Calculus
著者
書誌事項
Calculus
John Wiley & Sons, c2005
8th ed
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注記
Includes index
内容説明・目次
内容説明
You can work more effectively and check solutions as you go along with the text! This "Student Solutions Manual" that is designed to accompany "Anton's Calculus: Late Transcendentals, Single and Multivariable, 8th Edition" provides students with detailed solutions to odd numbered exercises from the text. Designed for the undergraduate Calculus I II III sequence, the eighth edition continues to evolve to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. The new edition retains the strengths of earlier editions such as Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level. Anton also incorporates new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students.
目次
- chapter one FUNCTIONS 1 1.1 Functions 1 1.2 Graphing Functions Using Calculators and Computer Algebra Systems16 1.3 New Functions from Old 27 1.4 Families of Functions40 1.5 Inverse Functions
- Inverse Trigonometric Functions 51 1.6 Mathematical Models 59 1.7 Parametric Equations 69 chapter two LIMITS AND CONTINUITY 84 2.1 Limits (An Intuitive Approach) 84 2.2 Computing Limits 96 2.3 Limits at Infinity
- End Behavior of a Function 105 2.4 Limits (Discussed More Rigorously) 116 2.5 Continuity 125 2.6 Continuity of Trigonometric and Inverse Functions 137 chapter three THE DERIVATIVE 146 3.1 Tangent Lines, Velocity, and General Rates of Change 146 3.2 The Derivative Function 159 3.3 Techniques of Differentiation 171 3.4 The Product and Quotient Rules 179 3.5 Derivatives of Trigonometric Functions 185 3.6 The Chain Rule 190 3.7 Implicit Differentiation 198 3.8 Related Rates 206 3.9 Local Linear Approximation
- Differentials 213 chapter four THE DERIVATIVE IN GRAPHING AND APPLICATIONS 225 4.1 Analysis of Functions I: Increase, Decrease, and Concavity 225 4.2 Analysis of Functions II: Relative Extrema
- Graphing Polynomials 234 4.3 More on Curve Sketching: Rational Functions
- Curves with Cusps and Vertical Tangent Lines
- Using Technology 245 4.4 Absolute Maxima and Minima 254 4.5 Applied Maximum and Minimum Problems 262 4.6 Newton's Method 276 4.7 Rolle's Theorem
- Mean-Value Theorem 281 4.8 Rectilinear Motion 289 chapter five INTEGRATION 302 5.1 An Overview of the Area Problem 302 5.2 The Indefinite Integral 308 5.3 Integration by Substitution 318 5.4 The Definition of Area as a Limit
- Sigma Notation 324 5.5 The Definite Integral 337 5.6 The Fundamental Theorem of Calculus 347 5.7 Rectilinear Motion Revisited Using Integration 361 5.8 Evaluating Definite Integrals by Substitution 370 chapter six APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 380 6.1 Area Between Two Curves 380 6.2 Volumes by Slicing
- Disks and Washers 388 6.3 Volumes by Cylindrical Shells 397 6.4 Length of a Plane Curve 403 6.5 Area of a Surface of Revolution 409 6.6 Average Value of a Function and its Applications 414 6.7 Work 419 6.8 Fluid Pressure and Force 427 chapter seven EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS 435 7.1 Exponential and Logarithmic Functions 435 7.2 Derivatives and Integralsd Involving Logarithmic Functions 447 7.3 Derivatives of Inverse Functions
- Derivatives and Integrals Involving Exponential Functions 453 7.4 Graphs and Applications Involving Logarithmic and Exponential Functions 460 7.5 L'Hopital's Rule
- Indeterminate Forms 467 7.6 Logarithmic Functions from the Integral Point of View 476 7.7 Derivatives and Integrals Involving Inverse Trigonometric Functions 488 7.8 Hyperbolic Functions and Hanging Cables 498 chapter eight PRINCIPLES OF INTEGRAL EVALUATION 514 8.1 An Overview of Integration Methods 514 8.2 Integration by Parts 517 8.3 Trigonometric Integrals 526 8.4 Trigonometric Substitutions 534 8.5 Integrating Rational Functions by Partial Fractions 5441 8.6 Using Computer Algebra Systems and Tables of Integrals 549 8.7 Numerical Integration
