Methods of Mathematics Applied to Calculus, Probability, and Statistics.

Format:

Book

Author/Creator:

Hamming, Richard W.

Series:

Dover Books on Mathematics

Language:

English

Subjects (All):

Mathematics.

Physical Description:

1 online resource (1583 p.)

Edition:

1st ed.

Place of Publication:

Newburyport : Dover Publications, 2012.

Language Note:

English

Summary:

Understanding calculus is vital to the creative applications of mathematics in numerous areas. This text focuses on the most widely used applications of mathematical methods, including those related to other important fields such as probability and statistics. The four-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. In addition to three helpful appendixes, the text features answers to some of the exercises. Appropriate for advanced undergraduates and graduate students,

Contents:

Cover; Title Page; Copyright Page; Contents; Preface; I - Algebra and Analytic Geometry; 1 Prologue; 1.1 The Importance of Mathematics; 1.2 The Uniqueness of Mathematics; 1.3 The Unreasonable Effectiveness of Mathematics; 1.4 Mathematics as a Language; 1.5 What is Mathematics?; 1.6 Mathematical Rigor; 1.7 Advice to You; 1.8 Remarks on Learning the Course; References; 2 The Integers; 2.1 The Integers; 2.2 On Proving Theorems; 2.3 Mathematical Induction; 2.4 The Binomial Theorem; 2.5 Mathematical Induction Using Undetermined Coefficients; 2.6 The Ellipsis Method

2.7 Review and Fallacies in Algebra2.8 Summary; 3 Fractions-Rational Numbers; 3.1 Rational Numbers; 3.2 Euclid's Algorithm; 3.3 The Rational Number System; 3.4 Irrational Numbers; 3.5 On Finding Irrational Numbers; 3.6 Decimal Representation of a Rational Number; 3.7 Inequalities; 3.8 Exponents-An Application of Rational Numbers; 3.9 Summary and Further Remarks; 4 Real Numbers, Functions, and Philosophy; 4.1 The Real Line; 4.2 Philosophy; 4.3 The Idea of a Function; 4.4 The Absolute Value Function; 4.5 Assumptions About Continuity; 4.6 Polynomials and Integers; 4.7 Linear Independence

4.8 Complex Numbers4.9 More Philosophy; 4.10 Summary; 5 Analytic Geometry; 5.1 Cartesian Coordinates; 5.2 The Pythagorean Distance; 5.3 Curves; 5.4 Linear Equations-Straight Lines; 5.5 Slope; 5.6 Special Forms of the Straight Line; 5.7 On Proving Geometric Theorems in Analytic Geometry; 5.8* The Normal Form of the Straight Line; 5.9 Translation of the Coordinate Axes; 5.10* The Area of a Triangle; 5.11* A Problem in Computer Graphics; 5.12 The Complex Plane; 5.13 Summary; 6 Curves of Second Degree-Conics; 6.1 Strategy; 6.2 Circles; 6.3 Completing the Square

7.10 On the Formal Differentiation of Functions7.11 Summary; 8 Geometric Applications; 8.1 Tangent and Normal Lines; 8.2 Higher Derivatives-Notation; 8.3 Implicit Differentiation; 8.4 Curvature; 8.5 Maxima and Minima; 8.6 Inflection Points; 8.7 Curve Tracing; 8.8 Functions, Equations, and Curves; 8.9 Summary; 9 Nongeometric Applications; 9.1 Scaling Geometry; 9.2 Equivalent Ideas; 9.3 Velocity; 9.4 Acceleration; 9.5 Simple Rate Problems; 9.6 More Rate Problems; 9.7 Newton's Method for Finding Zeros; 9.8 Multiple Zeros; 9.9 The Summation Notation; 9.10 Generating Identities

9.11 Generating Functions-Place Holders

Notes:

Description based upon print version of record.

Description based on publisher supplied metadata and other sources.

ISBN:

0-486-13887-9

1-62198-605-5

OCLC:

898421376