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Calculus for Scientists and Engineers William Briggs

Calculus for Scientists and Engineers By William Briggs

Calculus for Scientists and Engineers by William Briggs


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Calculus for Scientists and Engineers Summary

Calculus for Scientists and Engineers by William Briggs

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.

About William Briggs

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.

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'Hopital'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'Hopital'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 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 Review 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 Review 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 Review 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 Review

Additional information

CIN0321826698G
9780321826695
0321826698
Calculus for Scientists and Engineers by William Briggs
Used - Good
Hardback
Pearson Education (US)
20120807
1344
N/A
Book picture is for illustrative purposes only, actual binding, cover or edition may vary.
This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

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