Drawing on their decades of teaching experience, William Briggs and Lyle Cochran have created a calculus text that carries the teacher's voice beyond the classroom. That voice-evident in the narrative, the figures, and the questions interspersed in the narrative-is a master teacher leading readers to deeper levels of understanding. The authors appeal to readers' geometric intuition to introduce fundamental concepts and lay the foundation for the more rigorous development that follows. Comprehensive exercise sets have received praise for their creativity, quality, and scope.
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1. Functions 1.1 Review of Functions 1.2 Representing Functions1.3 Inverse, Exponential, and Logarithm Functions1.4 Trigonometric Functions and Their Inverses 2. Limits2.1 The Idea of Limits2.2 Definitions of Limits2.3 Techniques for Computing Limits 2.4 Infinite Limits 2.5 Limits at Infinity 2.6 Continuity2.7 Precise Definitions of Limits 3. Derivatives 3.1 Introducing the Derivative3.2 Rules of Differentiation3.3 The Product and Quotient Rules3.4 Derivatives of Trigonometric Functions 3.5 Derivatives as Rates of Change 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Logarithmic and Exponential Functions3.9 Derivatives of Inverse Trigonometric Functions3.10 Related Rates 4. Applications of the Derivative4.1 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'Hopital's Rule 4.8 Antiderivatives 5. Integration5.1 Approximating Areas under Curves5.2 Definite Integrals 5.3 Fundamental Theorem of Calculus 5.4 Working with Integrals 5.5 Substitution Rule 6. Applications of Integration6.1 Velocity and Net Change6.2 Regions between Curves6.3 Volume by Slicing6.4 Volume by Shells6.5 Length of Curves6.6 Physical Applications6.7 Logarithmic and exponential functions revisited6.8 Exponential models 7. Integration Techniques7.1 Integration by Parts 7.2 Trigonometric Integrals 7.3 Trigonometric Substitution7.4 Partial Fractions 7.5 Other Integration Strategies7.6 Numerical Integration7.7 Improper Integrals7.8 Introduction to Differential Equations 8. Sequences and Infinite Series8.1 An Overview 8.2 Sequences8.3 Infinite Series 8.4 The Divergence and Integral Tests8.5 The Ratio and Comparison Tests8.6 Alternating Series 9. Power Series9.1 Approximating Functions with Polynomials9.2 Power Series 9.3 Taylor Series 9.4 Working with Taylor Series 10. Parametric and Polar Curves 10.1 Parametric Equations10.2 Polar Coordinates 10.3 Calculus in Polar Coordinates 10.4 Conic Sections 11. Vectors and Vector-Valued Functions11.1 Vectors in the Plane11.2 Vectors in Three Dimensions11.3 Dot Products11.4 Cross Products11.5 Lines and Curves in Space 11.6 Calculus of Vector-Valued Functions 11.7 Motion in Space11.8 Length of Curves11.9 Curvature and Normal Vectors 12. Functions of Several Variables12.1 Planes and Surfaces12.2 Graphs and Level Curves12.3 Limits and Continuity12.4 Partial Derivatives12.5 The Chain Rule 12.6 Directional Derivatives and the Gradient12.7 Tangent Planes and Linear Approximation12.8 Maximum/Minimum Problems12.9 Lagrange Multipliers 13. Multiple Integration13.1 Double Integrals over Rectangular Regions13.2 Double Integrals over General Regions13.3 Double Integrals in Polar Coordinates13.4 Triple Integrals13.5 Triple Integrals in Cylindrical and Spherical Coordinates13.6 Integrals for Mass Calculations13.7 Change of Variables in Multiple Integrals 14. Vector Calculus14.1 Vector Fields14.2 Line Integrals14.3 Conservative Vector Fields14.4 Green's Theorem14.5 Divergence and Curl14.6 Surface Integrals14.7 Stokes' Theorem14.8 Divergence Theorem
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Produktdetaljer

ISBN
9780321570567
Publisert
2010-02-05
Utgiver
Vendor
Pearson
Vekt
2440 gr
Høyde
280 mm
Bredde
222 mm
Dybde
49 mm
Aldersnivå
05, U
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
1216

Biographical note

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.