Pro SQL Server Relational Database Design and Implementation : Best Practices for Scalability and Performance, Sixth Edition

This book is for instructors who think that most calculus textbooks are too long. In writing the book, James Stewart asked himself: What is essential for a three-semester calculus course for scientists and engineers? ESSENTIAL CALCULUS, Second Edition, offers a concise approach to teaching calculus that focuses on major concepts, and supports those concepts with precise definitions, patient explanations, and carefully graded problems. The book is only 900 pages—two-thirds the size of Stewart's other calculus texts, and yet it contains almost all of the same topics. The author achieved this relative brevity primarily by condensing the exposition and by putting some of the features on the book's website, www.StewartCalculus.com. Despite the more compact size, the book has a modern flavor, covering technology and incorporating material to promote conceptual understanding, though not as prominently as in Stewart's other books. ESSENTIAL CALCULUS features the same attention to detail, eye for innovation, and meticulous accuracy that have made Stewart's textbooks the best-selling calculus texts in the world. Contents Preface To the Student Diagnostic Tests Ch 1: Functions and Limits 1.1 Functions and Their Representations 1.1 Exercises 1.2 A Catalog of Essential Functions 1.2 Exercises 1.3 The Limit of a Function 1.3 Exercises 1.4 Calculating Limits 1.4 Exercises 1.5 Continuity 1.5 Exercises 1.6 Limits Involving Infinity 1.6 Exercises Chapter 1: Review Ch 2: Derivatives 2.1 Derivatives and Rates of Change 2.1 Exercises 2.2 The Derivative as a Function 2.2 Exercises 2.3 Basic Differentiation Formulas 2.3 Exercises 2.4 The Product and Quotient Rules 2.4 Exercises 2.5 The Chain Rule 2.5 Exercises 2.6 Implicit Differentiation 2.6 Exercises 2.7 Related Rates 2.7 Exercises 2.8 Linear Approximations and Differentials 2.8 Exercises Chapter 2: Review Ch 3: Applications of Differentiation 3.1 Maximum and Minimum Values 3.1 Exercises 3.2 The Mean Value Theorem 3.2 Exercises 3.3 Derivatives and the Shapes of Graphs 3.3 Exercises 3.4 Curve Sketching 3.4 Exercises 3.5 Optimization Problems 3.5 Exercises 3.6 Newton's Method 3.6 Exercises 3.7 Antiderivatives 3.7 Exercises Chapter 3: Review Ch 4: Integrals 4.1 Areas and Distances 4.1 Exercises 4.2 The Definite Integral 4.2 Exercises 4.3 Evaluating Definite Integrals 4.3 Exercises 4.4 The Fundamental Theorem of Calculus 4.4 Exercises 4.5 The Substitution Rule 4.5 Exercises Chapter 4: Review Ch 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions 5.1 Inverse Functions 5.1 Exercises 5.2 The Natural Logarithmic Function 5.2 Exercises 5.3 The Natural Exponential Function 5.3 Exercises 5.4 General Logarithmic and Exponential Functions 5.4 Exercises 5.5 Exponential Growth and Decay 5.5 Exercises 5.6 Inverse Trigonometric Functions 5.6 Exercises 5.7 Hyperbolic Functions 5.7 Exercises 5.8 Indeterminate Forms and L'Hospital's Rule 5.8 Exercises Chapter 5: Review Ch 6: Techniques of Integration 6.1 Integration by Parts 6.1 Exercises 6.2 Trigonometric Integrals and Substitutions 6.2 Exercises 6.3 Partial Fractions 6.3 Exercises 6.4 Integration with Tables and Computer Algebra Systems 6.4 Exercises 6.5 Approximate Integration 6.5 Exercises 6.6 Improper Integrals 6.6 Exercises Chapter 6: Review Ch 7: Applications of Integration 7.1 Areas between Curves 7.1 Exercises 7.2 Volumes 7.2 Exercises 7.3 Volumes by Cylindrical Shells 7.3 Exercises 7.4 Arc Length 7.4 Exercises 7.5 Area of a Surface of Revolution 7.5 Exercises 7.6 Applications to Physics and Engineering 7.6 Exercises 7.7 Differential Equations 7.7 Exercises Chapter 7: Review Ch 8: Series 8.1 Sequences 8.1 Exercises 8.2 Series 8.2 Exercises 8.3 The Integral and Comparison Tests 8.3 Exercises 8.4 Other Convergence Tests 8.4 Exercises 8.5 Power Series 8.5 Exercises 8.6 Representing Functions as Power Series 8.6 Exercises 8.7 Taylor and Maclaurin Series 8.7 Exercises 8.8 Applications of Taylor Polynomials 8.8 Exercises Chapter 8: Review Ch 9: Parametric Equations and Polar Coordinates 9.1 Parametric Curves 9.1 Exercises 9.2 Calculus with Parametric Curves 9.2 Exercises 9.3 Polar Coordinates 9.3 Exercises 9.4 Areas and Lengths in Polar Coordinates 9.4 Exercises 9.5 Conic Sections in Polar Coordinates 9.5 Exercises Chapter 9: Review Ch 10: Vectors and the Geometry of Space 10.1 Three-Dimensional Coordinate Systems 10.1 Exercises 10.2 Vectors 10.2 Exercises 10.3 The Dot Product 10.3 Exercises 10.4 The Cross Product 10.4 Exercises 10.5 Equations of Lines and Planes 10.5 Exercises 10.6 Cylinders and Quadric Surfaces 10.6 Exercises 10.7 Vector Functions and Space Curves 10.7 Exercises 10.8 Arc Length and Curvature 10.8 Exercises 10.9 Motion in Space: Velocity and Acceleration 10.9 Exercises Chapter 10: Review Ch 11: Partial Derivatives 11.1 Functions of Several Variables 11.1 Exercises 11.2 Limits and Continuity 11.2 Exercises 11.3 Partial Derivatives 11.3 Exercises 11.4 Tangent Planes and Linear Approximations 11.4 Exercises 11.5 The Chain Rule 11.5 Exercises 11.6 Directional Derivatives and the Gradient Vector 11.6 Exercises 11.7 Maximum and Minimum Values 11.7 Exercises 11.8 Lagrange Multipliers 11.8 Exercises Chapter 11: Review Ch 12: Multiple Integrals 12.1 Double Integrals over Rectangles 12.1 Exercises 12.2 Double Integrals over General Regions 12.2 Exercises 12.3 Double Integrals in Polar Coordinates 12.3 Exercises 12.4 Applications of Double Integrals 12.4 Exercises 12.5 Triple Integrals 12.5 Exercises 12.6 Triple Integrals in Cylindrical Coordinates 12.6 Exercises 12.7 Triple Integrals in Spherical Coordinates 12.7 Exercises 12.8 Change of Variables in Multiple Integrals 12.8 Exercises Chapter 12: Review Ch 13: Vector Calculus 13.1 Vector Fields 13.1 Exercises 13.2 Line Integrals 13.2 Exercises 13.3 The Fundamental Theorem for Line Integrals 13.3 Exercises 13.4 Green's Theorem 13.4 Exercises 13.5 Curl and Divergence 13.5 Exercises 13.6 Parametric Surfaces and Their Areas 13.6 Exercises 13.7 Surface Integrals 13.7 Exercises 13.8 Stokes' Theorem 13.8 Exercises 13.9 The Divergence Theorem 13.9 Exercises Chapter 13: Review Appendixes Appendix A: Trigonometry Appendix B: Sigma Notation Appendix C: Proofs Appendix D: Answers to Odd-Numbered Exercises Index