CALCU THIRD EDITION Monfy J. Strauss Texas Tech Unversty Gerald L Bradley Claremont McKenna College Karl J. Smth Santa Rosa Junor College Prentce Hall, Upper Saddle Rver, New Jersey 07458
Preface x 1 Functons and Graphs Input value x ' SljL.1l.. L. 1.1 Prelmnares 2 1.2 Lnes n the Plane 13 1.3 Functons and Graphs 19 1.4 Inverse Functons; Inverse Trgonometrc Functons 33 Chapter 1 Revew 42 Guest Essay: Calculus Was Inevtable, John Troutman 46 Mathematcal Essays 48 Output value 5A: 2 + 2 2 Lmts and Contnuty 49 2.1 The Lmt of a Functon 50 2.2 Algebrac Computaton of Lmts 61 2.3 Contnuty 70 2.4 Exponental and Logarthmc Functons 80 Chapter 2 Revew 92
- v 3 Dfferentaton 97 I I y e" 7 --^ _!_ A fs lor \I fl a It ne 3.1 An Introducton to the Dervatve: Tangents 98 3.2 Technques of Dfferentaton 110 3.3 Dervatves of Trgonometrc, Exponental, and Logarthmc Functons 3.4 Rates of Change: Modelng Rectlnear Moton 125 3.5 The Chan Rule 138 119 X 3.6 Implct Dfferentaton 146-3.7 Related Rates and Applcatons 157 1 1 3.8 Lnear Approxmaton and Dfferentals 165 Chapter 3 Revew 177 Group Research Project: Chaos 181 4 Addtonal Applcatons of the Dervatve 183 a rad/sec Drvng shaft 4.1 Extreme Values of a Contnuous Functon 184 4.2 The Mean Value Theorem 195 4.3 Usng Dervatves to Sketch the Graph of a Functon 201 4.4 Curve Sketchng wth Asymptotes: Lmts Involvng Infnty 217 4.5 I'Hoptal's Rule 229 4.6 Optmzaton n the Physcal Scences and Engneerng 238 4.7 Optmzaton n Busness, Economcs, and the Lfe Scences 250 Chapter 4 Revew 263 Group Research Project: Wne Barrel Capacty 269 5 Integraton 271 5.1 Antdfferentaton 272 5.2 Area as the Lmt of a Sum 282 5.3 Remann Sums and the Defnte Integral 290 5.4 The Fundamental Theorems of Calculus 302 5.5 Integraton by Substtuton 309 5.6 Introducton to Dfferental Equatons 316 5.7 The Mean Value Theorem for Integrals; Average Value 328 5.8 Numercal Integraton: The Trapezodal Rule and Smpson's Rule 5.9 An Alternatve Approach: The Logarthm as an Integral 342 Chapter 5 Revew 346 Guest Essay: Knematcs of Joggng, Ralph Boas 351 Mathematcal Essays 352 Cumulatve Revew: Chapters 1-5 353 334
6 Addtonal Applcatons of the Integral 355 6.1 Area between Two Curves 356 6.2 Volume 362 6.3 Polar Forms and Area 375 6.4 Arc Length and Surface Area 385 6.5 Physcal Applcatons: Work, Lqud Force, and Centrods 6.6 Applcatons to Busness, Economcs, and Lfe Scences Chapter 6 Revew 417 Group Research Project: Houdn's Escape 424 407 395 7 Methods of Integraton 425 7.1 Revew of Substtuton and Integraton by Table 426 7.2 Integraton by Parts 435 7.3 Trgonometrc Methods 441 7.4 Method of Partal Fractons 448 7.5 Summary of Integraton Technques 457 7.6 Frst-Order Dfferental Equatons 461 7.7 Improper Integrals 472 7.8 Hyperbolc and Inverse Hyperbolc Functons 481 Chapter 7 Revew 487 Group Research Project: Buoy Desgn 491 8 Infnte Seres 493 y 8.1 Sequences and Ther Lmts 494 8.2 Introducton to Infnte Seres: Geometrc Seres, 505-6- ( L e- ",» m 8.3 The ntegral Test; p-seres 514 8.4 Comparson Tests 521 8.5 The Rato Test and the Root Test 527 8.6 Alternatng Seres; Absolute and Condtonal Convergence 533 h. _ j! X 8.7 Power Seres 544 8.8 Taylor and Maclaurn Seres 553 Chapter 8 Revew 566 Group Research Project: Elastc Tghtrope 570 Cumulatve Revew: Chapters 6-8 571
v 9 Vectors n the Plane and n Space 573 9.1 Vectors n K 2 574 9.2 Coordnates and Vectors n R 3 582 9.3 The Dot Product 588 9.4 The Cross Product 597 9.5 Parametrc Representaton of Curves; Lnes n R 3 9.6 Planes n R 3 615 9.7 Quadrc Surfaces 622 Chapter 9 Revew 628 Group Research Project: Star Trek 632 606 10 Vector-Valued Functons 633 10.1 Introducton to Vector Functons 634 10.2 Dfferentaton and Integraton of Vector Functons 642 10.3 Modelng Ballstcs and Planetary Moton 651 10.4 Unt Tangent and Prncpal Unt Normal Vectors; Curvature 660 10.5 Tangental and Normal Components of Acceleraton 673 Chapter 10 Revew 679 Guest Essay: The Stmulaton of Scence, Howard Eves 684 Mathematcal Essays 687 Cumulatve Revew: Chapters 1-10 688 11 Partal Dfferentaton 693 11.1 Functons of Several Varables 694 11.2 Lmts and Contnuty 701 11.3 Partal Dervatves 710 11.4 Tangent Planes, Approxmatons, and Dfferentablty 11.5 Chan Rules 729 11.6 Drectonal Dervatves and the Gradent 737 11.7 Extreme of Functons of Two Varables 749 11.8 Lagrange Multplers 761 Chapter 11 Revew 770 Group Research Project: Desertfcaton 775 720
>.... ; - - 12 Multple Integraton v 777 R v Av Tangent plane 12.1 Double Integraton over Rectangular Regons 778 12.2 Double Integraton over Nonrectangular Regons 787 12.3 Double Integrals n Polar Coordnates 795 12.4 Surface Area 804 12.5 Trple Integrals 812 12.6 Mass, Moments, and Probablty Densty Functons 822 12.7 Cylndrcal and Sphercal Coordnates 833 12.8 Jacobans: Change of Varables 843 Chapter 12 Revew 852 Group Research Project: Space-Capsule Desgn 857 13 Vector Analyss 859 13.1 Propertes of a Vector Feld: Dvergence and Curl 860 13.2 Lne Integrals 867 13.3 The Fundamental Theorem and Path Independence 877 13.4 Green's Theorem 887 13.5 Surface Integrals 898 13.6 Stokes'Theorem 908 13.7 The Dvergence Theorem 916 Chapter 13 Revew 924 Guest Essay: Contnous vs. Dscrete Mathematcs 929 Cumulatve Revew: Chapters 11-13 930 Mathematcal Essays 931 Cumulatve Revew: Chapters 11-13 932 14 Introducton to Dfferental Equatons 935 g Ejcact soluton / t j 14.1 Frst-Order Dfferental Equatons 936 14.2 Second-Order Homogeneous Lnear Dfferental Equatons 947 14.3 Second-Order Nonhomogeneous Lnear Dfferental Equatons 957 Chapter 14 Revew 966 Group Research Project: Save the Perch Project 969 y n ). h \ x 0 ; X