Carol Ash, Robert B. Ash

The Calculus Tutoring Book

• Broschiertes Buch

Produktbeschreibung

This book fills an educational void by adapting unique classroom-tested techniques that students find most congenial. that strip the shroud of mystery from an esoteric subject. that prepare students for applications of calculus in later courses.

Produktdetails

• Verlag: Wiley & Sons
• 1. Auflage
• Seitenzahl: 544
• Erscheinungstermin: 19. Oktober 1993
• Englisch
• Abmessung: 246mm x 189mm x 29mm
• Gewicht: 1021g
• ISBN-13: 9780780310445
• ISBN-10: 0780310446
• Artikelnr.: 14910453

Autorenporträt

Carol Ash is the author of The Calculus Tutoring Book, published by Wiley. Robert B. Ash as written about, taught, or studied virtually every area of mathematics.

Inhaltsangabe

Preface. FUNCTIONS. Introduction. The Graph of a Function. The
Trigonometric Functions. Inverse Functions and the Inverse Trigonometric
Functions. Exponential and Logarithm Functions. Solving Inequalities
Involving Elementary Functions. Graphs of Translations, Reflections,
Expansions and Sums. Review of Problems for Chapter 1. LIMITS.
Introduction. Finding Limits of Combinations of Functions. Indeterminate
Limits. Review Problems for Chapter 2. THE DERIVATIVE PART I. Preview.
Definition and Some Applications of the Derivative. Derivatives of the
Basic Functions. Nondifferentiable Functions. Derivatives of Constant
Multiples, Sums, Products and Quotients. The Derivative of a Composition.
Implicit Differentiation and Logarithmic Differentiation.
Antidifferentiation. Review Problems for Chapter 3. THE DERIVATIVE PART II.
Relative Maxima and Minima. Absolute Maxima and Minima. L'Hôpital's Rule
and Orders of Magnitude. Indeterminate Products, Differences and
Exponential Forms. Drawing Graphs of Functions. Related Rates. Newton's
Method. Differentials. Separable Differential Equations. Review Problems
for Chapter 4. THE INTEGRAL PART I. Preview. Definition and Some
Applications of the Integral. The Fundamental Theorem of Calculus.
Numerical Integration. Nonintegrable Functions. Improper Integals. Review
Problems for Chapter 5. THE INTEGRAL PART II. Further Applications of the
Integral. The Centroid of a Solid Hemisphere. Area and Arc Length. The
Surface Area of a Cone and a Sphere. Integrals with a Variable Upper Limit.
Review Problems for Chapter 6. ANTIDIFFERENTIATION. Introduction.
Substitution. Pre-Table Algebra I. Pre-Table Algebra II: Partial Faction
Decomposition. Integration by Parts. Recursion Formulas. Trigonometric
Substitution. Choosing a Method. Combining Techniques of
Antidifferentiation with the Fundamental Theorem. Review Problems for
Chapter 7. SERIES. Introduction. Geometric Series. Convergence Tests for
Positive Series I. Convergence Tests for Positive Series II. Alternating
Series. Power Series Functions. Power Series Representations for Elementary
Functions I. Power Series Representations for Elementary Functions II
(Maclaurin Series). The Taylor Reminder Formula and an Estimate for the
Number e. Power Series in Powers of x - b (Taylor Series). Review Problems
for Chapter 8. VECTORS. Introduction. Vector Addition, Subtraction, Scalar
Multiplication and Norms. The Dot Product. The Cross Product. The Scalar
Triple Product. The Velocity Vector. The Acceleration Vector. Review
Problems for Chapter 9. TOPICS IN THREE-DIMENSIONAL ANALYTIC GEOMETRY.
Spheres. Planes. Lines. Cylindrical and Quadric Surfaces. Cylindrical and
Spherical Coordinates. Review Problems for Chapter 10. PARTIAL DERIVATIVES.
Graphs and Level Sets. Partial Derivatives. Chain Rules for First-Order
Partial Derivatives. Chain Rules for Second-Order Partial Derivatives.
Maxima and Minima. The Gradient. Differentials and Exact Differential
Equations. Review Problems for Chapter 11. MULTIPLE INTEGRALS. Definition
and Some Applications of the Double Integral. Computing Double Integrals.
Double Integration in Polar Coordinates. Area and Volume. Further
Applications of the Double Integral. Triple Integrals. Triple Integration
in Spherical Coordinates. Center of Mass. Review Problems for Chapter 12.
APPENDIX. A1: Distance and Slope. A2: Equations of Lines. A3: Circles,
Ellipses, Hyperbolas and Parabolas. A4: The Binomial Theorem. A5:
Determinants. A6: Polar Coordinates. Solutions to the Problems.
Abbreviations Used in the Solutions. List of Symbols. Index. Authors'
Biographies.