Resource. Appendix A: Review. Appendix B: Tables.

Edition details

• Publisher: Cengage Learning
• Publication date: 1980
• Language: English
• ISBN 10: 0030215595
• ISBN 13: 9780030215599
• Binding: Paperback
• Edition number: 2
• Number of pages: 725