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This book is for instructors who think that most calculus textbooks are too lengthy.

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In creating the book, James Stewart asked himself: What is necessary for a three-semester calculus course for researchers and also engineers? ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, Second Edition, supplies a concise approach to teaching calculus that focuses on significant concepts, and supports those ideas through specific definitions, patient explanations, and closely graded troubles. The book is only 900 pages–two-thirds the size of Stewart’s other calculus texts, and also yet it consists of practically every one of the same topics. The writer completed this family member brevity primarily by condensing the explace and also by placing some of the functions on the book’s webwebsite, www.StewartCalculus.com. In spite of the even more compact size, the book has a contemporary flavor, extending innovation and incorporating product to promote conceptual knowledge, though not as prominently as in Stewart’s other books. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS attributes the same attention to detail, eye for invention, and meticulous accuracy that have actually made Stewart’s textbooks the best-offering calculus texts in the human being.### Table of Contents

1. FUNCTIONS AND LIMITS.Functions and also Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity.2. DERIVATIVES.Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Liclose to Approximations and Differentials.3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.Exponential Functions. Inverse Functions and Logarithms. Derivatives of Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and also l’Hospital’s Rule.4. APPLICATIONS OF DIFFERENTIATION.Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton’s Method. Antiderivatives.5. INTEGRALS.Areas and also Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule.6. TECHNIQUES OF INTEGRATION.Integration by Parts. Trigonometric Integrals and also Substitutions. Partial Fractions. Integration via Tables and also Computer Algebra Systems. Approximate Integration. Improper Integrals.7. APPLICATIONS OF INTEGRATION.Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surchallenge of Rdevelopment. Applications to Physics and Engineering.

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Differential Equations.8. SERIES.Sequences. Series. The Integral and Compariboy Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials.9. PARAMETRIC EQUATIONS AND POLAR COORDINATES.Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and also Lengths in Polar Coordinates. Conic Sections in Polar Coordinates.10. VECTORS AND THE GEOMETRY OF SPACE.Three-Dimensional Coordinate Equipment. Vectors. The Dot Product. The Cross Product. Equations of Lines and also Planes. Cylinders and also Quadric Surfaces. Vector Functions and Space Curves. Arc Length and also Curvature. Motion in Space: Velocity and Acceleration.11. PARTIAL DERIVATIVES.Functions of Several Variables. Limits and also Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and also the Gradient Vector. Maximum and also Minimum Values. Lagarray Multipliers.12. MULTIPLE INTEGRALS.Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals.13. VECTOR CALCULUS.Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green’s Theorem. Curl and also Aberration. Parametric Surdeals with and also Their Areas. Surchallenge Integrals. Stokes’ Theorem. The Aberration Theorem.Appendix A. Trigonometry.Appendix B. Proofs.Appendix C. Sigma Notation.Appendix D. The Logarithm Defined as an Integral