Fundamentals of Calculus
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Fundamentals of Calculus

Fundamentals of Calculus


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About the Book

This book encourages students to use power, quotient, and product rules for solutions as well as stresses the importance of modeling skills. In addition to core integral and differential calculus coverage, the book features finite calculus, which lends itself to modeling and spreadsheets. Specifically, finite calculus is applied to marginal economic analysis, finance, growth, and decay. The book begins with "Linear Equations and Functions, "which reviews basic algebra skills including linear equations, graphing polynomials, factoring, the quadratic formula, and laws of exponents. "The Derivative" uses limits and difference quotients with a simple power rule and introduces concepts of differentiability and continuity and rules for differentiation such as the constant multiple rule, sum rule, and general power rule. "Using the Derivative" applies extrema in word problems to inventory theory and other real-world examples. "Exponential and Logarithmic Functions" reviews logarithmic functions and their derivatives as well as discusses exponential growth decay and decay models. "Techniques of Differentiation" includes implicit differentiation and related rates problems and introduces differentiation modeling for more complex functions including the product rule, quotient rule, chain rule, and its relationship to the general power rule. "Integral Calculus"introduces integration (or antidifferentiation) and features a section in Riemann Sums that reveals the connection between integration and areas between curves. In addition, "Integration Techniques" develops basic techniques of integration including integration by substitution, by parts, and by partial fractions. "Functions of Several Variables"evaluates multivariable functions, level curves for bivariate functions, and extrema of bivariate functions while "Series and Summations" considers infinite series, the integral test, and ratio tests. The book concludes with "Applications of Probability," which features examples of using the Monte Carlo method to either approximate an integral or find a probability, and the expected value and variance of data are determined by calculus techniques.


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Product Details
  • ISBN-13: 9781119015307
  • Publisher: John Wiley & Sons
  • Publisher Imprint: John Wiley & Sons
  • Language: English
  • ISBN-10: 1119015308
  • Publisher Date: 17 Apr 2015
  • Binding: Digital (delivered electronically)
  • No of Pages: 352


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