Title: Calculus and analytic geometry. Second edition
Abstract:This book presents the details of calculus and analytic geometry. The topics covered are: Introduction. Real Numbers. Graphing. The Straight Line. Functions and Their Graphs. Operations on Functions; ...This book presents the details of calculus and analytic geometry. The topics covered are: Introduction. Real Numbers. Graphing. The Straight Line. Functions and Their Graphs. Operations on Functions; Types of Functions. Composite Functions. Inverse Functions. Limits from an Intuitive Point of View. Algebraic Techniques for Finding Limits. One-Sided Limits. Continuous Functions. Limit Theorems (If Time Permits). Historical Perspectives. The Derivative. Average Rate of Change. Instantaneous Rate of Change; the Derivative. Two Interpretations of the Derivative Formulas for Finding Derivatives. Formulas for Finding Derivatives (Continued). Higher-Order Derivatives. Derivatives of Trigonometric Functions. The Chain Rule. Implicit Differentiation. Derivative of an Inverse Function; Rational Exponents. Newton's Method of Solving Equations. Functions that are not Differentiable at c., Applications of the Derivative. Related Rates. Differentials. Maxima and Minima. Rolle's Theorem; Mean Value Theorem. Increasing and Decreasing Functions; First Derivative Test. Concavity; Second Derivative Test. Limits at Infinity; Infinite Limits; Asymptotes. Applied Extrema Problems. Antiderivatives. Application to Economics (If Time Permits), The Definite Integral. Area. Evaluation of Area. The Definite Integral. The Fundamental Theorem of Calculus. Properties of the Definite Integral. The Indefinite Integral; Method of Substitution. Historical Perspectives. Applications of the Integral. Area. Volume of a Solid of Revolution: Disk Method. Volume of amore » Solid of Revolution: Shell Method. Volume by Slicing. Arc Length. Work. Liquid Pressure and Force. Average Value of a Function.« lessRead More
Publication Year: 1986
Publication Date: 1986-01-01
Language: en
Type: article
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot