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Full-Text Articles in Education

The Definite Integrals Of Cauchy And Riemann, Dave Ruch Jul 2017

The Definite Integrals Of Cauchy And Riemann, Dave Ruch

Analysis

Rigorous attempts to define the definite integral began in earnest in the early 1800's. One of the pioneers in this development was A. L. Cauchy (1789-1857). In this project, students will read from his 1823 study of the definite integral for continuous functions . Then students will read from Bernard Riemann's 1854 paper, in which he developed a more general concept of the definite integral that could be applied to functions with infinite discontinuities.


Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett Jul 2017

Rigorous Debates Over Debatable Rigor: Monster Functions In Introductory Analysis, Janet Heine Barnett

Analysis

No abstract provided.


Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, Dave Ruch Jan 2017

Bolzano's Definition Of Continuity, His Bounded Set Theorem, And An Application To Continuous Functions, Dave Ruch

Analysis

No abstract provided.


The Mean Value Theorem, Dave Ruch Jan 2017

The Mean Value Theorem, Dave Ruch

Analysis

No abstract provided.


Euler's Rediscovery Of E With Instructor Notes, Dave Ruch Jan 2017

Euler's Rediscovery Of E With Instructor Notes, Dave Ruch

Analysis

No abstract provided.


An Introduction To A Rigorous Definition Of Derivative, Dave Ruch Jan 2017

An Introduction To A Rigorous Definition Of Derivative, Dave Ruch

Analysis

No abstract provided.


Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch Jan 2017

Abel And Cauchy On A Rigorous Approach To Infinite Series, Dave Ruch

Analysis

No abstract provided.


Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, Dave Ruch Jan 2017

Investigations Into D'Alembert's Definition Of Limit: A Student Project With Primary Sources, Dave Ruch

Analysis

No abstract provided.


Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett Jul 2016

Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett

Analysis

No abstract provided.


Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett Jul 2016

Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett

Analysis

No abstract provided.