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This title in other editionsCalculus (3RD 08 - Old Edition)by Robert T Smith
Synopses & ReviewsPublisher Comments:Smith/Minton: Mathematically Precise. Student-Friendly. Superior Technology. Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors approach which combines the most reliable aspects of mainstream Calculus teaching with the best elements of reform, resulting in a motivating, challenging book. Smith/Minton wrote the book for the students who will use it, in a language that they understand, and with the expectation that their backgrounds may have some gaps. Smith/Minton provide exceptional, reality-based applications that appeal to students interests and demonstrate the elegance of math in the world around us. New features include: • Many new exercises and examples (for a total of 7,000 exercises and 1000 examples throughout the book) provide a careful balance of routine, intermediate and challenging exercises • New exploratory exercises in every section that challenge students to make connections to previous introduced material. • New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, “Today in Mathematics,” stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus. • Exceptional Media Resources: Within MathZone, instructors and students have access to a series of unique Conceptual Videos that help students understand key Calculus concepts proven to be most difficult to comprehend, 248 Interactive Applets that help students master concepts and procedures and functions, 1600 algorithms , and 113 e-Professors.
Table of Contents Chapter 0: Preliminaries 0.2 Lines and Functions 0.4 Trigonometric Functions Chapter 1: Limits and Continuity 1.2 The Concept of Limit 1.4 Continuity and its Consequences 1.5 Limits Involving Infinity 1.6 The Formal Definition of the Limit Computer Representation or Real Numbers 2.1 Tangent Lines and Velocity Alternative Derivative Notations 2.3 Computation of Derivatives: The Power Rule Acceleration 2.5 The Chain Rule 2.7 Implicit Differentiation Chapter 3: Applications of Differentiation 3.2 Maximum and Minimum Values 3.4 Concavity and the Second Derivative Test 3.6Optimization 3.8Rates of Change in Economics and the Sciences 4.1 Antiderivatives Principle of Mathematical Induction 4.4 The Definite Integral 4.5 The Fundamental Theorem of Calculus 4.7 Numerical Integration Chapter 5: Applications of the Definite Integral 5.2 Volume: Slicing, Disks, and Washers 5.4 Arc Length and Srface Area 5.6 Applications of Integration to Physics and Engineering 6.1 The Natural Logarithm 6.3 Exponentials 6.5 The Calculus of the Inverse Trigonometric Functions Chapter 7: First-Order Differential Equations Growth and Decay Problems 7.2 Separable Differential Equations 7.3 Direction Fields and Euler's Method Predator-Prey Systems Improper Integrals 7.8 Probability 8.1 modeling with Differential Equations Compound Interest Logistic Growth Systems of First Order Equations 9.1 Sequences of Real Numbers 9.3 The Integral Test and Comparison Tests Estimating the Sum of an Alternating Series The Root Test 9.6 Power Series Representations of Functions as Series 9.8 Applications of Taylor Series 9.9 Fourier Series 10.1 Plane Curves and Parametric Equations 10.3 Arc Length and Surface Area in Parametric Equations 10.5 Calculus and Polar Coordinates 10.7 Conic Sections in Polar Coordinates 11.1 Vectors in the Plane 11.3 The Dot Product 11.4 The Cross Product 11.6 Surfaces in Space 12.1 Vector-Valued Functions 12.3 Motion in Space 12.5 Tangent and Normal Vectors 11.6 Parametric Surfaces 13.1 Functions of Several Variables 13.3 Partial Derivatives Increments and Differentials Implicit Differentiation 13.7 Extrema of Functions of Several Variables Chapter 14: Multiple Integrals 14.2 Area, Volume, and Center of Mass 14.4 Surface Area Mass and Center of Mass 14.7 Spherical Coordinates Chapter 15: Vector Calculus 15.2 Line Integrals 15.4 Green's Theorem 15.6 Surface Integrals 15.8 Stokes' Theorem Chapter 16: Second-Order Differential Equations 16.2 Nonhomogeneous Equations: Undetermined Coefficients 16.4 Power Series Solutions of Differential Equations Appendix B: Answers to Odd-Numbered Exercises |
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