Opis: Calculus - Lyle Cochran, William Briggs, Bill Briggs

For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw 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 development that follows. The groundbreaking eBook contains over 650 Interactive Figures that can be manipulated to shed light on key concepts. This text offers a superior teaching and learning experience. Here's how: *Reflects how students use a textbook-they start with the exercises and flip back for help if they need it. *Organization and presentation of content facilitates learning of key concepts, skills, and applications.1. Functions 1.1 Review of functions 1.2 Representing functions 1.3 Trigonometric functions 1.4 Trigonometric functions 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 3. Derivatives 3.1 Introducing the derivative 3.2 Working with derivatives 3.3 Rules of differentiation 3.4 The product and quotient rules 3.5 Derivatives of trigonometric functions 3.6 Derivatives as rates of change 3.7 The Chain Rule 3.8 Implicit differentiation 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'Hopital's Rule 4.8 Newton's Method 4.9 Antiderivatives 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 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 7. Logarithmic and Exponential Functions 7.1 Inverse functions 7.2 The natural logarithmic and exponential functions 7.3 Logarithmic and exponential functions with other bases 7.4 Exponential models 7.5 Inverse trigonometric functions 7.6 L' Hopital's Rule and growth rates of functions 7.7 Hyperbolic 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 8.9 Introduction to differential equations 9. Sequences and Infinite Series 9.1 An overview 9.2 Sequences 9.3 Infinite series 9.4 The Divergence and Integral Tests 9.5 The Ratio, Root, and Comparison Tests 9.6 Alternating series 10. Power Series 10.1 Approximating functions with polynomials 10.2 Properties of Power series 10.3 Taylor series 10.4 Working with Taylor series 11. Parametric and Polar Curves 11.1 Parametric equations 11.2 Polar coordinates 11.3 Calculus in polar coordinates 11.4 Conic sections 12. Vectors and Vector-Valued Functions 12.1 Vectors in the plane 12.2 Vectors in three dimensions 12.3 Dot products 12.4 Cross products 12.5 Lines and curves in space 12.6 Calculus of vector-valued functions 12.7 Motion in space 12.8 Length of curves 12.9 Curvature and normal vectors 13. Functions of Several Variables 13.1 Planes and surfaces 13.2 Graphs and level curves 13.3 Limits and continuity 13.4 Partial derivatives 13.5 The Chain Rule 13.6 Directional derivatives and the gradient 13.7 Tangent planes and linear approximation 13.8 Maximum/minimum problems 13.9 Lagrange multipliers 14. Multiple Integration 14.1 Double integrals over rectangular regions 14.2 Double integrals over general regions 14.3 Double integrals in polar coordinates 14.4 Triple integrals 14.5 Triple integrals in cylindrical and spherical coordinates 14.6 Integrals for mass calculations 14.7 Change of variables in multiple integrals 15. Vector Calculus 15.1 Vector fields 15.2 Line integrals 15.3 Conservative vector fields 15.4 Green's theorem 15.5 Divergence and curl 15.6 Surface integrals 15.6 Stokes' theorem 15.8 Divergence theorem Appendix A. Algebra Review Appendix B. Proofs of Selected Theorems D1 Differential Equations (online) D1.1 Basic Ideas D1.2 Direction Fields and Euler's Method D1.3 Separable Differential Equations D1.4 Special First-Order Differential Equations D1.5 Modeling with Differential Equations D2 Second-Order Differential Equations (online) D2.1 Basic Ideas D2.2 Linear Homogeneous Equations D2.3 Linear Nonhomogeneous Equations D2.4 Applications D2.5 Complex Forcing Functions

Szczegóły: Calculus - Lyle Cochran, William Briggs, Bill Briggs

Tytuł: Calculus
Autor: Lyle Cochran, William Briggs, Bill Briggs
Producent: Pearson
ISBN: 9781292062327
Rok produkcji: 2014
Ilość stron: 1328
Oprawa: Miękka
Waga: 3.22 kg

Recenzje: Calculus - Lyle Cochran, William Briggs, Bill Briggs