- Simpson's Rule 560 8.8 Improper Integrals 573 chapter 9 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 586 9.1 First-Order Differential Equations and Applications 586 9.2 Slope Fields
- Euler's Method 600 9.3 Modeling with First-Order Differential Equations 607 9.4 Second-Order Linear Homogeneous Differential Equations
- The Vibrating Spring 616 chapter ten INFINITE SERIES 628 10.1 Sequences 628 10.2 Monotone Sequences 639 10.3 Infinite Series 647 10.4 Convergence Tests 656 10.5 The Comparison, Ratio, and Root Tests 663 10.6 Alternating Series
- Conditional Convergence 670 10.7 Maclaurin and Taylor Polynomials 679 10.8 Maclaurin and Taylor Series
- Power Series 689 10.9 Convergence of Taylor Series 698 10.10 Differentiating and Integrating Power Series
- Modeling with Taylor Series 708 chapter eleven ANALYTIC GEOMETRY IN CALCULUS 721 11.1 Polar Coordinates 721 11.2 Tangent Lines and Arc Length for Parametric and Polar Curves 735 11.3 Area in Polar Coordinates 744 11.4 Conic Sections in Calculus 750 11.5 Rotation of Axes
- Second-Degree Equations 769 11.6 Conic Sections in Polar Coordinates 775 Horizon Module: Comet Collision 787 chapter twelve THREE-DIMENSIONAL SPACE
- VECTORS 790 12.1 Rectangular Coordinates in 3-Space
- Spheres
- Cylindrical Surfaces 790 12.2 Vectors 796 12.3 Dot Product
- Projections 808 12.4 Cross Product 817 12.5 Parametric Equations of Lines 828 12.6 Planes in 3-Space 835 12.7 Quadric Surfaces 843 12.8 Cylindrical and Spherical Coordinates 854 chapter thirteen VECTOR-VALUED FUNCTIONS 863 13.1 Introduction to Vector-Valued Functions 863 13.2 Calculus of Vector-Valued Functions 869 13.3 Change of Parameter
- Arc Length 880 13.4 Unit Tangent, Normal, and Binormal Vectors 890 13.5 Curvature 8926 13.6 Motion Along a Curve 905 13.7 Kepler's Laws of Planetary Motion 918 chapter fourteen PARTIAL DERIVATIVES 928 14.1 Functions of Two or More Variables 928 14.2 Limits and Continuity 940 14.3 Partial Derivatives 949 14.4 Differentiability, Differentials, and Local Linearity 963 14.5 The Chain Rule 972 14.6 Directional Derivatives and Gradients 982 14.7 Tangent Planes and Normal Vectors 993 14.8 Maxima and Minima of Functions of Two Variables 1000 14.9 Lagrange Multipliers 10128 chapter fifteen MULTIPLE INTEGRALS 1022 15.1 Double Integrals 1022 15.2 Double Integrals over Nonrectangular Regions 1030 15.3 Double Integrals in Polar Coordinates 1039 15.4 Parametric Surfaces
- Surface Area 1047 15.5 Triple Integrals 1060 15.6 Centroid, Center of Gravity, Theorem of Pappus 1069 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 1080 15.8 Change of Variables in Multiple Integrals
- Jacobians 1091 chapter sixteen TOPICS IN VECTOR CALCULUS 1106 16.1 Vector Fields 1106 16.2 Line Integrals 1116 16.3 Independence of Path
- Conservative Vector Fields 1133 16.4 Green's Theorem 1143 16.5 Surface Integrals 1151 16.6 Applications of Surface Integrals
- Flux 1159 16.7 The Divergence Theorem 1168 16.8 Stokes'Theorem 1177 Horizon Module: Hurricane Modeling 1187 appendix a TRIGONOMETRY REVIEW A1 appendix b SOLVING POLYNOMIAL EQUATIONS A15 appendix c SELECTED PROOFS A22 ANSWERS A33 PHOTOCREDITS C1 INDEX I-1 web appendix d REAL NUMBERS,INTERVALS, AND INEQUALITIES W1 web appendix e ABSOLUTE VALUE W11 web appendix f COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS W16 web appendix g DISTANCE, CIRCLES, AND QUADRATIC FUNCTIONS W32 web appendix h THE DISCRIMINANT W41
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