Calculus, matrix version (6° ed )
Langue : Anglais
Auteurs : EDWARDS C. Henry, PENNEY David
For three-semester undergraduate-level courses in Calculus and for standard undergraduate Calculus courses.
The Matrix version combines traditional mainstream calculus with the most flexible approach to new ideas and calculator/computer technology. It contains superb problem sets and a fresh conceptual emphasis flavored by new technological possibilities. The Calculus II portion now has a new focus on differential equations, and Calculus III now includes a full chapter on matrices and eigenvalues and the integrations of matrix notation. The new edition of the Early Transcendental version is nearly a new book. Previous Chapters 7 and 8 on transcendental functions have been eliminated by being integrated fully into Chapters 1-6. Thus Chapters 1-6 have been completely rewritten. Calculus II now has a new focus on differential equations, anchored by a new Chapter 8. However, in the midst of these changes, this book still retains its reputation for accuracy, mathematical precision, and appropriate rigor.
1. Functions, Graphs, and Models.
2. Prelude to Calculus.
3. The Derivative.
4. Additional Applications of the Derivative.
5. The Integral.
6. Applications of the Integral.
7. Calculus of Transcendental Functions.
8. Techniques of Integration.
9. Differential Equations.
10. Polar Coordinates and Parametric Curves.
11. Infinite Series.
12. Vectors and Matrices.
13. Curves and Surfaces in Space.
14. Partial Differentiation.
15. Multiple Integrals.
Functions and Mathematical Modeling. Graphs of Equations and Functions. Polynomials and Algebraic Functions. Transcendental Functions. Preview: What Is Calculus?
2. Prelude to Calculus.
Tangent Lines and Slope Predictors. The Limit Concept. More about Limits. The Concept of Continuity.
3. The Derivative.
The Derivative and Rates of Change. Basic Differentiation Rules. The Chain Rule. Derivatives of Algebraic Functions. Maxima and Minima of Functions on Closed Intervals. Applied Optimization Problems. Derivatives of Trigonometric Functions. Successive Approximations and Newtons Method.
4. Additional Applications of the Derivative.
Introduction. Implicit Differentiation and Related Rates. Increments, Differentials, and Linear Approximation. Increasing and Decreasing Functions and the Mean Value Theorem. The First Derivative Test and Applications. Simple Curve Sketching. Higher Derivatives and Concavity. Curve Sketching and Asymptotes.
5. The Integral.
Introduction. Antiderivatives and Initial Value Problems. Elementary Area Computations. Riemann Sums and the Integral. Evaluation of Integrals. The Fundamental Theorem of Calculus. Integration by Substitution. Areas of Plane Regions. Numerical Integration.
6. Applications of the Integral.
Riemann Sum Approximations. Volumes by the Method of Cross Sections. Volumes by the Method of Cylindrical Shells. Arc Length and Surface Area of Revolution. Force and Work. Centroids of Plane Regions and Curves.
7. Calculus of Transcendental Functions.
Exponential and Logarithmic Functions. Indeterminate Forms of LH pitals Rule. More Indeterminate Forms. The Logarithm as an Integral. Inverse Trigonometric Functions. Hyperbolic Functions.
8. Techniques of Integration.
Introduction. Integral Tables and Simple Substitutions. Integration by Parts. Trigonometric Integrals. Rational Functions and Partial Fractions. Trigonometric Substitutions. Integrals Involving Quadratic Polynomials. Improper Integrals.
9. Differential Equations.
Simple Equations and Models. Slope Fields and Eulers Method. Separable Equations and Applications. Linear Equations and Applications. Population Models. Linear Second-Order Equations. Mechanical Vibrations.
10. Polar Coordinates and Parametric Curves.
Analytic Geometry and the Conic Sections. Polar Coordinates. Area Computations in Polar Coordinates. Parametric Curves. Integral Computations with Parametric Curves. Conic Sections and Applications.
11. Infinite Series.
Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations.
12. Vectors and Matrices.
Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Two Vectors. Lines and Planes in Space. Linear Systems and Matrices. Matrix Operations. Eigenvalues and Rotated Conics.
13. Curves and Surfaces in Space.
Curves and Motion in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates.
14. Partial Differentiation.
Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimizations Problems. Linear Approximation and Matrix Derivatives. The Multivariable Chain Rule. Directional Derivatives and Gradient Vectors. Lagrange Multipliers and Constrained Optimization. Critical Points of Multivariable Functions.
15. Multiple Integrals.
Double Integrals. Double Integrals over
- NEW - Free CD-ROM - Includes animations of nearly all the text examples, homework starters, quizzes, and interactive computer projects. It also contains the entire book in Maple notebooks.
- NEW - An entire chapter devoted to calculus of transcendental functions - Combines parts of two previous chapters into the new Ch. 7.
- Provides students with a clearer explanation of this subject within one solid, unified, and fully rewritten chapter. - NEW - Expanded treatment of differential equations (New Chapter 9).
- Introduces students to both direction fields and Eulers method together with the more symbolic elementary methods and applications for both first- and second-order equations. - NEW - 1040 new True/False Questions - Available on the CD. They focus on theory and p
Date de parution : 09-2002
Ouvrage de 1264 p.
27.9x22.2 cm
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