Calculus

Designed for the three-semester engineering calculus course, Calculus: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the fourth of Calculus: Early Transcendental Functions, 4/e has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.

ISBN 0618606246   Pages 1344 ISBN13 9780618606245 (What's this?)   Volumes 1 Publisher Cengage Learning, Inc   Weight (grammes) 2676 Imprint Houghton Mifflin   Published in Boston Format Hardback   Previous ISBN 9780618223077 Publication date 02 Feb 2006   Height (mm) 269 Library of Congress 2005933918   Width (mm) 224 DEWEY 515   Spine width (mm) 53 DEWEY edition DC22   Academic level Undergraduate

Note: Each chapter includes Review Exercises and P.S. Problem Solving. 1. Preparation for Calculus 1.1 Graphs and Models 1.2 Linear Models and Rates of Change 1.3 Functions and Their Graphs 1.4 Fitting Models to Data 1.5 Inverse Functions 1.6 Exponential and Logarithmic Functions 2. Limits and Their Properties 2.1 A Preview of Calculus 2.2 Finding Limits Graphically and Numerically 2.3 Evaluating Limits Analytically 2.4 Continuity and One-Sided Limits 2.5 Infinite Limits Section Project: Graphs and Limits of Trigonometric Functions 3. Differentiation 3.1 The Derivative and the Tangent Line Problem 3.2 Basic Differentiation Rules and Rates of Change 3.3 Product and Quotient Rules and Higher-Order Derivatives 3.4 The Chain Rule 3.5 Implicit Differentiation Section Project: Optical Illusions 3.6 Derivatives of Inverse Functions 3.7 Related Rates 3.8 Newton's Method 4. Applications of Differentiation 4.1 Extrema on an Interval 4.2 Rolle's Theorem and the Mean Value Theorem 4.3 Increasing and Decreasing Functions and the First Derivative Test Section Project: Rainbows 4.4 Concavity and the Second Derivative Test 4.5 Limits at Infinity 4.6 A Summary of Curve Sketching 4.7 Optimization Problems Section Project: Connecticut River 4.8 Differentials 5. Integration 5.1 Antiderivatives and Indefinite Integration 5.2 Area 5.3 Riemann Sums and Definite Integrals 5.4 The Fundamental Theorem of Calculus Section Project: Demonstrating the Fundamental Theorem 5.5 Integration by Substitution 5.6 Numerical Integration 5.7 The Natural Logarithmic Function: Integration 5.8 Inverse Trigonometric Functions: Integration 5.9 Hyperbolic Functions Section Project: St. Louis Arch 6. Differential Equations 6.1 Slope Fields and Euler's Method 6.4 Differential Equations: Growth and Decay 6.5 Differential Equations: Separation of Variables 6.4 The Logistic Equation 6.5 First-Order Linear Differential Equations Section Project: Weight Loss 6.6 Predator-Prey Differential Equations 7. Applications of Integration 7.1 Area of a Region Between Two Curves 7.2 Volume: The Disk Method 7.3 Volume: The Shell Method Section Project: Saturn 7.4 Arc Length and Surfaces of Revolution 7.5 Work Section Project: Tidal Energy 7.6 Moments, Centers of Mass, and Centroids 7.7 Fluid Pressure and Fluid Force 8. Integration Techniques, L'Hopital's Rule, and Improper Integrals 8.1 Basic Integration Rules 8.2 Integration by Parts 8.3 Trigonometric Integrals Section Project: Power Lines 8.4 Trigonometric Substitution 8.5 Partial Fractions 8.6 Integration by Tables and Other Integration Techniques 8.7 Indeterminate Forms and L'Hopital's Rule 8.8 Improper Integrals 9. Infinite Series 9.1 Sequences 9.2 Series and Convergence Section Project: Cantor's Disappearing Table 9.3 The Integral Test and p-Series Section Project: The Harmonic Series 9.4 Comparisons of Series Section Project: Solera Method 9.5 Alternating Series 9.6 The Ratio and Root Tests 9.7 Taylor Polynomials and Approximations 9.8 Power Series 9.9 Representation of Functions by Power Series 9.10 Taylor and Maclaurin Series 10. Conics, Parametric Equations, and Polar Coordinates 10.1 Conics and Calculus 10.2 Plane Curves and Parametric Equations Section Projects: Cycloids 10.3 Parametric Equations and Calculus 10.4 Polar Coordinates and Polar Graphs Section Project: Anamorphic Art 10.5 Area and Arc Length in Polar Coordinates 10.6 Polar Equations of Conics and Kepler's Laws 11. Vectors and the Geometry of Space 11.1 Vectors in the Plane 11.2 Space Coordinates and Vectors in Space 11.3 The Dot Product of Two Vectors 11.4 The Cross Product of Two Vectors in Space 11.5 Lines and Planes in Space Section Project: Distances in Space 11.6 Surfaces in Space 11.7 Cylindrical and Spherical Coordinates 12. Vector-Valued Functions 12.1 Vector-Valued Functions Section Project: Witch of Agnesi 12.2 Differentiation and Integration of Vector-Valued Functions 12.3 Velocity and Acceleration 12.4 Tangent Vectors and Normal Vectors 12.5 Arc Length a

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