# Calculus for Scientists and Engineers, Single Variable

##### Description

**For a two-semester or three-quarter calculus course covering single variable calculus for mathematics, engineering, and science majors.**

**Briggs/Cochran** is the most successful new calculus series published in the last two decades. The authors’ years of teaching experience resulted in a text that reflects how students generally use a textbook: they start in the exercises and refer back to the narrative for help as needed. The text therefore builds from a foundation of meticulously crafted exercise sets, then draws students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the rigorous development that follows.

To further support student learning, the MyMathLab course features an eBook with 700 Interactive Figures that can be manipulated to shed light on key concepts. In addition, the *Instructor’s Resource Guide and Test Bank* features quizzes, test items, lecture support, guided projects, and more.

**This book covers chapters single variable topics (chapters 1–12) of*Calculus for Scientists and Engineers,

*which*

*is an expanded version of*Calculus

*by the same authors*.

##### Table of contents

**1. Functions**

1.1 Review of functions

1.2 Representing functions

1.3 Trigonometric functions and their inverses

Review

**2. Limits**

2.1 The idea of limits

2.2 Definitions of limits

2.3 Techniques for computing limits

2.4 Infinite limits

2.5 Limits at infinity

2.6 Continuity

2.7 Precise definitions of limits

Review

**3. Derivatives**

3.1 Introducing the derivative

3.2 Rules of differentiation

3.3 The product and quotient rules

3.4 Derivatives of trigonometric functions

3.5 Derivatives as rates of change

3.6 The Chain Rule

3.7 Implicit differentiation

3.8 Derivatives of inverse trigonometric functions

3.9 Related rates

Review

**4. Applications of the Derivative**

4.1 Maxima and minima

4.2 What derivatives tell us

4.3 Graphing functions

4.4 Optimization problems

4.5 Linear approximation and differentials

4.6 Mean Value Theorem

4.7 L'Hôpital's Rule

4.8 Newton's method

4.9 Antiderivatives

Review

**5. Integration**

5.1 Approximating areas under curves

5.2 Definite integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with integrals

5.5 Substitution rule

Review

**6. Applications of Integration**

6.1 Velocity and net change

6.2 Regions between curves

6.3 Volume by slicing

6.4 Volume by shells

6.5 Length of curves

6.6 Surface area

6.7 Physical applications

6.8 Hyperbolic functions

Review

**7. Logarithmic and Exponential Functions**

7.1 Inverse functions

7.2 The natural logarithm and exponential functions

7.3 Logarithmic and exponential functions with general bases

7.4 Exponential models

7.5 Inverse trigonometric functions

7.6 L'Hôpital's rule and growth rates of functions

Review

**8. Integration Techniques**

8.1 Basic approaches

8.2 Integration by parts

8.3 Trigonometric integrals

8.4 Trigonometric substitutions

8.5 Partial fractions

8.6 Other integration strategies

8.7 Numerical integration

8.8 Improper integrals

Review

**9. Differential Equations**

9.1 Basic ideas

9.2 Direction fields and Euler's method

9.3 Separable differential equations

9.4 Special first-order differential equations

9.5 Modeling with differential equations

Review

**10. Sequences and Infinite Series**

10.1 An overview

10.2 Sequences

10.3 Infinite series

10.4 The Divergence and Integral Tests

10.5 The Ratio, Root, and Comparison Tests

10.6 Alternating series

Review

**11. Power Series**

11.1 Approximating functions with polynomials

11.2 Properties of power series

11.3 Taylor series

11.4 Working with Taylor series

Review

**12. Parametric and Polar Curves**

12.1 Parametric equations

12.2 Polar coordinates

12.3 Calculus in polar coordinates

12.4 Conic sections

Review

##### Features & benefits

- Topics are introduced through
**concrete examples, geometric arguments, applications, and analogies**rather than through abstract arguments. The authors appeal to students’ intuition and geometric instincts to make calculus natural and believable. **Figures**are designed to help today’s visually oriented learners. They are conceived to convey important ideas and facilitate learning, annotated to lead students through the key ideas, and rendered using the latest software for unmatched clarity and precision.**Comprehensive exercise sets**provide for a variety of student needs and are consistently structured and labeled to facilitate the creation of homework assignments by inspection.**Review Questions**check that students have a general conceptual understanding of the essential ideas from the section.**Basic Skills**exercises are linked to examples in the section so students get off to a good start with homework.**Further Explorations**exercises extend students’ abilities beyond the basics.**Applications**present practical and novel applications and models that use the ideas presented in the section.**Additional Exercises**challenge students to stretch their understanding by working through abstract exercises and proofs.