# Calculus & Its Applications, Global Edition (14e)

##### Description

** 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.

##### 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
**11. Taylor Polynomials and Infinite Series**- 11.1 Taylor Polynomials
- 11.2 The Newton-Raphson Algorithm
- 11.3 Infinite Series
- 11.4 Series with Positive Terms
- 11.5 Taylor Series
**12. Probability and Calculus**- 12.1 Discrete Random Variables
- 12.2 Continuous Random Variables
- 12.3 Expected Value and Variance
- 12.4 Exponential and Normal Random Variables
- 12.5 Poisson and Geometric Random Variables

##### New to this edition

**New to the Book**

**M****ore intuitive organization and explanation within examples**makes properties and theorems easier to follow and recall.- 225 new exercises and 30 worked examples have been added, bringing the total to 4,200 exercises and 520 examples.
**“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.-
**Graphing calculator screens have been updated**to the TI-84 Plus CE format and are now in color. - All
**3-dimensional figures in the text have been re-rendered**using the latest software. The authors took full advantage of the capabilities of the rendering software to make the figures more effective pedagogically. - In cases where properties or theorems that were formerly numbered (e.g., Property 4) have a commonly used name (e.g., Power of a Quotient Rule), the authors used the name rather than the number. This allows for more intuitive explanations within examples and is better aligned to how concepts are explained in class.

**Content Updates**

**Chapter 0**

- Added an example and exercises in 0.1 to illustrate the concept of piecewise-defined functions.
- Rewrote and simplified the introduction to 0.5 Exponents and Power Functions to make it more intuitive and easier to reference. Additionally, we added several examples to illustrate the rules of exponents.
- Modified the discussion of compound interest to make it more suitable for the applications in later chapters.
- Added Examples 8 and 9 in 0.5 to illustrate the role of multiple factors in compound interest and investment accounts.
- Added Example 7 in 0.6 to illustrate various concepts from economics.
- Added four new exercises (45-48) in 0.6 to illustrate variations on the standard topic of compound interest.
- Modified over thirty exercises in the chapter.

**Chapter 1**

- Removed some of the proofs related to review material to simplify the presentation in 1.1.
- Added four new exercises (5-8) in 1.2 to illustrate the geometric meaning of the slope of a graph as the slope of the tangent line. Additionally, we modified two other exercises requiring reading and interpreting slopes of graphs.
- Simplified the discussion of limits in Examples 2 and 4 in 1.4.
- Included a discussion and a new Example 4 in 1.8 to illustrate the concepts of displacement and velocity.

**Chapters 2 and 3**

- Modified the Technology Exercises in 2.1 to make them more straightforward for students to answer.
- Improved and simplified the solutions within Example 4 in 2.4.
- Removed Example 4 in 2.6 which required more symbolic manipulation and use of constants than students would encounter in the exercises.
- Rewrote five examples in the Summary section of Chapter 2.
- Added ten new exercises in Chapter 3.

**Chapter 4**

- Revised Example 2 in 4.2 to better prepare students for the variety of exercises within the homework.
- Moved the material on the properties and graphs of exponential functions from 4.3 to 4.2.
- Replaced Examples 1, 2, and 3 from 4.3 with new examples that better build on the properties of derivatives introduced earlier. Example 3 introduces a new concept of combined returns to illustrate applications of linear combinations of exponential functions.
- Moved the material on differential equations in 4.3 to Chapter 5.
- Introduced forty new exercises in 4.3, including one on investment portfolios.
- Rewrote the introduction of 4.4 to better display and present the properties of logarithms.
- Changed Example 1 in 4.4 to better match the types of exercises in the homework.
- Used investment portfolios to illustrate applications involving solutions of equations with logarithms in Example 4 in 4.4.
- Rewrote the introduction of 4.5 to better display properties of the natural logarithm and its derivative.
- Added a new example on differentiation of the natural logarithm in 4.5.
- Modified and added over twenty exercises in 4.5.
- Rewrote the introduction of 4.6 to better present further properties of the logarithm.

**Chapter 5**

- Rewrote 5.1 to better show the applications of the derivative as a rate of change in setting up and solving differential equations. Changes to 5.1 also include:
- Stated the solutions of the differential equation
*y*′ =*ky*in a theorem. - Added an example on solving differential equations.
- Stated the solutions of the initial value problem
*y*′ =*ky*,*y*(0)=*P*_{0}in a theorem. - Illustrated the solutions of initial value problems with examples and a figure that a student can easily relate to.
- Simplified the discussion on exponential decay and carbon dating.
- Added twenty-three new exercises on differential equations and their applications.
- Rewrote and simplified the introduction to 5.2. Also in 5.2:
- Introduced continuous compounding as a limit of the ordinary compounding from Chapter 0 and as a solution of a differential equation of the type that was discussed in 5.1.
- Added narrative that compares continuous to ordinary compounding.
- Added discussion, an example, and exercises on negative interest rates.
- Rewrote the introduction to 5.3 to better explain the concept of relative rate of change and how it relates to common pricing applications.
- Added an example in 5.3 on logarithmic derivatives.
- Included a summary of solutions of differential equations and their properties in the Chapter Summary.

**Chapter 6**

- Simplified Example 1 in 6.1 by adding more details to the solution.
- Rewrote the introduction to 6.2 and simplified the presentation by relating the new concept of definite integral to a common problem involving velocity and position.
- Simplified the numerical computations in Examples 3 and 5 in 6.2.
- Added nine new exercises to 6.2.
- Added a new example on online transportation in 6.4, as an application of area between two curves.

**Chapter 7**

- Revised all 3-dimensional figures in the chapter using the latest software.
- Added more help to Example 1 in 7.2 and added a 3-dimensional graph.
- In Example 4 in 7.3, added a new application of the second derivative test in two dimensions.
- Added twenty new exercises to 7.2, ten new exercises to 7.4, and two new exercises to 7.5.

**Chapters 8-12**

- Removed the application on population genetics from 10.6 (as this is now covered in Chapter 5).
- Revised exercises and examples to update real-world data.

**Also available with MyLab Math**

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

**New to **MyLab Math

- Many improvements have been made to the overall functionality of MyLab Math since the previous edition. However, beyond that, we have also increased and improved the content specific to this text.
**Setup & Solve exercises**require students to first describe how they will set up and approach the problem. This reinforces conceptual understanding of the process applied in approaching the problem, promotes long term retention of the skill and mirrors what students will be expected to do on a test.**Conceptual Question Library exercises**provide additional conceptual, application-focused questions for instructors to use on homework or assessments.**MathTalk videos**connect the math to the real world (particularly business). The videos include assignable exercises to gauge students’ understanding of video content.**Interactive Figures**illustrate key concepts and allow manipulation for use as teaching and learning tools. These are now in HTML format (no plug-in required) and are supported by assignable exercises and tutorial videos.**Over 275 Example-based videos**, 97 of which are new to this edition, are available as learning aids within exercises and for self-study. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which MyLab Math exercises correspond to each video.**Skills for Success Modules**help students with the life skills that can make the difference between passing and failing.- An
**Integrated Review MyLab Math course**contains pre-made quizzes to assess the prerequisite skills needed for each chapter, plus personalized remediation for any gaps in skills that are identified. **Graphing Calculator and Excel Spreadsheet Manuals,**specific to this course, are now downloadable from MyMathLab.**Instructor’s Answers document**(downloadable from MyLab Math) provides all answers in one place and augments the downloadable Instructor’s Solutions Manual, which contains all solutions.

##### Features & benefits

- 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.

##### Author biography

**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.