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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.
List of contents
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.
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About the author
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.
Summary
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.
