CALCU THIRD EDITION. Monfy J. Strauss. Texas Tech University. Gerald L Bradley. Claremont McKenna College. Karl J. Smith. Santa Rosa Junior College
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1 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
2 Preface x 1 Functons and Graphs Input value x ' SljL.1l.. L. 1.1 Prelmnares Lnes n the Plane Functons and Graphs Inverse Functons; Inverse Trgonometrc Functons 33 Chapter 1 Revew 42 Guest Essay: Calculus Was Inevtable, John Troutman 46 Mathematcal Essays 48 Output value 5A: Lmts and Contnuty The Lmt of a Functon Algebrac Computaton of Lmts Contnuty Exponental and Logarthmc Functons 80 Chapter 2 Revew 92
3 - 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 Technques of Dfferentaton Dervatves of Trgonometrc, Exponental, and Logarthmc Functons 3.4 Rates of Change: Modelng Rectlnear Moton The Chan Rule X 3.6 Implct Dfferentaton Related Rates and Applcatons Lnear Approxmaton and Dfferentals 165 Chapter 3 Revew 177 Group Research Project: Chaos Addtonal Applcatons of the Dervatve 183 a rad/sec Drvng shaft 4.1 Extreme Values of a Contnuous Functon The Mean Value Theorem Usng Dervatves to Sketch the Graph of a Functon Curve Sketchng wth Asymptotes: Lmts Involvng Infnty I'Hoptal's Rule Optmzaton n the Physcal Scences and Engneerng Optmzaton n Busness, Economcs, and the Lfe Scences 250 Chapter 4 Revew 263 Group Research Project: Wne Barrel Capacty Integraton Antdfferentaton Area as the Lmt of a Sum Remann Sums and the Defnte Integral The Fundamental Theorems of Calculus Integraton by Substtuton Introducton to Dfferental Equatons The Mean Value Theorem for Integrals; Average Value 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
4 6 Addtonal Applcatons of the Integral Area between Two Curves Volume Polar Forms and Area Arc Length and Surface Area 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 Methods of Integraton Revew of Substtuton and Integraton by Table Integraton by Parts Trgonometrc Methods Method of Partal Fractons Summary of Integraton Technques Frst-Order Dfferental Equatons Improper Integrals Hyperbolc and Inverse Hyperbolc Functons 481 Chapter 7 Revew 487 Group Research Project: Buoy Desgn Infnte Seres 493 y 8.1 Sequences and Ther Lmts Introducton to Infnte Seres: Geometrc Seres, ( L e- ",» m 8.3 The ntegral Test; p-seres Comparson Tests The Rato Test and the Root Test Alternatng Seres; Absolute and Condtonal Convergence 533 h. _ j! X 8.7 Power Seres Taylor and Maclaurn Seres 553 Chapter 8 Revew 566 Group Research Project: Elastc Tghtrope 570 Cumulatve Revew: Chapters
5 v 9 Vectors n the Plane and n Space Vectors n K Coordnates and Vectors n R The Dot Product The Cross Product Parametrc Representaton of Curves; Lnes n R Planes n R Quadrc Surfaces 622 Chapter 9 Revew 628 Group Research Project: Star Trek Vector-Valued Functons Introducton to Vector Functons Dfferentaton and Integraton of Vector Functons Modelng Ballstcs and Planetary Moton Unt Tangent and Prncpal Unt Normal Vectors; Curvature 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 Partal Dfferentaton Functons of Several Varables Lmts and Contnuty Partal Dervatves Tangent Planes, Approxmatons, and Dfferentablty 11.5 Chan Rules Drectonal Dervatves and the Gradent Extreme of Functons of Two Varables Lagrange Multplers 761 Chapter 11 Revew 770 Group Research Project: Desertfcaton
6 >.... ; Multple Integraton v 777 R v Av Tangent plane 12.1 Double Integraton over Rectangular Regons Double Integraton over Nonrectangular Regons Double Integrals n Polar Coordnates Surface Area Trple Integrals Mass, Moments, and Probablty Densty Functons Cylndrcal and Sphercal Coordnates Jacobans: Change of Varables 843 Chapter 12 Revew 852 Group Research Project: Space-Capsule Desgn Vector Analyss Propertes of a Vector Feld: Dvergence and Curl Lne Integrals The Fundamental Theorem and Path Independence Green's Theorem Surface Integrals Stokes'Theorem The Dvergence Theorem 916 Chapter 13 Revew 924 Guest Essay: Contnous vs. Dscrete Mathematcs 929 Cumulatve Revew: Chapters Mathematcal Essays 931 Cumulatve Revew: Chapters Introducton to Dfferental Equatons 935 g Ejcact soluton / t j 14.1 Frst-Order Dfferental Equatons Second-Order Homogeneous Lnear Dfferental Equatons 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
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