University calculus : elements with early transcendentals
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Bibliographic Information
University calculus : elements with early transcendentals
（Pearson international edition）
Pearson/Addison Wesley, c2009
- : pbk.
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Note
Includes bibliographical references and index
Description and Table of Contents
Description
University Calculus: Elements is a three semester, short early transcendentals science and engineering majors calculus book. It maintains the high standards and careful development that have been the hallmark of the Thomas' Calculus series, but this text follows a bee line to the essential elements of calculus. This text is designed for those instructors teaching an early transcendentals course who want a short book that covers everything in their syllabus with none of the verbiage and weight of the larger books.
Table of Contents
- 1. Functions and Limits 1.1 Functions and Their Graphs 1.2 Combining Functions
- Shifting and Scaling Graphs 1.3 Rates of Change and Tangents to Curves 1.4 Limit of a Function and Limit Laws 1.5 Precise Definition of a Limit 1.6 One-Sided Limits 1.7 Continuity 1.8 Limits Involving Infinity Questions to Guide Your Review Practice and Additional Exercises 2. Differentiation 2.1 Tangents and Derivatives at a Point 2.2 The Derivative as a Function 2.3 Differentiation Rules 2.4 The Derivative as a Rate of Change 2.5 Derivatives of Trigonometric Functions 2.6 Exponential Functions 2.7 The Chain Rule 2.8 Implicit Differentiation 2.9 Inverse Functions and Their Derivatives 2.10 Logarithmic Functions 2.11 Inverse Trigonometric Functions 2.12 Related Rates 2.13 Linearization and Differentials Questions to Guide Your Review Practice and Additional Exercises 3. Applications of Derivatives 3.1 Extreme Values of Functions 3.2 The Mean Value Theorem 3.3 Monotonic Functions and the First Derivative Test 3.4 Concavity and Curve Sketching 3.5 Parametrizations of Plane Curves 3.6 Applied Optimization 3.7 Indeterminate Forms and L'Hopital's Rule 3.8 Newton's Method 3.9 Hyperbolic Functions Questions to Guide Your Review Practice and Additional Exercises 4. Integration 4.1 Antiderivatives 4.2 Estimating with Finite Sums 4.3 Sigma Notation and Limits of Finite Sums 4.4 The Definite Integral 4.5 The Fundamental Theorem of Calculus 4.6 Indefinite Integrals and the Substitution Rule 4.7 Substitution and Area Between Curves Questions to Guide Your Review Practice and Additional Exercises 5. Techniques of Integration 5.1 Integration by Parts 5.2 Trigonometric Integrals 5.3 Trigonometric Substitutions 5.4 Integration of Rational Functions by Partial Fractions 5.5 Integral Tables and Computer Algebra Systems 5.6 Numerical Integration 5.7 Improper Integrals Questions to Guide Your Review Practice and Additional Exercises 6. Applications of Definite Integrals 6.1 Volumes by Slicing and Rotation About an Axis 6.2 Volumes by Cylindrical Shells 6.3 Lengths of Plane Curves 6.4 Exponential Change and Separable Differential Equations 6.5 Work and Fluid Forces 6.6 Moments and Centers of Mass Questions to Guide Your Review Practice and Additional Exercises 7. Infinite Sequences and Series 7.1 Sequences 7.2 Infinite Series 7.3 The Integral Test 7.4 Comparison Tests 7.5 The Ratio and Root Tests 7.6 Alternating Series, Absolute and Conditional Convergence 7.7 Power Series 7.8 Taylor and Maclaurin Series 7.9 Convergence of Taylor Series 7.10 The Binomial Series Questions to Guide Your Review Practice and Additional Exercises 8. Polar Coordinates and Conics 8.1 Polar Coordinates 8.2 Graphing in Polar Coordinates 8.3 Areas and Lengths in Polar Coordinates 8.4 Conics in Polar Coordinates 8.5 Conics and Parametric Equations
- The Cycloid Questions to Guide Your Review Practice and Additional Exercises 9. Vectors and the Geometry of Space 9.1 Three-Dimensional Coordinate Systems 9.2 Vectors 9.3 The Dot Product 9.4 The Cross Product 9.5 Lines and Planes in Space 9.6 Cylinders and Quadric Surfaces Questions to Guide Your Review Practice and Additional Exercises 10. Vector-Valued Functions and Motion in Space 10.1 Vector Functions and Their Derivatives 10.2 Integrals of Vector Functions 10.3 Arc Length and the Unit Tangent Vector T 10.4 Curvature and the Unit Normal Vector N 10.5 Torsion and the Unit Binormal Vector B 10.6 Planetary Motion Questions to Guide Your Review Practice and Additional Exercises 11. Partial Derivatives 11.1 Functions of Several Variables 11.2 Limits and Continuity in Higher Dimensions 11.3 Partial Derivatives 11.4 The Chain Rule 11.5 Directional Derivatives and Gradient Vectors 11.6 Tangent Planes and Differentials 11.7 Extreme Values and Saddle Points 11.8 Lagrange Multipliers Questions to Guide Your Review Practice and Additional Exercises 12. Multiple Integrals 12.1 Double and Iterated Integrals over Rectangles 12.2 Double Integrals over General Regions 12.3 Area by Double Integration 12.4 Double Integrals in Polar Form 12.5 Triple Integrals in Rectangular Coordinates 12.6 Moments and Centers of Mass 12.7 Triple Integrals in Cylindrical and Spherical Coordinates 12.8 Substitutions in Multiple Integrals Questions to Guide Your Review Practice and Additional Exercises 13. Integration in Vector Fields 13.1 Line Integrals 13.2 Vector Fields, Work, Circulation, and Flux 13.3 Path Independence, Potential Functions, and Conservative Fields 13.4 Green's Theorem in the Plane 13.5 Surface Area and Surface Integrals 13.6 Parametrized Surfaces 13.7 Stokes' Theorem 13.8 The Divergence Theorem and a Unified Theory Questions to Guide Your Review Practice and Additional Exercises Appendices 1. Real Numbers and the Real Line 2. Mathematical Induction 3. Lines, Circles, and Parabolas 4. Trigonometric Functions 5. Basic Algebra and Geometry Formulas 6. Proofs of Limit Theorems and L'Hopital's Rule 7. Commonly Occurring Limits 8. Theory of the Real Numbers 9. Convergence of Power Series and Taylor's Theorem 10. The Distributive Law for Vector Cross Products 11. The Mixed Derivative Theorem and the Increment Theorem 12. Taylor's Formula for Two Variables
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