Calculus, Single Variable: Late Transcendental Functions

This book is Smith/Minton's: mathematically precise; student-friendly; and, superior technology guide. 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 this 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 provides 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) that 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' that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present; and, 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 0.1 The Real Numbers and the Cartesian Plane 0.2 Lines and Functions 0.3 Graphing Calculators and Computer Algebra Systems 0.4 Trigonometric Functions 0.5 Transformations of Functions Chapter 1: Limits and Continuity 1.1 A Brief Preview of Calculus: Tangent Lines and the Length of a Curve 1.2 The Concept of Limit 1.3 Computation of Limits 1.4 Continuity and its Consequences The Method of Bisections 1.5 Limits Involving Infinity Asysmptotes 1.6 The Formal Definition of the Limit 1.7 Limits and Loss-of-Significance Errors Computer Representation or Real Numbers Chaper 2: Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative Alternative Derivative Notations Numerical Differentiation 2.3 Computation of Derivatives: The Power Rule Higher Order Derivatives Acceleration 2.4 The Product and Quotient Rules 2.5 The Chain Rule 2.6 Derivatives of the Trigonometric Functions 2.7 Implicit Differentiation 2.8 The Mean Value Theorem Chapter 3: Applications of Differentiation 3.1 Linear Approximations and Newton's Method 3.2 Maximum and Minimum Values 3.3 Increasing and Decreasing Functions 3.4 Concavity and the Second Derivative Test 3.5Overview of Curve Sketching 3.6Optimization 3.8Related Rates 3.8Rates of Change in Economics and the Sciences Chapter 4: Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation Principle of Mathematical Induction 4.3 Area under a Curve 4.4 The Definite Integral Average Value of a Function 4.5 The Fundamental Theorem of Calculus 4.6 Integration by Substitution 4.7 Numerical Integration Error bounds for Numerical Integration Chapter 5: Applications of the Definite Integral 5.1 Area Between Curves 5.2 Volume: Slicing, Disks, and Washers 5.3 Volumes by Cylindrical Shells 5.4 Arc Length and Srface Area 5.5 Projectile Motion 5.6 Applications of Integration to Physics and Engineering Chapter 6: Exponentials, Logarithms and other Transcendental Functions 6.1 The Natural Logarithm 6.2 Inverse Functions 6.3 Exponentials 6.4 The Inverse Trigonometric Functions 6.5 The Calculus of the Inverse Trigonometric Functions 6.6 The Hyperbolic Function Chapter 7: First-Order Differential Equations 7.1 Modeling with Differential Equations Growth and Decay Problems Compound Interest 7.2 Separable Differential Equations Logistic Growth 7.3 Direction Fields and Euler's Method 7.4 Systems of First-Order Differential Equations Predator-Prey Systems 7.6 Indeterminate Forms and L'Hopital's Rule Improper Integrals A Comparison Test 7.8 Probability Chapter 8: First-Order Differential Equations 8.1 modeling with Differential Equations Growth and Decay Problems Compound Interest 8.2 Separable Differential Equations Logistic Growth 8.3 Direction Fields and Euler's Method Systems of First Order Equations Chapter 9: Infinite Series 9.1 Sequences of Real Numbers 9.2 Infinite Series 9.3 The Integral Test and Comparison Tests 9.4 Alternating Series Estimating the Sum of an Alternating Series 9.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Test 9.6 Power Series 9.7 Taylor Series Representations of Functions as Series Proof of Taylor's Theorem 9.8 Applications of Taylor Series The Binomial Series 9.9 Fourier Series Chapter 10: Parametric Equations and Polar Coordinates 10.1 Plane Curves and Parametric Equations 10.2 Calculus and Parametric Equations 10.3 Arc Length and Surface Area in Parametric Equations 10.4 Polar Coordinates 10.5 Calculus and Polar Coordinates 10.6 Conic Sections 10.7 Conic Sections in Polar Coordinates Chapter 11: Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Vectors in Space 11.3 The Dot Product Components and Projections 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Surfaces in Space Chapter 12: Vector-Valued Functions 12.1 Vector-Valued Functions 12.2 The Calculus Vector-Valued Functions 12.3 Motion in Space 12.4 Curvature 12.5 Tangent and Normal Vectors Components of Acceleration, Kepler's Laws 11.6 Parametric Surfaces Chapter 13: Functions of Several Variables and Partial Differentiation 13.1 Functions of Several Variables 13.2 Limits and Continuity 13.3 Partial Derivatives 13.4 Tangent Planes and Linear Approximations Increments and Differentials 13.5 The Chain Rule Implicit Differentiation 13.6 The Gradient and Directional Derivatives 13.7 Extrema of Functions of Several Variables 13.8 Constrained Optimization and Lagrange Multipliers Chapter 14: Multiple Integrals 14.1 Double Integrals 14.2 Area, Volume, and Center of Mass 14.3 Double Integrals in Polar Coordinates 14.4 Surface Area 14.5 Triple Integrals Mass and Center of Mass 14.6 Cylindrical Coordinates 14.7 Spherical Coordinates 14.8 Change of Variables in Multiple Integrals Chapter 15: Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Independence of Path and Conservative Vector Fields 15.4 Green's Theorem 15.5 Curl and Divergence 15.6 Surface Integrals 15.7 The Divergence Theorem 15.8 Stokes' Theorem 15.9 Applications of Vector Calculus Chapter 16: Second-Order Differential Equations 16.1 Second-Order Equations with Constant Coefficients 16.2 Nonhomogeneous Equations: Undetermined Coefficients 16.3 Applications of Second-Order Differential Equations 16.4 Power Series Solutions of Differential Equations Appendix A: Proofs of Selected Theorems Appendix B: Answers to Odd-Numbered Exercises