Opis: Thomas' Calculus Early Transcendentals - Joel Hass, Maurice Weir, George Thomas

This text is designed for a three-semester or four-quarter calculus course (math, engineering, and science majors). Calculus hasn't changed, but your students have. Today's students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas' Calculus: Early Transcendentals, Twelfth Edition, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching. The text is available with a robust MyMathLab(R) course-an online homework, tutorial, and study solution designed for today's students. In addition to interactive multimedia features like Java(TM) applets and animations, thousands of MathXL(R) exercises are available for students to get the practice they need.1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions; Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Calculators and Computers 1.5 Exponential Functions 1.6 Inverse Functions and Logarithms 2. Limits and Derivatives 2.1 Rates of Change and Tangents to Curves 2.2 Limit of a Function and Limit Laws 2.3 Precise Definition of a Limit 2.4 One-Sided Limits 2.5 Continuity 2.6 Limits Involving Infinity, Asymptotes of Graphs 3. Differentiation 3.1 Tangents and the Derivative at a Point 3.2 The Derivative as a Function 3.3 Rules for Polynomials, Exponentials, Products, and Quotients 3.4 The Derivative as a Rate of Change 3.5 Derivatives of Trigonometric Functions 3.6 The Chain Rule 3.7 Implicit Differentiation 3.8 Derivatives of Inverse Functions and Logarithms 3.9 Inverse Trigonometric Functions 3.10 Related Rates 3.11 Linearization and Differentials 4. Applications of Derivatives 4.1 Extreme Values of Functions 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Indeterminate Forms and L'Hopital's Rule 4.6 Applied Optimization 4.7 Newton's Method 4.8 Antiderivatives 5. Integration 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Rule 5.6 Substitution and Area Between Curves 6. Applications of Definite Integrals 6.1 Volumes Using Cross-Sections 6.2 Volumes Using Cylindrical Shells 6.3 Arc Length 6.4 Areas of Surfaces of Revolution 6.5 Work and Fluid Forces 6.6 Moments and Centers of Mass 7. Integrals and Transcendental Functions 7.1 The Logarithm Defined as an Integral 7.2 Exponential Change and Separable Differential Equations 7.3 Hyperbolic Functions 7.4 Relative Rates of Growth 8. Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals 9. First-Order Differential Equations 9.1 Solutions, Slope Fields, and Euler's Method 9.2 First-Order Linear Equations 9.3 Applications 9.4 Graphical Solutions of Autonomous Equations 9.5 Systems of Equations and Phase Planes 10. Infinite Sequences and Series 10.1 Sequences 10.2 Infinite Series 10.3 The Integral Test 10.4 Comparison Tests 10.5 The Ratio and Root Tests 10.6 Alternating Series, Absolute and Conditional Convergence 10.7 Power Series 10.8 Taylor and Maclaurin Series 10.9 Convergence of Taylor Series 10.10 The Binomial Series and Applications of Taylor Series 11. Parametric Equations and Polar Coordinates 11.1 Parametrizations of Plane Curves 11.2 Calculus with Parametric Curves 11.3 Polar Coordinates 11.4 Graphing in Polar Coordinates 11.5 Areas and Lengths in Polar Coordinates 11.6 Conic Sections 11.7 Conics in Polar Coordinates 12. Vectors and the Geometry of Space 12.1 Three-Dimensional Coordinate Systems 12.2 Vectors 12.3 The Dot Product 12.4 The Cross Product 12.5 Lines and Planes in Space 12.6 Cylinders and Quadric Surfaces 13. Vector-Valued Functions and Motion in Space 13.1 Curves in Space and Their Tangents 13.2 Integrals of Vector Functions; Projectile Motion 13.3 Arc Length in Space 13.4 Curvature and Normal Vectors of a Curve 13.5 Tangential and Normal Components of Acceleration 13.6 Velocity and Acceleration in Polar Coordinates 14. Partial Derivatives 14.1 Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions 14.3 Partial Derivatives 14.4 The Chain Rule 14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials 14.7 Extreme Values and Saddle Points 14.8 Lagrange Multipliers 14.9 Taylor's Formula for Two Variables 14.10 Partial Derivatives with Constrained Variables 15. Multiple Integrals 15.1 Double and Iterated Integrals over Rectangles 15.2 Double Integrals over General Regions 15.3 Area by Double Integration 15.4 Double Integrals in Polar Form 15.5 Triple Integrals in Rectangular Coordinates 15.6 Moments and Centers of Mass 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.8 Substitutions in Multiple Integrals 16. Integration in Vector Fields 16.1 Line Integrals 16.2 Vector Fields and Line Integrals: Work, Circulation, and Flux 16.3 Path Independence, Conservative Fields, and Potential Functions 16.4 Green's Theorem in the Plane 16.5 Surfaces and Area 16.6 Surface Integrals 16.7 Stokes' Theorem 16.8 The Divergence Theorem and a Unified Theory 17. Second-Order Differential Equations (online) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power Series Solutions Appendices 1. Real Numbers and the Real Line 2. Mathematical Induction 3. Lines, Circles, and Parabolas 4. Proofs of Limit Theorems 5. Commonly Occurring Limits 6. Theory of the Real Numbers 7. Complex Numbers 8. The Distributive Law for Vector Cross Products 9. The Mixed Derivative Theorem and the Increment Theorem

Szczegóły: Thomas' Calculus Early Transcendentals - Joel Hass, Maurice Weir, George Thomas

Tytuł: Thomas' Calculus Early Transcendentals
Autor: Joel Hass, Maurice Weir, George Thomas
Producent: Pearson
ISBN: 9781292021232
Rok produkcji: 2013
Ilość stron: 1136
Oprawa: Miękka
Waga: 2.09 kg

Recenzje: Thomas' Calculus Early Transcendentals - Joel Hass, Maurice Weir, George Thomas