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Calculus

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Articles 181 - 193 of 193

Full-Text Articles in Mathematics

A Maple Package For The Variational Calculus, Cinnamon Hillyard May 1992

A Maple Package For The Variational Calculus, Cinnamon Hillyard

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The HELMHOLTZ package, written in Maple V, is a collection of commands to support research in the variational calculus. These commands include the standard operators on differential forms, Euler-Lagrange operators, homotopy operators, Lie bracket, Lie derivatives, and the prolongation of a vector field. We give a brief introduction to the variational calculus. We describe each of the commands in the HELMHOLTZ package completely along with numerous examples of each. Applications of the package include verification of symmetry groups for differential equations, solving the inverse problem of the calculus of variations, computing generalized symmetries, and finding variational integrating factors. A complete …

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Applications Of The Calculus For Factorial Arrangements And Allied Topics., Mausumi Bose Dr. Mar 1989

Applications Of The Calculus For Factorial Arrangements And Allied Topics., Mausumi Bose Dr.

Doctoral Theses

This thesis deals primarily with the application of the calculus for factorial ar- rangements (Kurkjian and Zelen (1962, 1963)) to various designs. The thesis has been divided into six chapters. We have made extensive use of Kronecker products and various other results from matrix theory. The results in the first two chapters involve the use of projection operators.In the first four chapters, different classes of factorial experiments have been studied by applying the calculus. Chapter 5 deals with another class of designs called repeated measurements designs (RMD's). It has been shown that the calculus for factorial arrangements serves as a …

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Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner Mar 1983

Who Gave You The Epsilon? The Origins Of Cauchy's Rigorous Calculus, Judith V. Grabiner

Pitzer Faculty Publications and Research

This paper recounts the history of how calculus came to get a rigorous basis in terms of the algebra of inequalities. The result is a brief history of the 150 years from Newton and Leibniz to Cauchy that produced the foundations of analysis.

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Boole's Algebra Isn't Boolean Algebra (Article Review), Calvin Jongsma, John Corcoran Jan 1981

Boole's Algebra Isn't Boolean Algebra (Article Review), Calvin Jongsma, John Corcoran

Faculty Work Comprehensive List

Reviewed Title: Boole's Algebra Isn't Boolean Algebra by Theodore Hailperin. Mathematics Magazine, v. 54:4, pp. 172-184. ISSN: 0025-570X

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Závisí Matematická Pravda Od Času?, Judith V. Grabiner Jan 1980

Závisí Matematická Pravda Od Času?, Judith V. Grabiner

Pitzer Faculty Publications and Research

This is a Slovak translation of Judith Grabiner's "Is Mathematical Truth Time-Dependent?," published in Volume 81 of American Mathematical Monthly (April 1974).

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Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma Jun 1979

Axiomatic Structure And The Method Of Analysis: Shifting Styles In The History Of Mathematics, Calvin Jongsma

Faculty Work Comprehensive List

No abstract provided.

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Is Mathematical Truth Time-Dependent?, Judith V. Grabiner Apr 1974

Is Mathematical Truth Time-Dependent?, Judith V. Grabiner

Pitzer Faculty Publications and Research

Another such mathematical revolution occurred between the eighteenth and nineteenth centuries, and was focused primarily on the calculus. This change was a rejection of the mathematics of powerful techniques and novel results in favor of the mathematics of clear definitions and rigorous proofs. Because this change, however important it may have been for mathematicians themselves, is not often discussed by historians and philosophers, its revolutionary character is not widely understood. In this paper, I shall first try to show that this major change did occur. Then, I shall investigate what brought it about. Once we have done this, we can …

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Calculus And The Computer: A Conservative Approach, Melvin Henriksen Jan 1970

Calculus And The Computer: A Conservative Approach, Melvin Henriksen

All HMC Faculty Publications and Research

This paper describes a program for making the use of numerical methods an integral part of the freshman college course in single variable calculus.

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Decision Problems, Lowell Anderson May 1965

Decision Problems, Lowell Anderson

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

From an intuitive point of view the notion of effective procedure consists of a set of rules or instructions that enables one, in a finite number of steps and in a purely mechanical way, to answer yes or no to any one of a given class of questions. This procedure requires no intelligence to carry out the instructions and, in fact, it is con­ceivable that some mechanical contrivance may be constructed to carry out these instructions. Should such an effective procedure exist, that answers either yes or no, then the group of problems in question is said to be effectively …

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A Brief Consideration Of The Different Methods Of Integration, Donald Golden Nov 1937

A Brief Consideration Of The Different Methods Of Integration, Donald Golden

Master's Theses or Doctor of Nursing Practice

Any student of mathematics is familiar with the importance of the process of integration. Integration is as fundamental to analysis as the basic principles of the number theory are to arithmetical calculation. Some of the common applications of integration are, finding the distance a falling body has travelled during a particular interval of time; to determine the equation of a curve, given different conditions (such as slope of the curve equal numerically to one-half the abscissa, or some similar problem); motion of a projectile; motion in a resisting medium; finding areas and volumes of revolution; length of a curve; areas …

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The Theory Of Determinants: Some Special Forms And Applications, William Ralph Eikelberger May 1937

The Theory Of Determinants: Some Special Forms And Applications, William Ralph Eikelberger

Master's Theses or Doctor of Nursing Practice

The theory of determinants is a relatively new branch of mathematics; it was not firmly established until a brief 200 years ago. It was not until the middle of the 18th century that Cramer, one of the independent discoverers of the fundamental idea, was fortunate enough to attract attention to the theory of determinants. Much of the literature is written on the assumption that its reader has a good background in the subject. Then other authors just give the fundamental properties of determinants without proof of their statements. These latter authors are not interested in the mathematical theory of determinants, …

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Methods Of Obtaining Asymptotes, Paul Sweetland May 1933

Methods Of Obtaining Asymptotes, Paul Sweetland

Master's Theses or Doctor of Nursing Practice

The purpose of this thesis is to present in logical order the more important methods of obtaining asymptotes. In several cases where two or more different methods for obtaining the same type of asymptotes were found the simpler method is given first and then the more difficult method. Most of the simpler methods are based on Analytic Geometry, while the more difficult are based on the Calculus.

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General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf Jul 1931

General Steps In The Evolution Of The Calculus From The Time Of The Ancients To The Present, Sister Mary Virginia Ssf

Electronic Theses and Dissertations

This thesis, submitted to Xavier University in partial fulfillment of requirements for a Bachelor of Science degree in 1931, traces the historical development of the calculus from ancient Greek mathematics through the early twentieth century. The study is organized chronologically across eight sections. The introduction defines key mathematical terms including calculus, variable, and limit, and situates the calculus as the most powerful instrument of mathematical investigation. The thesis then examines the Method of Exhaustion developed by Greek mathematicians including Antiphon (430 B.C.), Eudoxus (370 B.C.), and Archimedes (225 B.C.), whose summation of infinite series represents the nearest ancient approach to …

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