Opis: Calculus for Scientists and Engineers - Eric Schulz, Bernard Gillett, Lyle Cochran

For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors. Briggs/Cochran is the most successful new calculus series published in the last two decades. The authors' decades of teaching experience resulted in a text that reflects how students generally use a textbook-i.e., 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 is an expanded version of Calculus: Early Transcendentalsby 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. Functions 1.1 Review of functions 1.2 Representing functions 1.3 Inverse, exponential, and logarithmic functions 1.4 Trigonometric functions and their inverses 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 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 logarithmic and exponential functions 3.9 Derivatives of inverse trigonometric functions 3.10 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 6.8 Logarithmic and exponential functions revisited 6.9 Exponential models 6.10 Hyperbolic functions 7. Integration Techniques 7.1 Integration Strategies 7.2 Integration by parts 7.3 Trigonometric integrals 7.4 Trigonometric substitutions 7.5 Partial fractions 7.6 Other integration strategies 7.7 Numerical integration 7.8 Improper integrals 8. Differential Equations 8.1 Basic ideas 8.2 Direction fields and Euler's method 8.3 Separable differential equations 8.4 Special first-order differential equations 8.5 Modeling with 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 Appendix A. Algebra Review Appendix B. Proofs of Selected Theorems

Szczegóły: Calculus for Scientists and Engineers - Eric Schulz, Bernard Gillett, Lyle Cochran

Tytuł: Calculus for Scientists and Engineers
Autor: Eric Schulz, Bernard Gillett, Lyle Cochran
Producent: Pearson
ISBN: 9781292024806
Rok produkcji: 2013
Ilość stron: 1696
Oprawa: Miękka
Waga: 3.09 kg

Recenzje: Calculus for Scientists and Engineers - Eric Schulz, Bernard Gillett, Lyle Cochran