University calculus
著者
書誌事項
University calculus
Pearson Addison Wesley, c2008
Alternate ed
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注記
Includes index
内容説明・目次
内容説明
Calculus hasn't changed, but your students have. Many of today's students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. University Calculus: Alternate Edition responds to the needs of today's students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.
The Alternate Edition is the perfect alternative for instructors who want the same quality and quantity of exercises as Thomas' Calculus, Media Upgrade, Eleventh Edition but prefer a faster-paced presentation.
University Calculus: Alternate Edition is now available with an enhanced MyMathLab (TM) course-the ultimate homework, tutorial and study solution for today's students. The enhanced MyMathLab (TM) course includes a rich and flexible set of course materials and features innovative Java (TM) Applets, Group Projects, and new MathXL (R) exercises. This text is also available with WebAssign (R) and WeBWorK (R).
目次
- 1. Functions 1.1 Functions and Their Graphs 1.2 Combining Functions
- Shifting and Scaling Graphs 1.3 Trigonometric Functions 1.4 Graphing with Calculators and Computers 2. Limits and Continuity 2.1 Rates of Change and Tangents to Curves 2.2 Limit of a Function and Limit Laws 2.3 The Precise Definition of a Limit 2.4 One-Sided Limits and Limits at Infinity 2.5 Infinite Limits and Vertical Asymptotes 2.6 Continuity 2.7 Tangents and Derivatives at a Point 3. Differentiation 3.1 The Derivative as a Function 3.2 Differentiation Rules 3.3 The Derivative as a Rate of Change 3.4 Derivatives of Trigonometric Functions 3.5 The Chain Rule 3.6 Implicit Differentiation 3.7 Related Rates 3.8 Linearization and Differentials 3.9 Parametrizations of Plane Curves 4. Applications of Derivatives 4.1 Extreme Values of Functions 4.2 The Mean Value Theorem 4.3 Monotonic Functions and the First Derivative Test 4.4 Concavity and Curve Sketching 4.5 Applied Optimization 4.6 Newton's Method 4.7 Antiderivatives 5. Integration 5.1 Area and Estimating with Finite Sums 5.2 Sigma Notation and Limits of Finite Sums 5.3 The Definite Integral 5.4 The Fundamental Theorem of Calculus 5.5 Indefinite Integrals and the Substitution Rule 5.6 Substitution and Area Between Curves 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 Areas of Surfaces of Revolution 6.5 Work 6.6 Moments and Centers of Mass 6.7 Fluid Pressures and Forces 7. Transcendental Functions 7.1 Inverse Functions and Their Derivatives 7.2 Natural Logarithms 7.3 Exponential Functions 7.4 Inverse Trigonometric Functions 7.5 Exponential Change and Separable Differential Equations 7.6 Indeterminate Forms and L'Hopital's Rule 7.7 Hyperbolic Functions 8. Techniques of Integration 8.1 Integration by Parts 8.2 Trigonometric Integrals 8.3 Trigonometric Substitutions 8.4 Integration of Rational Functions by Partial Fractions 8.5 Integral Tables and Computer Algebra Systems 8.6 Numerical Integration 8.7 Improper Integrals 9. Infinite Sequences and Series 9.1 Sequences 9.2 Infinite Series 9.3 The Integral Test 9.4 Comparison Tests 9.5 The Ratio and Root Tests 9.6 Alternating Series, Absolute and Conditional Convergence 9.7 Power Series 9.8 Taylor and Maclaurin Series 9.9 Convergence of Taylor Series 9.10 The Binomial Series 10. Polar Coordinates and Conics 10.1 Polar Coordinates 10.2 Graphing in Polar Coordinates 10.3 Areas and Lengths in Polar Coordinates 10.4 Conic Sections 10.5 Conics in Polar Coordinates 10.6 Conics and Parametric Equations
- The Cycloid 11. Vectors and the Geometry of Space 11.1 Three-Dimensional Coordinate Systems 11.2 Vectors 11.3 The Dot Product 11.4 The Cross Product 11.5 Lines and Planes in Space 11.6 Cylinders and Quadric Surfaces 12. Vector-Valued Functions and Motion in Space 12.1 Vector Functions and Their Derivatives 12.2 Integrals of Vector Functions 12.3 Arc Length in Space 12.4 Curvature of a Curve 12.5 Tangential and Normal Components of Acceleration 12.6 Velocity and Acceleration in Polar Coordinates 13. Partial Derivatives 13.1 Functions of Several Variables 13.2 Limits and Continuity in Higher Dimensions 13.3 Partial Derivatives 13.4 The Chain Rule 13.5 Directional Derivatives and Gradient Vectors 13.6 Tangent Planes and Differentials 13.7 Extreme Values and Saddle Points 13.8 Lagrange Multipliers 13.9 Taylor's Formula for Two Variables 14. Multiple Integrals 14.1 Double and Iterated Integrals over Rectangles 14.2 Double Integrals over General Regions 14.3 Area by Double Integration 14.4 Double Integrals in Polar Form 14.5 Triple Integrals in Rectangular Coordinates 14.6 Moments and Centers of Mass 14.7 Triple Integrals in Cylindrical and Spherical Coordinates 14.8 Substitutions in Multiple Integrals 15. Integration in Vector Fields 15.1 Line Integrals 15.2 Vector Fields, Work, Circulation, and Flux 15.3 Path Independence, Potential Functions, and Conservative Fields 15.4 Green's Theorem in the Plane 15.5 Surfaces and Area 15.6 Surface Integrals and Flux 15.7 Stokes' Theorem 15.8 The Divergence Theorem and a Unified Theory 16. First-Order Differential Equations (online) 16.1 Solutions, Slope Fields, and Picard's Theorem 16.2 First-Order Linear Equations 16.3 Applications 16.4 Euler's Method 16.5 Graphical Solutions of Autonomous Equations 16.6 Systems of Equations and Phase Planes 17. Second-Order Differential Equations (online) 17.1 Second-Order Linear Equations 17.2 Nonhomogeneous Linear Equations 17.3 Applications 17.4 Euler Equations 17.5 Power Series Solutions Appendices 1 Real Numbers and the Real Line 2 Mathematical Induction 3 Lines, Circles, and Parabolas 4 Trigonometry Formulas 5 Proofs of Limit Theorems 6 Commonly Occurring Limits 7 Theory of the Real Numbers 8 The Distributive Law for Vector Cross Products 9 The Mixed Derivative Theorem and the Increment Theorem
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