Fundamentals of Calculus

Description

Features the techniques, methods, and applications of calculus using real-world examples from business and economics as well as the life and social sciences An introduction to differential and integral calculus, Fundamentals of Calculus presents key topics suited for a variety of readers in fields ranging from entrepreneurship and economics to environmental and social sciences. Practical examples from a variety of subject areas are featured throughout each chapter and step-by-step explanations for the solutions are presented. Specific techniques are also applied to highlight important information in each section, including symbols interspersed throughout to further reader comprehension. In addition, the book illustrates the elements of finite calculus with the varied formulas for power, quotient, and product rules that correlate markedly with traditional calculus. Featuring calculus as the “mathematics of change,” each chapter concludes with a historical notes section.  Fundamentals of Calculus chapter coverage includes: Linear Equations and Functions The Derivative Using the Derivative Exponents and Logarithms Differentiation Techniques Integral Calculus Integrations Techniques Functions of Several Variables Series and Summations Applications to Probability Supplemented with online instructional support materials, Fundamentals of Calculus is an ideal textbook for undergraduate students majoring in business, economics, biology, chemistry, and environmental science. Cover Title Page Copyright Contents Preface About the Authors Chapter 1 Linear Equations and Functions 1.1 Solving Linear Equations 1.2 Linear Equations and their Graphs 1.3 Factoring and the Quadratic Formula 1.4 Functions and their Graphs 1.5 Laws of Exponents 1.6 Slopes and Relative Change Chapter 2 The Derivative 2.1 Slopes of Curves 2.2 Limits 2.3 Derivatives 2.4 Differentiability and Continuity 2.5 Basic Rules of Differentiation 2.6 Continued Differentiation 2.7 Introduction to Finite Differences Chapter 3 Using The Derivative 3.1 Describing Graphs 3.2 First and Second Derivatives 3.3 Curve Sketching 3.4 Applications of Maxima and Minima 3.5 Marginal Analysis Chapter 4 Exponential and Logarithmic Functions 4.1 Exponential Functions 4.2 Logarithmic Functions 4.3 Derivatives of Exponential Functions 4.4 Derivatives of Natural Logarithms 4.5 Models of Exponential Growth and Decay 4.6 Applications to Finance Chapter 5 Techniques of Differentiation 5.1 Product and Quotient Rules 5.2 The Chain Rule and General Power Rule 5.3 Implicit Differentiation and Related Rates 5.4 Finite Differences and Antidifferences Chapter 6 Integral Calculus 6.1 Indefinite Integrals 6.2 Riemann Sums 6.3 Integral Calculus - The Fundamental Theorem 6.4 Area Between Intersecting Curves Chapter 7 Techniques of Integration 7.1 Integration by Substitution 7.2 Integration by Parts 7.3 Evaluation of Definite Integrals 7.4 Partial Fractions 7.5 Approximating Sums 7.6 Improper Integrals Chapter 8 Functions of Several Variables 8.1 Functions of Several Variables 8.2 Partial Derivatives 8.3 Second-Order Partial Derivatives - Maxima and Minima 8.4 Method of Least Squares 8.5 Lagrange Multipliers 8.6 Double Integrals Chapter 9 Series and Summations 9.1 Power Series 9.2 Maclaurin and Taylor Polynomials 9.3 Taylor and Maclaurin Series 9.4 Convergence and Divergence of Series 9.5 Arithmetic and Geometric Sums Chapter 10 Applications to Probability 10.1 Discrete and Continuous Random Variables 10.2 Mean and Variance; Expected Value 10.3 Normal Probability Density Function Answers to Odd Numbered Exercises Index Derivatives Integrals EULA