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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). Calculus hasn't changed, but your students have. Today's students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. Thomas' Calculus: Early Transcendentals, Twelfth Edition, (contains only chapters 1-11) helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, and improved conceptual flow. This is the standalone book,(contains only chapters 1-11) if you want the book/access card order the ISBN below. 0321705408 / 9780321705402 Thomas' Calculus Early Transcendentals, Single Variable(contains only chapters 1-11) with MML/MSL Student Access Code Card Package consists of: 0321431308 / 9780321431301 MyMathLab/MyStatLab -- Access Card0321628837 / 9780321628831 Thomas' Calculus Early Transcendentals, Single Variable 0321654064 / 9780321654069 MyMathLab Inside Star Sticker
Contents
1. Functions1.1 Functions and Their Graphs1.2 Combining Functions; Shifting and Scaling Graphs1.3 Trigonometric Functions1.4 Graphing with Calculators and Computers1.5 Exponential Functions1.6 Inverse Functions and Logarithms 2. Limits and Derivatives2.1 Rates of Change and Tangents to Curves2.2 Limit of a Function and Limit Laws2.3 Precise Definition of a Limit2.4 One-Sided Limits2.5 Continuity2.6 Limits Involving Infinity, Asymptotes of Graphs 3. Differentiation3.1 Tangents and the Derivative at a Point3.2 The Derivative as a Function3.3 Rules for Polynomials, Exponentials, Products, and Quotients3.4 The Derivative as a Rate of Change3.5 Derivatives of Trigonometric Functions3.6 The Chain Rule3.7 Implicit Differentiation3.8 Derivatives of Inverse Functions and Logarithms3.9 Inverse Trigonometric Functions3.10 Related Rates3.11 Linearization and Differentials 4. 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 Indeterminate Forms and L'Hopital's Rule4.6 Applied Optimization4.7 Newton's Method4.8 Antiderivatives 5. 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 Rule5.6 Substitution and Area Between Curves 6. 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 Mass 7. Integrals and Transcendental Functions7.1 The Logarithm Defined as an Integral7.2 Exponential Change and Separable Differential Equations7.3 Hyperbolic Functions7.4 Relative Rates of Growth 8. Techniques of Integration8.1 Integration by Parts8.2 Trigonometric Integrals8.3 Trigonometric Substitutions8.4 Integration of Rational Functions by Partial Fractions8.5 Integral Tables and Computer Algebra Systems8.6 Numerical Integration8.7 Improper Integrals 9. 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 Planes 10. Infinite Sequences and Series10.1 Sequences10.2 Infinite Series10.3 The Integral Test10.4 Comparison Tests10.5 The Ratio and Root Tests10.6 Alternating Series, Absolute and Conditional Convergence10.7 Power Series10.8 Taylor and Maclaurin Series10.9 Convergence of Taylor Series10.10 The Binomial Series and Applications of Taylor Series 11. Parametric Equations and Polar Coordinates11.1 Parametrizations of Plane Curves11.2 Calculus with Parametric Curves11.3 Polar Coordinates11.4 Graphing in Polar Coordinates11.5 Areas and Lengths in Polar Coordinates11.6 Conic Sections11.7 Conics in Polar Coordinates
