Thomas' calculus : early transcendentals / Joel Hass ... [et al.].

Updated ed. of: Thomas' calculus : early transcendentals. 11th ed. / as revised by Maurice D. Weir, Joel Hass, Frank R. Giordano. c2006.

Updated ed. of: Thomas' calculus : early transcendentals. 11th ed. / as revised by Maurice D. Weir, Joel Hass, Frank R. Giordano. c2006.

1. Functions Functions and Their Graphs Identifying Functions; Mathematical Models Combining Functions; Shifting and Scaling Graphs Graphing with Calculators and Computers Exponential Functions Inverse Functions and Logarithms 2. Limits and Continuity 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 3. Differentiation The Derivative as a Function Differentiation Rules for Polynomials, Exponentials, Products and Quotients The Derivative as a Rate of Change Derivatives of Trigonometric Functions The Chain Rule and Parametric Equations Implicit Differentiation Derivatives of Inverse Functions and Logarithms Inverse Trigonometric Functions Related Rates Linearization and Differentials 4. 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 5. 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 6. 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 7. Integrals and Transcendental Functions The Logarithm Defined as an Integral Exponential Growth and Decay Relative Rates of Growth Hyperbolic Functions 8. 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 9. 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 10. 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 11. 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 12. 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 13. Vector-Valued Functions and Motion in Space Vector Functions Modeling Projectile Motion Arc Length and the Unit Tangent Vector T Curvature and the Unit Normal Vector N Torsion and the Unit Binormal Vector B Planetary Motion and Satellites 14. Partial Derivatives Functions of Several Variables Limits and Continuity in Higher Dimensions Partial Derivatives The Chain Rule Directional Derivatives and Gradient Vectors Tangent Planes and Differentials Extreme Values and Saddle Points Lagrange Multipliers *Partial Derivatives with Constrained Variables Taylor’s Formula for Two Variables 15. Multiple Integrals Double Integrals Areas, Moments and Centers of Mass* Double Integrals in Polar Form Triple Integrals in Rectangular Coordinates Masses and Moments in Three Dimensions Triple Integrals in Cylindrical and Spherical Coordinates Substitutions in Multiple Integrals 16. Integration in Vector Fields Line Integrals Vector Fields, Work, Circulation, and Flux Path Independence, Potential Functions, and Conservative Fields Green’s Theorem in the Plane Surface Area and Surface Integrals Parametrized Surfaces Stokes’ Theorem The Divergence Theorem and a Unified Theory Appendices. Mathematical Induction Proofs of Limit Theorems Commonly Occurring Limits Theory of the Real Numbers Complex Numbers The Distributive Law for Vector Cross Products Determinants and Cramer’s Rule The Mixed Derivative Theorem and the Increment Theorem The Area of a Parallelogram’s Projection on a Plane

Thomas' Calculus Early Transcendentals Media Upgrade, Eleventh Edition, responds 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.

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