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(Each Chapter ends with Chapter Equations, Review Exercises, and a Practice Test).
1. Functions and Graphs.
Introduction to Functions.
Algebraic Functions.
Rectangular Coordinates.
The Graph of a Function.
2. Plane Analytic Geometry.
Basic Definitions.
The Straight Line.
The Circle.
The Parabola.
The Ellipse.
The Hyperbola.
Translation of Axes.
The Second Degree Equation.
3. The Derivative.
Limits.
The Slope of a Tangent to a Curve.
The Derivative.
The Derivative as an Instantaneous Rate of Change.
Derivatives of Polynomials.
Derivatives of Products and Quotients of Functions.
The Derivative of a Power of a Function.
Differentiation of Implicit Functions.
Higher Derivatives.
4. Applications of the Derivative.
Tangents and Normals.
Newton's Method for Solving Equations.
Curvilinear Motion.
Related Rates.
Using Derivatives in Curve Sketching.
More on Curve Sketching.
Applied Maximum and Minimum Problems.
Differentials and Linear Approximations.
5. Integration.
Antiderivatives.
The Indefinite Integral.
The Area Under a Curve.
The Definite Integral.
Numerical Integration; The Trapezoidal Rule.
Simpson's Rule.
6. Applications of Integration.
Applications of the Indefinite Integral.
Areas by Integration.
Volumes by Integration.
Centroids.
Moments of Inertia.
Work by a Variable Force.
Force Due to Liquid Pressure.
Other Applications.
7. Differentiation of the Trigonometric and Inverse Trigonometric Functions.
The Trigonometric Functions.
Basic Trigonometric Relations.
Derivatives of the Sine and Cosine Functions.
Derivatives of Other Trigonometric Functions.
The Inverse Trigonometric Functions.
Derivatives of the Inverse Trigonometric Functions.
Applications.
8. Derivatives of the Exponential and Logarithmic Functions.
Exponential and Logarithmic Functions.
Derivative of the Logarithmic Function.
Derivative of the Exponential Function.
Applications.
9. Integration by Standard Forms.
The General Power Formula.
The Basic Logarithmic Form.
The Exponential Form.
Basic Trigonometric Forms.
Other Trigonometric Forms.
Inverse Trigonometric Forms.
10. Methods of Integration.
Integration by Parts.
Integration by Substitution.
Integration by Trigonometric Substitution.
Integration by Partial Fractions: Nonrepeated Linear Factors.
Integration by Partial Fractions: Other Cases.
Integration by Use of Tables.
Improper Integrals.
11. Introduction to Partial Derivatives and Double Integrals.
Functions of Two Variables.
Curves and Surfaces in Three Dimensions.
Partial Derivatives.
Certain Applications of Partial Derivatives.
Double Integrals.
Centroids and Moments of Inertia by Double Integration.
12. Polar and Cylindrical Coordinates.
Polar Coordinates.
Curves in Polar Coordinates.
Applications of Differentiation and Integration in Polar Coordinates.
Cylindrical Coordinates.
13. Expansion of Functions in Series.
Infinite Series.
Maclaurin Series.
Certain Operations with Series.
Computations by Use of Series Expansions.
Taylor Series.
Introduction to Fourier Series.
More About Fourier Series.
14. First-Order Differential Equations.
Solutions of Differential Equations.
Separation of Variables.
Integrating Combinations.
The Linear Differential Equation of the First Order.
Elementary Applications.
15. Higher-Order Differential Equations.
Higher-Order Homogeneous Equations.
Auxiliary Equation with Repeated or Complex Roots.
Solutions of Nonhomogeneous Equations.
Applications of Higher Order Equations.
16. Other Methods of Solving Differential Equations.
Numerical Solutions.
A Method of Successive Approximations.
Laplace Transforms.
Solving Differential Equations by Laplace Tansforms.
Appendix A. Supplementary Topics.
Rotations of Axes.
Regression.
Appendix B. Units of Measurement.
Appendix C. Introduction.
The Graphing Calculator.
Graphing Calculator Programs.
Appendix D. Newton's Method.
Appendix E. A Table of Integrals.
Answers to Odd-Numbered Exercises.
Solutions to Practice Test Problems.
Index of Applications.
Index of Writing Exercises.
Index.
| Price | Condition | Delivery | Seller | Action |
| $99.99 | Digital |
| WonderClub |
Markus Kirschner
reviewed Technical Calculus With Analytic Geometry on March 19, 2018
Technical Calculus With Analytic Geometry
In writing "A Tour of the Calculus", there are three things that David Berlinski would like you to know, in order:
1. David Berlinski has read more books than you.
2. David Berlinski is well regarded among mathematicians.
3. The motivations and concepts that support calculus as a foundational achievement of modern thought.
Let me offer this praise: Berlinski faithfully and artfully expresses what almost every math teacher misses; The motivation for creating calculus was to understand a world of varying forces, flows, and influences. Questions like "Why do the planets move like they do?", "How fast is a cannonball moving in mid-flight?", and "How much concrete will I need to dam this river?" were not really answerable before calculus. Calculus gives us a way to quantify the nuances of natural phenomenon that was never available before in history. This is exciting, and the author communicates this excitement in the mirror of his own excitement.
This enthusiasm is quickly buried, however, in a mountain of cheeky literary references and irrelevant, boring asides. The author tries to bind all these together with metaphors, which are stretched to ludicrous lengths and ultimately break. These overlong side trips are neither explanatory nor entertaining.
Don't get me wrong. I do not wish mathematics to remain dry and unattainable. Ostensibly, neither does David Berlinski. I so wanted to be able to point to this book and tell others, "See, this is why calculus exists. This is why math is central to every aspect of modern life!" Alas, the book fails in this regard. It fails also in its stated mission to illustrate the formal, stuffy proofs that underpin calculus in a down-to-earth way. Every time such an illustration is attempted, it turns into a bizarre shaggy dog story that is a blend of historical fiction and motorcycle rides.
I cannot recommend this book; either as a calculus tutorial, or as entertainment.
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