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This book is for instructors that think that a lot of calculus textpublications are also lengthy. In writing the book, James Stewart asked himself: What is important for a three-semester calculus course for researchers and engineers? ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS, 2nd Edition, supplies a concise strategy to teaching calculus that focuses on major principles, and also supports those principles with specific meanings, patient explanations, and carefully graded problems. The book is just 900 pages–two-thirds the size of Stewart’s other calculus messages, and yet it consists of almost all of the same topics. The writer completed this family member brevity mostly by condensing the explace and also by placing some of the attributes on the book’s website, www.StewartCalculus.com. In spite of the even more compact dimension, the book has actually a contemporary flavor, covering technology and incorporating material to promote conceptual expertise, though not as prominently as in Stewart’s various other publications. ESSENTIAL CALCULUS: EARLY TRANSCENDENTALS attributes the very same attention to detail, eye for invention, and meticulous accuracy that have made Stewart’s textpublications the best-selling calculus texts in the people.
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 also Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials.3. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.Exponential Functions. Inverse Functions and also Logarithms. Derivatives of Logarithmic and also Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l’Hospital’s Rule.4. APPLICATIONS OF DIFFERENTIATION.Maximum and also Minimum Values. The Average Value Theorem. Derivatives and also the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton’s Method. Antiderivatives.5. INTEGRALS.Areas and also Distances. The Definite Integral. Analyzing Definite Integrals. The Fundapsychological Theorem of Calculus. The Substitution Rule.6. TECHNIQUES OF INTEGRATION.Integration by Parts. Trigonometric Integrals and 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. Differential Equations.8. SERIES.Sequences. Series. The Integral and also Comparikid 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 via 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 Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surencounters. Vector Functions and Void Curves. Arc Length and also Curvature. Motion in Space: Velocity and also Acceleration.11. PARTIAL DERIVATIVES.Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and also Linear Approximations. The Chain Rule. Directional Derivatives and also the Gradient Vector. Maximum and also Minimum Values. Lagvariety 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 Fundapsychological Theorem for Line Integrals. Green’s Theorem. Curl and Aberration. Parametric Surencounters and Their Areas. Surchallenge Integrals. Stokes’ Theorem. The Divergence Theorem.Appendix A. Trigonomeattempt.Appendix B. Proofs.Appendix C.
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Sigma Notation.Appendix D. The Logarithm Defined as an Integral