Thomas' Calculus including Second-order Differential Equations
by Weir, Maurice D.; Hass, Joel R.; Giordano, Frank R.Edition: 1st
Format: Hardcover
Pub. Date: 2006-08-17
Publisher(s): Pearson
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Summary
KEY Message:Thomas'Calculus including Second-order Differential Equationsresponds to the needs of today's readers by developing their conceptual understanding while strengthening their skills in algebra and trigonometry,two areas of knowledge vital to the mastery of calculus. This book offers a full range of exercises, a precise and conceptual presentation, and a new media package designed specifically to meet the needs of today's readers. The exercises gradually increase in difficulty, helping readers learn to generalize and apply the concepts. The refined table of contents introduces the exponential, logarithmic, and trigonometric functions in Chapter 7 of the text. KEY TOPICS: Limits and Derivatives, Differentiation, Applications of Derivatives, Integration, Applications of Definite Integrals, Transcendental Functions, Techniques of Integration, Further Applications of Integration, Conic Sections and Polar Coordinates, Infinite Sequences and Series, Vectors and the Geometry of Space, Vector-Valued Functions and Motion in Space, Partial Derivatives, Multiple Integrals, Integration in Vector Fields, Second-order Differential Equations. MARKET: For all readers interested in Calculus.
Table of Contents
| (Practice Exercises, Additional Exercises, and Questions to Guide Your Review appear at the end of each chapter | |
| Preliminaries | |
| Real Numbers and the Real Line Lines, Circles, and Parabolas Functions and Their Graphs Identifying Functions | |
| Mathematical Models Combining Functions | |
| Shifting and Scaling Graphs Trigonometric Functions Graphing with Calculators and Computers | |
| Limits and Derivatives | |
| Rates of Change and Limits Calculating Limits | |
| Using the Limit Laws Precise | |
| Definition of a Limit | |
| One-Sided Limits and Limits at Infinity | |
| Infinite Limits and Vertical Asymptotes Continuity | |
| Tangents and Derivatives | |
| Differentiation | |
| The Derivative as a Function Differentiation Rules | |
| The Derivative as a Rate of Change Derivatives of Trigonometric Functions | |
| The Chain Rule and Parametric Equations Implicit Differentiation Related Rates Linearization and Differentials | |
| Applications of Derivatives | |
| Extreme Values of Functions | |
| The Mean Value Theorem | |
| Monotonic Functions and the First Derivative Test | |
| Concavity and Curve Sketching | |
| Applied Optimization Problems | |
| Indeterminate Forms and L'Hopital's Rule Newton's Method | |
| Antiderivatives | |
| Integration | |
| Estimating with Finite Sums | |
| Sigma Notation and Limits of Finite Sums | |
| The Definite Integral | |
| The Fundamental Theorem of Calculus Indefinite Integrals and the Substitution | |
| Rule Substitution and Area Between Curves | |
| Applications of Definite Integrals | |
| Volumes by Slicing and Rotation About an Axis | |
| Volumes by Cylindrical Shells Lengths of Plane Curves | |
| Moments and Centers of Mass Areas of Surfaces of Revolution and The Theorems of Pappus | |
| Work Fluid Pressures and Forces | |
| Transcendental Functions | |
| Inverse Functions and their Derivatives Natural Logarithms | |
| The Exponential Function ax and loga x | |
| Exponential Growth and Decay Relative Rates of Growth | |
| Inverse Trigonometric Functions Hyperbolic Functions | |
| Techniques of Integration | |
| Basic Integration Formulas | |
| Integration by Parts | |
| Integration of Rational Functions by Partial Fractions | |
| Trigonometric Integrals | |
| Trigonometric Substitutions | |
| Integral Tables and Computer Algebra Systems | |
| Numerical Integration | |
| Improper Integrals | |
| Further Applications of Integration | |
| Slope Fields and Separable Differential Equations | |
| First-Order Linear Differential Equations | |
| Euler's Method Graphical Solutions of Autonomous Equations | |
| Applications of First-Order Differential Equations | |
| Conic Sections and Polar Coordinates | |
| Conic Sections and Quadratic Equations | |
| Classifying Conic Sections by Eccentricity Quadratic Equations and Rotations Conics and Parametric Equations | |
| The Cycloid Polar Coordinates | |
| Graphing in Polar Coordinates | |
| Area and Lengths in Polar Coordinates | |
| Conic Sections in Polar Coordinates | |
| Infinite Sequences and Series | |
| Sequences Infinite Series | |
| The Integral Test Comparison Tests | |
| The Ratio and Root Tests Alternating Series, Absolute and Conditional Convergence Power Series Taylor and Maclaurin | |
| Series Convergence of Taylor Series | |
| Error Estimates Applications of Power Series Fourier Series | |
| Vectors and the Geometry of Space | |
| Three-Dimensional Coordinate Systems Vectors | |
| The Dot Product | |
| The Cross Product | |
| Lines and Planes in Space Cylinders and Quadric Surfaces | |
| Vector-Valu | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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