Ebook: An Atlas of Functions: with Equator, the Atlas Function Calculator

This second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families of interest to scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in two- or three- dimensions depict their shape and qualitative features and flesh out the reader’s familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family.
Features that make the Atlas an invaluable reference tool, yet simple to use, include:
full coverage of those functions—elementary and "special”—that meet everyday needs
a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus
extensive cross-referencing and comprehensive indexing, with useful appendices
the inclusion of innovative software--Equator, the Atlas Function Calculator
the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.

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This second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families of interest to scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in two- or three- dimensions depict their shape and qualitative features and flesh out the reader’s familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family.
Features that make the Atlas an invaluable reference tool, yet simple to use, include:
full coverage of those functions—elementary and "special”—that meet everyday needs
a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus
extensive cross-referencing and comprehensive indexing, with useful appendices
the inclusion of innovative software--Equator, the Atlas Function Calculator
the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.

---

This second edition of An Atlas of Functions, with Equator, the Atlas Function Calculator, provides comprehensive information on several hundred functions or function families of interest to scientists, engineers and mathematicians who are concerned with the quantitative aspects of their field. Beginning with simple integer-valued functions, the book progresses to polynomials, exponential, trigonometric, Bessel, and hypergeometric functions, and many more. The 65 chapters are arranged roughly in order of increasing complexity, mathematical sophistication being kept to a minimum while stressing utility throughout. In addition to providing definitions and simple properties for every function, each chapter catalogs more complex interrelationships as well as the derivatives, integrals, Laplace transforms and other characteristics of the function. Numerous color figures in two- or three- dimensions depict their shape and qualitative features and flesh out the reader’s familiarity with the functions. In many instances, the chapter concludes with a concise exposition on a topic in applied mathematics associated with the particular function or function family.
Features that make the Atlas an invaluable reference tool, yet simple to use, include:
full coverage of those functions—elementary and "special”—that meet everyday needs
a standardized chapter format, making it easy to locate needed information on such aspects as: nomenclature, general behavior, definitions, intrarelationships, expansions, approximations, limits, and response to operations of the calculus
extensive cross-referencing and comprehensive indexing, with useful appendices
the inclusion of innovative software--Equator, the Atlas Function Calculator
the inclusion of new material dealing with interesting applications of many of the function families, building upon the favorable responses to similar material in the first edition.

Content:
Front Matter....Pages i-xi
General Considerations....Pages 1-11
The Factorial Function n!....Pages 13-19
The Zeta Numbers and Related Functions....Pages 21-27
The Linear Function bx + c and Its Reciprocal....Pages 29-38
Modifying Functions....Pages 39-44
The Heaviside u(x?a) And Dirac ?(x?a) Functions....Pages 45-48
Polynomial Functions....Pages 49-56
The Logarithmic Function ln(x)....Pages 57-65
The Exponential Function exp(±x)....Pages 67-74
The Hyperbolic Cosine Cosh(x) and Sine Sinh(x) Functions....Pages 75-80
The Hyperbolic Secant Sech(x) and Cosecant Csch(x) Functions....Pages 81-93
The Hyperbolic Tangent tanh(x) and Cotangent coth(x) Functions....Pages 95-102
The Inverse Hyperbolic Functions....Pages 103-112
The Cosine cos(x) and Sine sin(x) Functions....Pages 113-120
The Secant sec(x) And cosecant csc(x) Functions....Pages 121-130
The Tangent tan(x) and Cotangent cot(x) Functions....Pages 131-138
The Inverse Circular Functions....Pages 139-146
Periodic Functions....Pages 147-158
The Exponential Integrals Ei(x) and Ein(x)....Pages 159-174
Sine and Cosine Integrals....Pages 175-180
The Fresnel Integrals C(x) and S(x)....Pages 181-186
The Error Function erf(x) and Its Complement erfc(x)....Pages 187-196
Dawson’s Integral daw(x)....Pages 197-208
The Gamma Function ?(v)....Pages 209-216
The Digamma Function ?(v)....Pages 217-227
The Incomplete Gamma Functions....Pages 229-239
The Kummer Function M(a,c,x)....Pages 241-253
The Tricomi Function U(a,c,x)....Pages 255-267
The Kelvin Functions....Pages 269-279
The Airy Functions Ai(x) and Bi(x)....Pages 281-288
The Incomplete Beta Function B(v,?,x)....Pages 289-296
The Gauss Hypergeometric Function F(a,b,c,x)....Pages 297-307
The Complete Elliptic Integrals K(k) and E(k)....Pages 309-328
The Incomplete Elliptic Integrals F(k,?) AND E(k,?)....Pages 329-338
The Jacobian Elliptic Functions....Pages 339-350
The Hurwitz Function ?(v, u)....Pages 351-366
Back Matter....Pages 367-374
....Pages 375-383