title: Scientist & Diversity Program Manager

industry: Defense & Space

state: RI, zip: 2840

country: United States

degree: B.A. (Philo)

year: 1973

graduate: Teachers College & Grad. Sch Arts & Sciences, Columbia

degree: M.A., M.Phil., Ph.D.

year: 1980

A Note is added to the original paper. An additional simpler proof of the limit is given. more>>

**Tags:**Calculus, proofs, limits, Stirlings Approximation factorials, factorials, derivatives, M Boas, Finney Thomas, L Bers, W Feller, Mathematica, C B Morrey

**Categories:**

We seek to provide a plausible elementary proof outline of derivative by the limit definition. This demonstration is not available in standard... ... more>>

Four related algebraic exponential formulas in Gradshteyn and Rhyzik are derived. Shows method of deriving integrals by "inspired guessing" and... ... more>>

In this paper we demonstrate a general limit for exponential functions by elementary differential calculus methods (log differentiation and... ... more>>

The author has created a small family of generalized indefinite and definite algebraic–exponential real variable integrals based on the gamma... ... more>>

A complete list of formulas solved in author's handbook, "500 Integrals of Elementary and Special Functions". more>>

**Tags:**integrals, nonelementary transcendental special ..., series, products, exponential functions, trigonometry, Frulanni integrals, gamma function, advanced calculus, Sokolnikoff, Gradshteyn Rhyzik, Table Integrals, Series, Products, Alan Jeffrey, Francis J OBrien, 500 Integrals Elementary Special Func...

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In this paper we show the derivation for two general algebraic-trigonometric integrals using elementary complex variables and the gamma function. ... ... more>>

**Tags:**algebraictrigonometric integrals, gamma function, complex variables, Eulers Formula, Gradshyetn Rhyzik , Table Integrals, Series Products, G S Carr, Formulas Theorems Pure Mathematics, complex conjugation, complexifying integral, MIT 1803 Differential Equations, Fresnel integral, polar equations, Lipman Bers, Aquidneck Indian Council, Francis J OBrien,

This paper provides derivations for a class of improper integrals of algebraic–exponential–trigonometric functions. The approach uses complex... ... more>>

**Tags:**algebraicexponentialtrigonometric int..., gamma function, complex variables, Eulers Formula, Gradshyetn Rhyzik , Table Integrals, Series Products, G S Carr, Formulas Theorems Pure Mathematics, complex conjugation, complexifying integral, MIT 1803 Differential Equations, polar equations, Lipman Bers, Aquidneck Indian Council, Francis J OBrien

**Categories:**

Demonstrates the evaluation of complicated algebraic-exponential-circular integrals by elementary complex numbers (Euler's Formula, DeMoivre's... ... more>>

**Tags:**algebraictrigonometric integrals, gamma function, complex numbers, Eulers Formula, Eulers Identity, complex conjugation, Gradshyetn Rhyzik , Table Integrals, Series Products, G S Carr, Formulas Theorems Pure Mathematics, complexifying integral, MIT 1803 Differential Equations, polar equations, Lipman Bers, Aquidneck Indian Council, Francis J OBrien

**Categories:**

A derivation of the expansion of ln(a x) by the Binomial Series. ERRATA: page 3, 3rd line: change "small h or" to "small h or large n" ERRATA:... ... more>>

**Tags:**natural log function , log expansion, Maclaurin Series, Binomial Series, infinite series, Ratio Test, interval convergence, endpoint testing, alternating series test, integral test, series representations, complex numbers, Eulers Identity, exponential theorem, Table Integrals, Series, Products

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Despite my field & interest being statistics Columbia requested that I do this field work among Rikers Island felons. Was resentful about this... ... more>>

**Tags:**Standard American English, Black English, reading comprehension, linguistics, dialectology, Rikers Island, New York City, prison inmates, Teachers College, Columbia University, Frank Waabu Moondancer

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This paper verifies Euler’s Formula by series expansions and graphical methods at an elementary level. Binomial and Exponential series expansions... ... more>>

**Tags:**complex numbers, Eulers Formula, series expansions, proofs, derivations, Aquidneck Indian Council, Francis JOBrien

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An essay on race and intelligence with emphasis on Americans Indians. 2nd ed. more>>

Shows solution of indefinite intergal of exp(ax) * cos(bx) for standard approach and by complex numbers (real parts only). Review of integrating and ... more>>

**Tags:**Calculus, Integration, differentiation, integration parts , trigonometric functions, real variables, complex variables, Crowell Slesnick, Calculus Analytic Geometry, Eulers Formula, Complex Conjugation, complex analysis, contour integration, complex exponential, Mathematica, Eulers Identity, Maclaurin series, Francis JOBrien, Aquidneck Indian Council, Gleason, M Fundamentals Abstract Analysis, differential equations, Fourier analysis, MIT, integration complex numbers

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Derivation for powers of trigonometric functions (cosine and sine) using complex numbers. NOTE : Equations still garbled in places, but reads... ... more>>

**Tags:**Powers trigonometric functions, circular identities, complex numbers, Eulers Formula, multipleangle formulas, GS Carr, Spiegel, Mathematical Handbook Formulas Tables

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