| Description |
xv, 930 pages, 117 unnumbered pages : illustrations (chiefly color) ; 27 cm |
| Contents |
Machine derived contents note: -l Functions 1 -- 1.1 Functions and Their Graphs 1 -- 1.2 Combining Functions; Shifting and Scaling Graphs 14 -- 1.3 Trigonometric Functions 22 -- 1.4 Exponential Functions 30 -- 1.5 Inverse Functions and Logarithms 36 -- 1.6 Graphing with Calculators and Computers 50 -- Limits and Continuity 55 -- 2.1 Rates of Change and Tangents to Curves 55 -- 2.2 Limit of a Function and Limit Laws 62 -- 2.3 The Precise Definition of a Limit 74 -- 2.4 One-Sided Limits and Limits at Infinity 84 -- 2.5 Infinite Limits and Vertical Asymptotes 97 -- 2.6 Continuity 103 -- 2.7 Tangents and Derivatives at a Point 115 -- QUESTIONS TO GUIDE YOUR REVIEW 119 -- PRACTICE EXERCISES 120 -- ADDITIONAL AND ADVANCED EXERCISES 122 -- Differentiation 125 -- 3.1 The Derivative as a Function 125 -- 3.2 Differentiation Rules for Polynomials, Exponentials, Products, and Quotients 134 -- 3.3 The Derivative as a Rate of Change 146 -- 3.4 Derivatives of Trigonometric Functions 157 -- 3.5 The Chain Rule and Parametric Equations 164 -- 3.6 Implicit Differentiation 177 -- 3.7 Derivatives of Inverse Functions and Logarithms 183 -- 3.8 Inverse Trigonometric Functions 194 -- 3.9 Related Rates 201 -- 3.10 Linearization and Differentials 209 -- 3.11 Hyperbolic Functions 221 -- QUESTIONS TO GUIDE YOUR REVIEW 227 -- PRACTICE EXERCISES 228 -- ADDITIONAL AND ADVANCED EXERCISES 234 -- B Applications of Derivatives 237 -- 4.1 Extreme Values of Functions 237 -- 4.2 The Mean Value Theorem 245 -- 4.3 Monotonic Functions and the First Derivative Test 254 -- 4.4 Concavity and Curve Sketching 260 -- 4.5 Applied Optimization 271 -- 4.6 Indeterminate Forms and L'Hdpital's Rule 283 -- 4.7 Newton's Method 291 -- 4.8 Antiderivatives 296 -- QUESTIONS TO GUIDE YOUR REVIEW 306 -- PRACTICE EXERCISES 307 -- ADDITIONAL AND ADVANCED EXERCISES 311 -- Integration 315 -- 5.1 Estimating with Finite Sums 315 -- 5.2 Sigma Notation and Limits of Finite Sums 325 -- 5.3 The Definite Integral 332 -- 5.4 The Fundamental Theorem of Calculus 345 -- 5.5 Indefinite Integrals and the Substitution Rule 354 -- 5.6 Substitution and Area Between Curves 360 -- 5.7 The Logarithm Defined as an Integral 370 -- QUESTIONS TO GUIDE YOUR REVIEW 381 -- PRACTICE EXERCISES 382 -- ADDITIONAL AND ADVANCED EXERCISES 386 -- B Applications of Definite Integrals 391 -- 6.1 Volumes by Slicing and Rotation About an Axis 391 -- 6.2 Volumes by Cylindrical Shells 401 -- 6.3 Lengths of Plane Curves 408 -- 6.4 Areas of Surfaces of Revolution 415 -- 6.5 Exponential Change and Separable Differential Equations 421 -- 6.6 Work 430 -- 6.7 Moments and Centers of Mass 437 -- QUESTIONS TO GUIDE YOUR REVIEW 444 -- PRACTICE EXERCISES 444 -- ADDITIONAL AND ADVANCED EXERCISES 446 -- Techniques of Integration 448 -- 7.1 Integration by Parts 448 -- 7.2 Trigonometric Integrals 455 -- 7.3 Trigonometric Substitutions 461 -- 7.4 Integration of Rational Functions by Partial Fractions 464 -- 7.5 Integral Tables and Computer Algebra Systems 471 -- 7.6 Numerical Integration 477 -- 7.7 Improper Integrals 487 -- QUESTIONS TO GUIDE YOUR REVIEW 497 -- PRACTICE EXERCISES 497 -- ADDITIONAL AND ADVANCED EXERCISES 500 -- Infinite Sequences and Series 502 -- 8.1 Sequences 502 -- 8.2 Infinite Series 515 -- 8.3 The Integral Test 523 -- 8.4 Comparison Tests 529 -- 8.5 The Ratio and Root Tests 533 -- 8.6 Alternating Series, Absolute and Conditional Convergence 537 -- 8.7 Power Series 543 -- 8.8 Taylor and Maclaurin Series 553 -- 8.9 Convergence of Taylor Series 559 -- 8.10 The