Calculus from Graphical,Numerical,and Symbolic Points of View,Volume 1 / Edition 2 available in Hardcover
- Pub. Date:
Ostebee and Zorn provide concrete strategies that help students understand and master concepts in calculus. This user-friendly text continues to help students interact with the main calculus objects (functions, derivatives, integrals, etc.) not only symbolically but also, where appropriate, graphically and numerically. Ostebee/Zorn strikes an appropriate balance among these points of view, without overemphasizing any of them. New exercises, examples, and much more have added tremendously to this great book.NAVIGATING CALCULUS, a new CD-ROM, is being released along with the second edition. The CD contains a variety of useful tools, and resources, including a powerful graphing calculator utility, a glossary with examples, and many live activities that deepen students' encounters with calculus ideas. The CD is keyed closely to the book's table of contents.Any treatment of calculus involves many choices among competing alternatives: how and when to treat limits, which applications to include, what to prove, etc.
Table of Contents1. FUNCTIONS AND DERIVATIVES: THE GRAPHICAL VIEW. Functions, Calculus Style. Graphs. A Field Guide to Elementary Functions. Amount Functions and Rate Functions: The Idea of the Derivative. Estimating Derivatives: A Closer Look. The Geometry of Derivatives. The Geometry of Higher-Order Derivatives. Chapter Summary. Interlude: Zooming in on Differences. 2. FUNCTIONS AND DERIVATIVES: THE SYMBOLIC VIEW. Defining the Derivative. Derivatives of Power Functions ad Polynomials. Limits. Derivatives, Antiderivatives, and Their Uses. Differential Equations; Modeling Motion. Derivatives of Exponential and Logarithm Functions; Modeling Growth. Derivatives of Trigonometric Functions; Modeling Oscillation. Chapter Summary. Interlude: Tangent Lines in History. Interlude: Limitthe Formal Definition. 3. NEW DERIVATIVES FROM OLD. Algebraic Combinations: The Product and Quotient Rules. Composition and the Chain Rule. Implicit Functions and Implicit Differentiation. Inverse Functions and their Derivatives; Inverse Trigonometric Functions. Miscellaneous Derivatives and Antiderivatives. Chapter Summary. Interlude: VibrationsSimple and Damped. Interlude: Hyperbolic Functions. 4. USING THE DERIVATIVE. Direction Fields; More on Growth and Motion. Limits Involving Infinity; l'Hôspital's Rule: Comparing Rates. More on Optimization. Parametric Equations. Related Rates. Newton's Method. Linear Approximation and Taylor Polynomials. Continuity. The Mean Value Theorem. Chapter Summary. Interlude: Growth with Interest. Interlude: Logistic Growth. Interlude: Digging Deeper for Roots (More on Newton's Method). 5. THE INTEGRAL. Areas and Integrals. TheArea Function. The Fundamental Theorem of Calculus. Finding Antiderivatives by Substitution. Finding Antiderivatives Using Tables and Computers. Approximating Sums: The Integral as a Limit. Working with Approximating Sums. Chapter Summary. Interlude: Mean Value Theorems and Integrals.