**Examples**are plentiful and stepped out in detail. Within examples, each step is annotated to help students understand what took place in that step.**Quick Check**exercises punctuate the narrative at key points to test understanding of basic ideas and encourage students to read with pencil in hand.- The
**MyMathLab**course for the text features the following: **More than 7,000 assignable exercises**provide you with the options you need to meet the needs of students. Most exercises can be algorithmically regenerated for unlimited practice.**Learning aids**include guided exercises, additional examples, and tutorial videos. You control how much help your students can get and when.**700 Interactive Figures**in the eBook can be manipulated to shed light on key concepts. The figures are also ideal for in-class demonstrations.**Interactive Figure Exercises**provide a way for you make the most of the Interactive Figures by including them in homework assignments.- A
**“Getting Ready for Calculus”**chapter, with built-in diagnostic tests, identifies each student’s gaps in skills and provides individual remediation directly to those skills that are lacking. **Ready to Go Courses**designed by experienced instructors to minimize the start-up time for new MyMathLab users.**Guided Projects**, available for each chapter, require students to carry out extended calculations (e.g., finding the arc length of an ellipse), derive physical models (e.g., Kepler’s Laws), or explore related topics (e.g., numerical integration). The “guided” nature of the projects provides scaffolding to help students tackle these more involved problems.- The
**Instructor’s Resource Guide and Test Bank**provides a wealth of instructional resources including Guided Projects, Lecture Support Notes with Key Concepts, Quick Quizzes for each section in the text, Chapter Reviews, Chapter Test Banks, Tips and Help for Interactive Figures, and Student Study Cards. - This book is an expanded version of
**Calculus**by the same authors. It contains an entire chapter devoted to differential equations and additional sections on other topics (Newton’s method, surface area of solids of revolution, and hyperbolic functions). Most sections also contain additional exercises, many of them mid-level skills exercises.

##### Author biography

**William Briggs **has been on the mathematics faculty at the University of Colorado at Denver for twenty-three years. He received his BA in mathematics from the University of Colorado and his MS and PhD in applied mathematics from Harvard University. He teaches undergraduate and graduate courses throughout the mathematics curriculum with a special interest in mathematical modeling and differential equations as it applies to problems in the biosciences. He has written a quantitative reasoning textbook, *Using and Understanding Mathematics; *an undergraduate problem solving book, *Ants, Bikes, and Clocks; *and two tutorial monographs, *The Multigrid Tutorial *and *The DFT: An Owner’s Manual for the Discrete Fourier Transform. *He is the Society for Industrial and Applied Mathematics (SIAM) Vice President for Education, a University of Colorado President’s Teaching Scholar, a recipient of the Outstanding Teacher Award of the Rocky Mountain Section of the Mathematical Association of America (MAA), and the recipient of a Fulbright Fellowship to Ireland.

**Lyle Cochran **is a professor of mathematics at Whitworth University in Spokane, Washington. He holds BS degrees in mathematics and mathematics education from Oregon State University and a MS and PhD in mathematics from Washington State University. He has taught a wide variety of undergraduate mathematics courses at Washington State University, Fresno Pacific University, and, since 1995, at Whitworth University. His expertise is in mathematical analysis, and he has a special interest in the integration of technology and mathematics education. He has written technology materials for leading calculus and linear algebra textbooks including the *Instructor’s Mathematica Manual *for *Linear Algebra and Its Applications *by David C. Lay and the *Mathematica Technology Resource Manual *for *Thomas’ Calculus. *He is a member of the MAA and a former chair of the Department of Mathematics and Computer Science at Whitworth University.

**Bernard Gillett** is a Senior Instructor at the University of Colorado at Boulder; his primary focus is undergraduate education. He has taught a wide variety of mathematics courses over a twenty-year career, receiving five teaching awards in that time. Bernard authored a software package for algebra, trigonometry, and precalculus; the Student’s Guide and Solutions Manual and the Instructor’s Guide and Solutions Manual for *Using and Understanding Mathematics *by Briggs and Bennett; and the Instructor’s Resource Guide and Test Bank for *Calculus *and *Calculus: Early Transcendentals *by Briggs, Cochran, and Gillett. Bernard is also an avid rock climber and has published four climbing guides for the mountains in and surrounding Rocky Mountain National Park.