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This publication is because that instructors that think that most calculus textbooks are too long. In writing the book, James Stewart request himself: What is crucial for a three-semester calculus course because that scientists and engineers? important CALCULUS: early on TRANSCENDENTALS, second Edition, supplies a concise technique to teaching calculus that focuses on significant concepts, and supports those principles with an accurate definitions, patient explanations, and also carefully graded problems. The book is just 900 pages–two-thirds the size of Stewart’s various other calculus texts, and yet it has almost every one of the same topics. The author achieved this relative brevity mostly by condensing the exposition and by placing some the the functions on the book’s website, In spite of the an ext compact size, the publication has a contemporary flavor, covering modern technology and incorporating product to promote theoretical understanding, though not as prominently as in Stewart’s other books. Necessary CALCULUS: early on TRANSCENDENTALS attributes the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart’s textbooks the best-selling calculus messages in the world.

Table that Contents

1. FUNCTIONS and also LIMITS.Functions and also Their Representations. A directory of necessary Functions. The limit of a Function. Calculating Limits. Continuity. Boundaries Involving Infinity.2. DERIVATIVES.Derivatives and also Rates that Change. The Derivative as a Function. Simple Differentiation Formulas. The Product and also Quotient Rules. The Chain Rule. Implicitly Differentiation. Associated Rates. Linear Approximations and also Differentials.3. Inverse FUNCTIONS: EXPONENTIAL, LOGARITHMIC, and INVERSE TRIGONOMETRIC FUNCTIONS.Exponential Functions. Station Functions and Logarithms. Derivatives that Logarithmic and Exponential Functions. Exponential Growth and Decay. Station Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and also l’Hospital’s Rule.4. APPLICATIONS that DIFFERENTIATION.Maximum and also Minimum Values. The average Value Theorem. Derivatives and also the forms of Graphs. Curve Sketching. Optimization Problems. Newton’s Method. Antiderivatives.5. INTEGRALS.Areas and Distances. The identify Integral. Analyzing Definite Integrals. The fundamental Theorem of Calculus. The Substitution Rule.6. Approaches OF INTEGRATION.Integration by Parts. Trigonometric Integrals and also Substitutions. Partial Fractions. Integration with Tables and also Computer Algebra Systems. Approximate Integration. Not correct Integrals.7. APPLICATIONS of INTEGRATION.Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area that a surface of Revolution. Applications to Physics and Engineering. Differential Equations.8. SERIES.Sequences. Series. The Integral and also Comparison 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 Lengths in Polar Coordinates. Conic sections in Polar Coordinates.10. VECTORS and also THE GEOMETRY of SPACE.Three-Dimensional coordinate Systems. Vectors. The dot Product. The cross Product. Equations the Lines and Planes. Cylinders and also Quadric Surfaces. Vector features and an are Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration.11. PARTIAL DERIVATIVES.Functions of numerous Variables. Limits and also Continuity. Partial Derivatives. Tangent Planes and also Linear Approximations. The Chain Rule. Directional Derivatives and also the Gradient Vector. Maximum and Minimum Values. Lagrange Multipliers.12. Many INTEGRALS.Double Integrals end Rectangles. Dual Integrals over general Regions. Twin Integrals in Polar Coordinates. Applications of dual Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Readjust of Variables in multiple Integrals.13. VECTOR CALCULUS.Vector Fields. Heat Integrals. The an essential Theorem because that Line Integrals. Green’s Theorem. Curl and also Divergence. Parametric Surfaces and Their Areas. Surface ar Integrals. Stokes’ Theorem. The aberration Theorem.Appendix A. Trigonometry.Appendix B. Proofs.Appendix C.

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Sigma Notation.Appendix D. The Logarithm identified as an Integral