- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
This text is designed for the single-variable component of a three-semester or four-quarter calculus course (math, engineering, and science majors). Thomas' Calculus, Single Variable, Thirteenth Edition, introduces readers to the intrinsic beauty of calculus and the power of its applications. For more than half a century, this text has been revered for its clear and precise explanations, thoughtfully chosen examples, superior figures, and time-tested exercise sets. With this new edition, the exercises were refined, updated, and expanded-always with the goal of developing technical competence while furthering readers' appreciation of the subject. Co-authors Hass and Weir have made it their passion to improve the text in keeping with the shifts in both the preparation and ambitions of today's learners.
Contents
1. Functions1.1 Functions and Their Graphs1.2 Combining Functions; Shifting and Scaling Graphs1.3 Trigonometric Functions1.4 Graphing with Software2. Limits and Continuity2.1 Rates of Change and Tangents to Curves2.2 Limit of a Function and Limit Laws2.3 The Precise Definition of a Limit2.4 One-Sided Limits2.5 Continuity2.6 Limits Involving Infinity; Asymptotes of Graphs3. Differentiation3.1 Tangents and the Derivative at a Point3.2 The Derivative as a Function3.3 Differentiation Rules3.4 The Derivative as a Rate of Change3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Implicit Differentiation3.8 Related Rates3.9 Linearization and Differentials4. Applications of Derivatives4.1 Extreme Values of Functions4.2 The Mean Value Theorem4.3 Monotonic Functions and the First Derivative Test4.4 Concavity and Curve Sketching4.5 Applied Optimization4.6 Newton's Method4.7 Antiderivatives5. Integration5.1 Area and Estimating with Finite Sums5.2 Sigma Notation and Limits of Finite Sums5.3 The Definite Integral5.4 The Fundamental Theorem of Calculus5.5 Indefinite Integrals and the Substitution Method5.6 Substitution and Area Between Curves6. Applications of Definite Integrals6.1 Volumes Using Cross-Sections6.2 Volumes Using Cylindrical Shells6.3 Arc Length6.4 Areas of Surfaces of Revolution6.5 Work and Fluid Forces6.6 Moments and Centers of Mass7. Transcendental Functions7.1 Inverse Functions and Their Derivatives7.2 Natural Logarithms7.3 Exponential Functions7.4 Exponential Change and Separable Differential Equations7.5 Indeterminate Forms and L'Hopital's Rule7.6 Inverse Trigonometric Functions7.7 Hyperbolic Functions7.8 Relative Rates of Growth8. Techniques of Integration8.1 Using Basic Integration Formulas8.2 Integration by Parts8.3 Trigonometric Integrals8.4 Trigonometric Substitutions8.5 Integration of Rational Functions by Partial Fractions8.6 Integral Tables and Computer Algebra Systems8.7 Numerical Integration8.8 Improper Integrals8.9 Probability9. First-Order Differential Equations9.1 Solutions, Slope Fields, and Euler's Method9.2 First-Order Linear Equations9.3 Applications9.4 Graphical Solutions of Autonomous Equations9.5 Systems of Equations and Phase Planes10. Infinite Sequences and Series10.1 Sequences10.2 Infinite Series10.3 The Integral Test10.4 Comparison Tests10.5 Absolute Convergence; The Ratio and Root Tests10.6 Alternating Series and Conditional Convergence10.7 Power Series10.8 Taylor and Maclaurin Series10.9 Convergence of Taylor Series10.10 The Binomial Series and Applications of Taylor Series11. Parametric Equations and Polar Coordinates11.1 Parametrizations of Plane Curves11.2 Calculus with Parametric Curves11.3 Polar Coordinates11.4 Graphing Polar Coordinate Equations11.5 Areas and Lengths in Polar Coordinates11.6 Conic Sections11.7 Conics in Polar Coordinates
