Calculus & Its Applications, Global Edition

Larry J. Goldstein / David I. Schneider / David C. Lay / Nakhle H. Asmar  
Total pages
April 2018
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Calculus & Its Applications, Global Edition
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Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums.

The strategic organisation of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.


The student-oriented presentation enables them to study and learn independently, while showing them how the concepts apply to their future careers.

  • In the 14th edition, the author revised examples to more closely align with exercises sets.
  • Relevant and varied applications contain real data and provide a realistic look at how calculus applies to other disciplines and everyday life. Whenever possible, applications are used to motivate the mathematics. The variety of applications is evident in the Index of Applications.
  • Time-tested exercise sets give instructors flexibility when building assignments, with exercises sorted by level and exercises that encourage students to use technology to solve problems. In the 14th Edition, 225 new exercises and 30 worked examples are added, bringing the total to 4,200 exercises and 520 examples.
  • Just-in-time support throughout the chapters helps students of all skill levels study more efficiently.
  • Prerequisite Skills Diagnostic Test within the text helps students gauge their level of readiness for this course.
  • 350 worked-out examples provide support for students as they work exercises and learn the content.
  • “Help text” within examples (shown in blue type) helps students understand key algebraic and numerical transitions.
  • “For Review”side margin features remind students of a concept that is needed and direct them back to the section in which it was covered earlier in the text.
  • “Now Try” Exercises appear after select examples, mirroring how an instructor might stop in class to ask students to try a problem, allowing them to immediately apply their understanding.
  • Check Your Understanding problems appear at the end of each section to prepare students for the exercise sets, encouraging them to reflect on what they’ve learned before applying it further.
  • End-of-Chapter study aids help students recall key ideas and focus on the relevance of these concepts.
  • Integrating Technology features within sections allow students to incorporate technology into the learning process, including graphing calculators.
  • In the 14th Edition, graphing calculator screens have been updated to the TI-84 Plus CE format and are now in colour.

Table of Contents

  • 0. Functions
  • 0.1 Functions and Their Graphs
  • 0.2 Some Important Functions
  • 0.3 The Algebra of Functions
  • 0.4 Zeros of Functions - The Quadratic Formula and Factoring
  • 0.5 Exponents and Power Functions
  • 0.6 Functions and Graphs in Applications
  • 1. The Derivative
  • 1.1 The Slope of a Straight Line
  • 1.2 The Slope of a Curve at a Point
  • 1.3 The Derivative and Limits
  • 1.4 Limits and the Derivative
  • 1.5 Differentiability and Continuity
  • 1.6 Some Rules for Differentiation
  • 1.7 More About Derivatives
  • 1.8 The Derivative as a Rate of Change
  • 2. Applications of the Derivative
  • 2.1 Describing Graphs of Functions
  • 2.2 The First and Second Derivative Rules
  • 2.3 The First and Section Derivative Tests and Curve Sketching
  • 2.4 Curve Sketching (Conclusion)
  • 2.5 Optimization Problems
  • 2.6 Further Optimization Problems
  • 2.7 Applications of Derivatives to Business and Economics
  • 3. Techniques of Differentiation
  • 3.1 The Product and Quotient Rules
  • 3.2 The Chain Rule
  • 3.3 Implicit Differentiation and Related Rates
  • 4. The Exponential and Natural Logarithm Functions
  • 4.1 Exponential Functions
  • 4.2 The Exponential Function ex
  • 4.3 Differentiation of Exponential Functions
  • 4.4 The Natural Logarithm Function
  • 4.5 The Derivative of ln x 4.6 Properties of the Natural Logarithm Function
  • 5. Applications of the Exponential and Natural Logarithm Functions
  • 5.1 Exponential Growth and Decay
  • 5.2 Compound Interest
  • 5.3. Applications of the Natural Logarithm Function to Economics
  • 5.4. Further Exponential Models
  • 6. The Definite Integral
  • 6.1 Anti-differentiation
  • 6.2 The Definite Integral and Net Change of a Function
  • 6.3 The Definite Integral and Area Under a Graph
  • 6.4 Areas in the xy-Plane
  • 6.5 Applications of the Definite Integral
  • 7. Functions of Several Variables
  • 7.1 Examples of Functions of Several Variables
  • 7.2 Partial Derivatives
  • 7.3 Maxima and Minima of Functions of Several Variables
  • 7.4 Lagrange Multipliers and Constrained Optimization
  • 7.5 The Method of Least Squares
  • 7.6 Double Integrals
  • 8. The Trigonometric Functions
  • 8.1 Radian Measure of Angles
  • 8.2 The Sine and the Cosine
  • 8.3 Differentiation and Integration of sin t and cos t
  • 8.4 The Tangent and Other Trigonometric Functions
  • 9. Techniques of Integration
  • 9.1 Integration by Substitution
  • 9.2 Integration by Parts
  • 9.3 Evaluation of Definite Integrals
  • 9.4 Approximation of Definite Integrals
  • 9.5 Some Applications of the Integral
  • 9.6 Improper Integrals
  • 10. Differential Equations
  • 10.1 Solutions of Differential Equations
  • 10.2 Separation of Variables
  • 10.3 First-Order Linear Differential Equations
  • 10.4 Applications of First-Order Linear Differential Equations
  • 10.5 Graphing Solutions of Differential Equations
  • 10.6 Applications of Differential Equations
  • 10.7 Numerical Solution of Differential Equations
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Larry Goldstein has received several distinguished teaching awards, given more than fifty Conference and Colloquium talks & addresses, and written more than fifty books in math and computer programming.  He received his PhD at Princeton and his BA and MA at the University of Pennsylvania. He also teaches part time at Drexel University.


David Lay holds a BA from Aurora University (Illinois), and an MA and PhD from the University of California at Los Angeles. David Lay has been an educator and research mathematician since 1966, mostly at the University of Maryland, College Park. He has published more than 30 research articles on functional analysis and linear algebra, and he has written several popular textbooks. Lay has received four university awards for teaching excellence, including, in 1996, the title of Distinguished Scholar—Teacher of the University of Maryland. In 1994, he was given one of the Mathematical Association of America’s Awards for Distinguished College or University Teaching of Mathematics. Since 1992, he has served several terms on the national board of the Association of Christians in the Mathematical Sciences.


David Schneider, who is known widely for his tutorial software, holds a BA degree from Oberlin College and a PhD from MIT. He is currently an associate professor of mathematics at the University of Maryland. He has authored eight widely used math texts, fourteen highly acclaimed computer books, and three widely used mathematics software packages. He has also produced instructional videotapes at both the University of Maryland and the BBC.


Nakhle Asmar received his PhD from the University of Washington. He is currently a professor of mathematics and Chair of the Mathematics Department at the University of Missouri, Columbia. He is the author and coauthor of widely used calculus texts as well as textbooks on complex analysis, partial differential equations and Fourier series. He has received several awards for outstanding teaching. His popular textbooks have been translated into Chinese and Portuguese.