CiNii 図書 - Calculus : early transcendentals

Designed for the freshman/sophomore 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.

chapter one FUNCTIONS 11.1 Functions 11.2 Graphing Functions Using Calculators and Computer Algebra Systems161.3 New Functions from Old 271.4 Families of Functions 401.5 Inverse Functions
Inverse Trigonometric Functions 511.6 Exponential and Logarithmic Functions 651.6 Mathematical Models 761.7 Parametric Equations 86chapter two LIMITS AND CONTINUITY 1012.1 Limits (An Intuitive Approach) 1012.2 Computing Limits 1132.3 Limits at Infinity
End Behavior of a Function 1222.4 Limits (Discussed More Rigorously) 1342.5 Continuity 1442.6 Continuity of Trigonometric and Inverse Functions 155chapter three THE DERIVATIVE 1653.1 Tangent Lines, Velocity, and General Rates of Change 1653.2 The Derivative Function 1783.3 Techniques of Differentiation 1903.4 The Product and Quotient Rules 1983.5 Derivatives of Trigonometric Functions 2043.6 The Chain Rule 2093.7 Related Rates 2173.8 Local Linear Approximation
Differentials 224chapter four EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS 2354.1 Implicit Differentiation 2354.2 Derivatives of Logarithmic Functions 2434.3 Derivatives of Exponential and Inverse Trigonometric Functions 2484.4 L'Hopital's Rule
Indeterminate Forms 256chapter five THE DERIVATIVE IN GRAPHING AND APPLICATIONS 2675.1 Analysis of Functions I: Increase, Decrease, and Concavity 2675.2 Analysis of Functions II: Relative Extrema
Graphing Polynomials 2795.3 More on Curve Sketching: Rational Functions
Curves with Cusps and Vertical Tangent Lines
Using Technology 2895.4 Absolute Maxima and Minima 3015.5 Applied Maximum and Minimum Problems 3095.6 Newton's Method 3235.7 Rolle's Theorem
Mean-Value Theorem 3295.8 Rectilinear Motion 336 chapter six INTEGRATION 3496.1 An Overview of the Area Problem 3496.2 The Indefinite Integral 3556.3 Integration by Substitution 3656.4 The Definition of Area as a Limit
Sigma Notation 3736.5 The Definite Integral 3866.6 The Fundamental Theorem of Calculus 3966.7 Rectilinear Motion Revisited Using Integration 4106.8 Evaluating Definite Integrals by Substitution 419 chapter seven APPLICATIONS OF THE DEFINITE INTEGRAL IN GEOMETRY, SCIENCE, AND ENGINEERING 44207.1 Area Between Two Curves 4427.2 Volumes by Slicing
Disks and Washers 4507.3 Volumes by Cylindrical Shells 4597.4 Length of a Plane Curve 4657.5 Area of a Surface of Revolution 4717.6 Average Value of a Function and its Applications 4767.7 Work 4817.8 Fluid Pressure and Force 4907.9 Hyperbolic Functions and Hanging Cables 496 chapter eight PRINCIPLES OF INTEGRAL EVALUATION 5108.1 An Overview of Integration Methods 5108.2 Integration by Parts 5138.3 Trigonometric Integrals 5228.4 Trigonometric Substitutions 5308.5 Integrating Rational Functions by Partial Fractions 5378.6 Using Computer Algebra Systems and Tables of Integrals 5458.7 Numerical Integration
Simpson's Rule 5568.8 Improper Integrals 569 chapter 9 MATHEMATICAL MODELING WITH DIFFERENTIAL EQUATIONS 5829.1 First-Order Differential Equations and Applications 5829.2 Slope Fields
Euler's Method 5969.3 Modeling with First-Order Differential Equations 6039.4 Second-Order Linear Homogeneous Differential Equations
The Vibrating Spring 612 chapter ten INFINITE SERIES 62410.1 Sequences 62410.2 Monotone Sequences 63510.3 Infinite Series 64310.4 Convergence Tests 65210.5 The Comparison, Ratio, and Root Tests 65910.6 Alternating Series
Conditional Convergence 66610.7 Maclaurin and Taylor Polynomials 67510.8 Maclaurin and Taylor Series
PowerSeries 68510.9 Convergence of Taylor Series 69410.10 Differentiating and Integrating Power Series
Modeling with Taylor Series 704 chapter eleven ANALYTIC GEOMETRY IN CALCULUS 71711.1 Polar Coordinates 71711.2 Tangent Lines and Arc Length for Parametric and Polar Curves 73111.3 Area in Polar Coordinates 74011.4 Conic Sections in Calculus 74611.5 Rotation of Axes
Second-Degree Equations 76511.6 Conic Sections in Polar Coordinates 771Horizon Module: Comet Collision 783 appendix a TRIGONOMETRY REVIEW A1appendix b SOLVING POLYNOMIAL EQUATIONS A15appendix c SELECTED PROOFS A22ANSWERS A33PHOTOCREDITS C1INDEX I-1web appendix d REAL NUMBERS,INTERVALS, AND INEQUALITIES W1web appendix e ABSOLUTE VALUE W11web appendix f COORDINATE PLANES, LINES, AND LINEAR FUNCTIONS W16web appendix g DISTANCE, CIRCLES, AND QUADRATIC FUNCTIONS W32web appendix h THE DISCRIMINANT W41

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Calculus : early transcendentals

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