Calculus for Scientists and EngineersInternational Edition
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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.
* This book is an expanded version of Calculus by the same authors, with an entire chapter devoted to differential equations, additional sections on other topics, and additional exercises in most sections. See the “Features” section for more details.
1.1 Review of functions
1.2 Representing functions
1.3 Trigonometric functions and their inverses
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
2.7 Precise definitions of limits
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
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
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
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
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
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
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
10. Sequences and Infinite Series
10.1 An overview
10.3 Infinite series
10.4 The Divergence and Integral Tests
10.5 The Ratio, Root, and Comparison Tests
10.6 Alternating series
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
12. Parametric and Polar Curves
12.1 Parametric equations
12.2 Polar coordinates
12.3 Calculus in polar coordinates
12.4 Conic sections
13. Vectors and Vector-Valued Functions
13.1 Vectors in the plane
13.2 Vectors in three dimensions
13.3 Dot products
13.4 Cross products
13.5 Lines and curves in space
13.6 Calculus of vector-valued functions
13.7 Motion in space
13.8 Length of curves
13.9 Curvature and normal vectors
14. Functions of Several Variables
14.1 Planes and surfaces
14.2 Graphs and level curves
14.3 Limits and continuity
14.4 Partial derivatives
14.5 The Chain Rule
14.6 Directional derivatives and the gradient
14.7 Tangent planes and linear approximation
14.8 Maximum/minimum problems
14.9 Lagrange multipliers
15. Multiple Integration
15.1 Double integrals over rectangular regions
15.2 Double integrals over general regions
15.3 Double integrals in polar coordinates
15.4 Triple integrals
15.5 Triple integrals in cylindrical and spherical coordinates
15.6 Integrals for mass calculations
15.7 Change of variables in multiple integrals
16. Vector Calculus
16.1 Vector fields
16.2 Line integrals
16.3 Conservative vector fields
16.4 Green's theorem
16.5. Divergence and curl
16.6 Surface integrals
16.6 Stokes' theorem
16.8 Divergence theorem
- 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.
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.