Synopses & Reviews
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 thathelp students master concepts and procedures and functions, 1600 algorithms, and 113 e-Professors.
Table of Contents
0 Preliminaries 0.1 Polynomials and Rational Functions 0.2 Graphing Calculators and Computer Algebra Systems 0.3 Inverse Functions 0.4 Trigonometric and Inverse Trigonometric Functions 0.5 Exponential and Logarithmic Functions Hyperbolic Functions Fitting a Curve to Data 0.6 Transformations of Functions 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 Asymptotes 1.6 Formal Definition of the Limit Exploring the Definition of Limit Graphically 1.7 Limits and Loss-of-Significance Errors Computer Representation of Real Numbers 2 Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative 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 Derivatives of the Exponential and Logarithmic Functions 2.8 Implicit Differentiation and Inverse Trigonometric Functions 2.9 The Mean Value Theorem 3 Applications of Differentiation 3.1 Linear Approximations and Newtons Method 3.2 Indeterminate Forms and LHopitals Rule 3.3 Maximum and Minimum Values 3.4 Increasing and Decreasing Functions 3.5 Concavity and the Second Derivative Test 3.6 Overview of Curve Sketching 3.7 Optimization 3.8 Related Rates 3.9 Rates of Change in Economics and the Sciences 4 Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation Principle of Mathematical Induction 4.3 Area 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 4.8 The Natural Logarithm as an Integral The Exponential Function as the Inverse of the Natural Logarithm 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 Surface Area 5.5 Projectile Motion 5.6 Applications of Integration to Physics and Engineering 5.7 Probability 6 Integration Techniques 6.1 Review of Formulas and Techniques 6.2 Integration by Parts 6.3 Trigonometric Techniques of Integration Integrals Involving Powers of Trigonometric Functions Trigonometric Substitution 6.4 Integration of Rational Functions Using Partial Fractions Brief Summary of Integration Techniques 6.5 Integration Tables and Computer Algebra Systems 6.6 Improper Integrals A Comparison Test 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 8 Infinite Series 8.1 Sequences of Real Numbers 8.2 Infinite Series 8.3 The Integral Test and Comparison Tests 8.4 Alternating Series Estimating the Sum of an Alternating Series 8.5 Absolute Convergence and the Ratio Test The Root Test Summary of Convergence Tests 8.6 Power Series 8.7 Taylor Series Representations of Functions as Series Proof of Taylors Theorem 8.8 Applications of Taylor Series The Binomial Series 8.9 Fourier Series 9 Parametric Equations and Polar Coordinates 9.1 Plane Curves and Parametric Equations 9.2 Calculus and Parametric Equations 9.3 Arc Length and Surface Area in Parametric Equations 9.4 Polar Coordinates 9.5 Calculus and Polar Coordinates 9.6 Conic Sections 9.7 Conic Sections in Polar Coordinates 10 Vectors and the Geometry of Space 10.1 Vectors in the Plane 10.2 Vectors in Space 10.3 The Dot Product Components and Projections 10.4 The Cross Product 10.5 Lines and Planes in Space 10.6 Surfaces in Space 11 Vector-Valued Functions 11.1 Vector-Valued Functions 11.2 The Calculus of Vector-Valued Functions 11.3 Motion in Space 11.4 Curvature 11.5 Tangent and Normal Vectors Tangential and Normal Components of Acceleration Keplers Laws 11.6 Parametric Surfaces 12 Functions of Several Variables and Partial Differentiation 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Tangent Planes and Linear Approximations Increments and Differentials 12.5 The Chain Rule 12.6 The Gradient and Directional Derivatives 12.7 Extrema of Functions of Several Variables 12.8 Constrained Optimization and Lagrange Multipliers 13 Multiple Integrals 13.1 Double Integrals 13.2 Area, Volume, and Center of Mass 13.3 Double Integrals in Polar Coordinates 13.4 Surface Area 13.5 Triple Integrals Mass and Center of Mass 13.6 Cylindrical Coordinates 13.7 Spherical Coordinates 13.8 Change of Variables in Multiple Integrals 14 Vector Calculus 14.1 Vector Fields 14.2 Line Integrals 14.3 Independence of Path and Conservative Vector Fields 14.4 Green's Theorem 14.5 Curl and Divergence 14.6 Surface Integrals 14.7 The Divergence Theorem 14.8 Stokes' Theorem 14.9 Applications of Vector Calculus 15 Second-Order Differential Equations 15.1 Second-Order Equations with Constant Coefficients 15.2 Nonhomogeneous Equations: Undetermined Coefficients 15.3 Applications of Second-Order Differential Equations 15.4 Power Series Solutions of Differential Equations Appendix A: Proofs of Selected Theorems Appendix B: Answers to Odd-Numbered Exercises