Calculus with Applications, Global Edition

About our authors Marge Lial  (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received bachelor's and master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.Raymond N. Greenwell  earned a B.A. in Mathematics and Physics from the University of San Diego, and an M.S. in Statistics, an M.S. in Applied Mathematics, and a Ph.D. in Applied Mathematics from Michigan State University, where he earned the graduate student teaching award in 1979. After teaching at Albion College in Michigan for 4 years, he moved to Hofstra University in 1983, where he currently is Professor of Mathematics.Raymond has published articles on fluid mechanics, mathematical biology, genetic algorithms, combinatorics, statistics, and undergraduate mathematics education. He is a member of MAA, AMS, SIAM, NCTM, and AMATYC. He has served as governor of the Metropolitan New York Section of the MAA, as well as webmaster and liaison coordinator, and he received a distinguished service award from the Section in 2003. He is an outdoor enthusiast and leads trips in the Sierra Club's Inner City Outings program.Nathan P. Ritchey  earned a B.A. in Mathematics with a minor in Music from Mansfield University of Pennsylvania. He earned a M.S. in Applied Mathematics and a Ph.D. in Mathematics from Carnegie Mellon University. He is former chair of the Department of Mathematics and Statistics at Youngstown State University and is currently serving as the dean of the College of Science and Health Professions at Edinboro University. He has published articles in economics, honors education, medicine, mathematics, operations research, and student recruitment. Nate is a Consultant/Evaluator for the North Central Association's Higher Learning Commission and regularly participates in program evaluations.In recognition of his numerous activities, Nate has received the Distinguished Professor Award for University Service, the Youngstown Vindicator's "People Who Make a Difference Award," the Watson Merit Award for Department Chairs, the Spirit in Education Award from the SunTex corporation, and the Provost's Merit Award for significant contributions to the Honors Program. Katherine Ritchey earned a B.A. in Mathematics from the University of Notre Dame. She earned a Ph.D. in Mathematics from The Ohio State University, and her research interests include combinatorics and graph theory. While at OSU, she began her lifelong dream of teaching mathematics and was awarded several graduate student teaching awards. She is currently an Assistant Professor of Mathematics at the University of Mount Union in Ohio. Blain A. Patterson earned a B.S. in Mathematics Education with a minor in Mathematics from Youngstown State University. He earned both a M.S. and Ph.D. in Mathematics Education from North Carolina State University. He is currently an Assistant Professor of Applied Mathematics at Virginia Military Institute. He has published articles in various mathematics and education journals on mathematics teacher education, learning disabilities, middle school mathematics education, and cryptography. Blain is currently a Project NExT Fellow (Brown '20) and an active member of MAA, SIAM, SIMIODE and AWM. When he is not thinking about mathematics, Blain enjoys spending time outdoors with his dogs and playing board games. Sarah Ritchey Patterson earned a B.S. in Mathematics and Computer Science from Youngstown State University. She earned a Ph.D. in Mathematics from Duke University. Sarah is currently an assistant professor at the Virginia Military Institute. Her research interests include computational fluid dynamics, fluid-structure interaction problems, and mathematical modeling. Sarah actively advises undergraduate research projects and uses this perspective to enhance her teaching and the textbook.

• Preface Prerequisite Skills Diagnostic Test  R. Algebra Reference R.1 Polynomials R.2 Factoring R.3 Rational Expressions R.4 Equations R.5 Inequalities R.6 Exponents R.7 Radicals 1. Linear Functions 1.1 Slopes and Equations of Lines 1.2 Linear Functions and Applications 1.3 The Least Squares Line Chapter 1 Review Extended Application: Predicting Life Expectancy  2. Nonlinear Functions2.1 Properties of Functions 2.2 Quadratic Functions; Translation and Reflection 2.3 Polynomial and Rational Functions 2.4 Exponential Functions 2.5 Logarithmic Functions 2.6 Applications: Growth and Decay; Mathematics of Finance Chapter 2 Review Extended Application: Power Functions  3. The Derivative3.1 Limits 3.2 Continuity 3.3 Rates of Change 3.4 Definition of the Derivative 3.5 Graphical Differentiation Chapter 3 Review Extended Application: A Model for Drugs Administered Intravenously  4. Calculating the Derivative4.1 Techniques for Finding Derivatives 4.2 Derivatives of Products and Quotients 4.3 The Chain Rule 4.4 Derivatives of Exponential Functions 4.5 Derivatives of Logarithmic Functions Chapter 4 Review Extended Application: Electric Potential and Electric Field  5. Graphs and the Derivative5.1 Increasing and Decreasing Functions 5.2 Relative Extrema 5.3 Higher Derivatives, Concavity, and the Second Derivative Test 5.4 Curve Sketching Chapter 5 Review Extended Application: A Drug Concentration Model for Orally Administered Medications  6. Applications of the Derivative6.1 Absolute Extrema 6.2 Applications of Extrema 6.3 Further Business Applications 6.4 Implicit Differentiation 6.5 Related Rates 6.6 Differentials: Linear Approximation Chapter 6 Review Extended Application: A Total Model for a Training Program  7. Integration7.1 Antiderivatives 7.2 Substitution 7.3 Area and the Definite Integral 7.4 The Fundamental Theorem of Calculus 7.5 The Area Between Two Curves 7.6 Numerical Integration Chapter 7 Review Extended Application Estimating Depletion Dates for Minerals  8. Further Techniques and Applications of Integration8.1 Integration by Parts 8.2 Volume and Average Value 8.3 Continuous Money Flow 8.4 Improper Integrals Chapter 8 Review Extended Application: Estimating Learning Curves in Manufacturing With Integrals  9. Multivariable Calculus9.1 Functions of Several Variables 9.2 Partial Derivatives 9.3 Maxima and Minima 9.4 Lagrange Multipliers 9.5 Total Differentials and Approximations 9.6 Double Integrals Chapter 9 Review Extended Application: Using Multivariable Fitting to Create a Response Surface Design  10. Differential Equations10.1 Solutions of Elementary and Separable Differential Equations 10.2 Linear First-Order Differential Equations 10.3 Euler's Method 10.4 Applications of Differential Equations Chapter 10 Review Extended Application: Pollution of the Great Lakes 11. Probability and Calculus11.1 Continuous Probability Models 11.2 Expected Value and Variance of Continuous Random Variables 11.3 Special Probability Density Functions Chapter 11 Review Extended Application Exponential Waiting Times  12. Sequences and Series12.1 Geometric Sequences 12.2 Annuities: An Application of Sequences 12.3 Taylor Polynomials at 0 12.4 Infinite Series 12.5 Taylor Series at 0 12.6 Newton's Method 12.7 L'Hôpital's Rule Chapter 12 Review Extended Application: Living Assistance and Subsidized Housing  13. The Trigonometric Functions13.1 Definitions of the Trigonometric Functions 13.2 Derivatives of Trigonometric Functions 13.3 Integrals of Trigonometric Functions Chapter 13 Review Extended Application: The Shortest Time and the Cheapest Path  Appendix  Solutions to Prerequisite Skills Diagnostic Test Tables Complete Instructor Answers Credits Index of Applications Index Sources