Binomial Series 569 -- QUESTIONS TO GUIDE YOUR REVIEW 572 -- PRACTICE EXERCISES 573 -- ADDITIONAL AND ADVANCED EXERCISES 575 -- Polar Coordinates and Conics 577 -- 9.1 Polar Coordinates 577 -- 9.2 Graphing in Polar Coordinates 582 -- 9.3 Areas and Lengths in Polar Coordinates 586 -- 9.4 Conic Sections 590 -- 9.5 Conics in Polar Coordinates 599 -- 9.6 Conics and Parametric Equations; The Cycloid 606 -- QUESTIONS TO GUIDE YOUR REVIEW 610 -- PRACTICE EXERCISES 610 -- ADDITIONAL AND ADVANCED EXERCISES 612 -- Vectors and the Geometry of Space 614 -- 10.1 Three-Dimensional Coordinate Systems 614 -- 10.2 Vectors 619 -- 10.3 The Dot Product 628 -- 10.4 The Cross Product 636 -- 10.5 Lines and Planes in Space 642 -- 10.6 Cylinders and Quadric Surfaces 652 -- QUESTIONS TO GUIDE YOUR REVIEW 657 -- PRACTICE EXERCISES 658 -- ADDITIONAL AND ADVANCED EXERCISES 660 -- Vector-Valued Functions and Motion in Space 663 -- 11.1 Vector Functions and Their Derivatives 663 -- 11.2 Integrals of Vector Functions 672 -- 11.3 Arc Length in Space 678 -- 11.4 Curvature of a Curve 683 -- 11.5 Tangential and Normal Components of Acceleration 689 -- 11.6 Velocity and Acceleration in Polar Coordinates 694 -- QUESTIONS TO GUIDE YOUR REVIEW 698 -- PRACTICE EXERCISES 698 -- ADDITIONAL AND ADVANCED EXERCISES 700 -- Partial Derivatives 702 -- 12.1 Functions of Several Variables 702 -- 12.2 Limits and Continuity in Higher Dimensions 711 -- 12.3 Partial Derivatives 719 -- 12.4 The Chain Rule 731 -- 12.5 Directional Derivatives and Gradient Vectors 739 -- 12.6 Tangent Planes and Differentials 747 -- 12.7 Extreme Values and Saddle Points 756 -- 12.8 Lagrange Multipliers 765 -- 12.9 Taylor's Formula for Two Variables 775 -- QUESTIONS TO GUIDE YOUR REVIEW 779 -- PRACTICE EXERCISES 780 -- ADDITIONAL AND ADVANCED EXERCISES 783 -- Multiple Integrals 785 -- 13.1 Double and Iterated Integrals over Rectangles 785 -- 13.2 Double Integrals over General Regions 790 -- 13.3 Area by Double Integration 799 -- 13.4 Double Integrals in Polar Form 802 -- 13.5 Triple Integrals in Rectangular Coordinates 807 -- 13.6 Moments and Centers of Mass 816 -- 13.7 Triple Integrals in Cylindrical and Spherical Coordinates 825 -- 13.8 Substitutions in Multiple Integrals 837 -- QUESTIONS TO GUIDE YOUR REVIEW 846 -- PRACTICE EXERCISES 846 -- ADDITIONAL AND ADVANCED EXERCISES 848 -- I Integration in Vector Fields 851 -- 14.1 Line Integrals 851 -- 14.2 Vector Fields, Work, Circulation, and Flux 856 -- 14.3 Path Independence, Potential Functions, and Conservative Fields 867 -- 14.4 Green's Theorem in the Plane 877 -- 14.5 Surfaces and Area 887 -- 14.6 Surface Integrals and Flux 896 -- 14.7 Stokes' Theorem 905 -- 14.8 The Divergence Theorem and a Unified Theory 914 -- QUESTIONS TO GUIDE YOUR REVIEW 925 -- PRACTICE EXERCISES 925 -- ADDITIONAL AND ADVANCED EXERCISES 928 -- First-Order Differential Equations (online) -- 15.1 Solutions, Slope Fields, and Picard's Theorem -- 15.2 First-Order Linear Equations -- 15.3 Applications -- 15.4 Euler's Method -- 15.5 Graphical Solutions of Autonomous Equations -- 15.6 Systems of Equations and Phase Planes -- Second-Order Differential Equations (online) -- 16.1 Second-Order Linear Equations -- 16.2 Nonhomogeneous Linear Equations -- 16.3 Applications -- 16.4 Euler Equations -- 16.5 Power Series Solutions |
| Notes |
Includes index |
| Subject |
Calculus -- Textbooks.
|
|
Calculus.
|
| Genre/Form |
Textbooks.
|
| Author |
Thomas, George B., Jr. (George Brinton), 1914-2006.
|
|
Weir, Maurice D.
|
| LC no. |
2005048720 |
| ISBN |
0321350146 (hbk.) |
|
0321416309 (paperback: Pearson International edition) |
|
