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Cauchy's Calcul Infinitésimal
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Abstract
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Individual chapters are listed in the "Chapters" tab
Suggested Citation
DOI: 10.1007/978-3-030-11036-9
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Book Chapters
The following chapters of this book are listed in IDEAS- Dennis M. Cates, 2019. "Of Variables, Their Limits, And Infinitely Small Quantities," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 3-6, Springer.
- Dennis M. Cates, 2019. "Of Continuous And Discontinuous Functions. Geometric Representation Of Continuous Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 7-10, Springer.
- Dennis M. Cates, 2019. "Derivatives Of Functions Of A Single Variable," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 11-15, Springer.
- Dennis M. Cates, 2019. "Differentials Of Functions Of A Single Variable," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 17-20, Springer.
- Dennis M. Cates, 2019. "The Differential Of The Sum Of Several Functions Is The Sum Of Their Differentials. Consequences Of This Principle. Differentials Of Imaginary Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 21-25, Springer.
- Dennis M. Cates, 2019. "USE OF DIFFERENTIALS AND DERIVED FUNCTIONS IN THE SOLUTION OF SEVERAL PROBLEMS. MAXIMA AND MINIMA OF FUNCTIONS OF A SINGLE VARIABLE. VALUES OF FRACTIONS WHICH ARE PRESENTED UNDER THE FORM $$\frac{0}{0}$$ ," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 27-30, Springer.
- Dennis M. Cates, 2019. "VALUES OF SOME EXPRESSIONS WHICH ARE PRESENTED UNDER THE INDETERMINATE FORM $$\frac{\infty }{\infty }, \infty ^{0}, \, \dots .$$ A RELATIONSHIP WHICH EXISTS BETWEEN THE RATIO OF FINITE DIFFERENCES AND THE DERIVED FUNCTION," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 31-35, Springer.
- Dennis M. Cates, 2019. "Differentials Of Functions Of Several Variables. Partial Derivatives And Partial Differentials," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 37-41, Springer.
- Dennis M. Cates, 2019. "Use Of Partial Derivatives In The Differentiation Of Composed Functions. Differentials Of Implicit Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 43-47, Springer.
- Dennis M. Cates, 2019. "Theorem Of Homogeneous Functions. Maxima And Minima Of Functions Of Several Variables," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 49-52, Springer.
- Dennis M. Cates, 2019. "Use Of Indeterminate Factors In The Study Of Maxima And Minima," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 53-57, Springer.
- Dennis M. Cates, 2019. "Differentials And Derivatives Of Various Orders For Functions Of A Single Variable. Change Of The Independent Variable," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 59-64, Springer.
- Dennis M. Cates, 2019. "Differentials Of Various Orders For Functions Of Several Variables," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 65-69, Springer.
- Dennis M. Cates, 2019. "Methods That Work To Simplify The Study Of Total Differentials For Functions Of Several Independent Variables. Symbolic Values Of These Differentials," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 71-75, Springer.
- Dennis M. Cates, 2019. "Relationships Which Exist Between Functions Of A Single Variable And Their Derivatives Or Differentials Of Various Orders. Use Of These Differentials In The Study Of Maxima And Minima," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 77-80, Springer.
- Dennis M. Cates, 2019. "Use Of Differentials Of Various Orders In The Study Of Maxima And Minima Of Functions Of Several Variables," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 81-84, Springer.
- Dennis M. Cates, 2019. "Conditions Which Must Be Fulfilled For A Total Differential To Not Change Sign While We Change The Values Attributed To The Differentials Of The Independent Variables," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 85-89, Springer.
- Dennis M. Cates, 2019. "Differentials Of Any Function Of Several Variables Each Of Which Is In Its Turn A Linear Function Of Other Supposed Independent Variables. Decomposition Of Entire Functions Into Real Factors Of First Or Of Second Degree," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 91-96, Springer.
- Dennis M. Cates, 2019. "Use Of Derivatives And Differentials Of Various Orders In The Expansion Of Entire Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 97-102, Springer.
- Dennis M. Cates, 2019. "Decomposition Of Rational Fractions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 103-107, Springer.
- Dennis M. Cates, 2019. "Definite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 111-115, Springer.
- Dennis M. Cates, 2019. "Formulas For The Determination Of Exact Or Approximate Values Of Definite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 117-121, Springer.
- Dennis M. Cates, 2019. "DECOMPOSITION OF A DEFINITE INTEGRAL INTO SEVERAL OTHERS. IMAGINARY DEFINITE INTEGRALS. GEOMETRIC REPRESENTATION OF REAL DEFINITE INTEGRALS. DECOMPOSITION OF THE FUNCTION UNDER THE $$\int $$ SIGN INTO TWO FACTORS IN WHICH ONE ALWAYS MAINTAINS THE SAM," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 123-127, Springer.
- Dennis M. Cates, 2019. "Of Definite Integrals Whose Values Are Infinite Or Indeterminate. Principal Values Of Indeterminate Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 129-132, Springer.
- Dennis M. Cates, 2019. "Singular Definite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 133-136, Springer.
- Dennis M. Cates, 2019. "Indefinite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 137-141, Springer.
- Dennis M. Cates, 2019. "Various Properties Of Indefinite Integrals. Methods To Determine The Values Of These Same Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 143-148, Springer.
- Dennis M. Cates, 2019. "On Indefinite Integrals Which Contain Algebraic Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 149-154, Springer.
- Dennis M. Cates, 2019. "On The Integration And The Reduction Of Binomial Differentials And Of Any Other Differential Formulas Of The Same Type," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 155-160, Springer.
- Dennis M. Cates, 2019. "On Indefinite Integrals Which Contain Exponential, Logarithmic, Or Circular Functions," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 161-166, Springer.
- Dennis M. Cates, 2019. "ON THE DETERMINATION AND THE REDUCTION OF INDEFINITE INTEGRALS IN WHICH THE FUNCTION UNDER THE $$\int $$ SIGN IS THE PRODUCT OF TWO FACTORS EQUAL TO CERTAIN POWERS OF SINES AND OF COSINES OF THE VARIABLE," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 167-172, Springer.
- Dennis M. Cates, 2019. "On The Transition Of Indefinite Integrals To Definite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 173-178, Springer.
- Dennis M. Cates, 2019. "DIFFERENTIATION AND INTEGRATION UNDER THE $$\int $$ SIGN. INTEGRATION OF DIFFERENTIAL FORMULAS WHICH CONTAIN SEVERAL INDEPENDENT VARIABLES," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 179-184, Springer.
- Dennis M. Cates, 2019. "Comparison Of Two Types Of Simple Integrals Which Result In Certain Cases From A Double Integration," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 185-190, Springer.
- Dennis M. Cates, 2019. "DIFFERENTIAL OF A DEFINITE INTEGRAL WITH RESPECT TO A VARIABLE INCLUDED IN THE FUNCTION UNDER THE $$\int $$ SIGN AND IN THE LIMITS OF INTEGRATION. INTEGRALS OF VARIOUS ORDERS FOR FUNCTIONS OF A SINGLE VARIABLE," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 191-196, Springer.
- Dennis M. Cates, 2019. "TRANSFORMATION OF ANY FUNCTIONS OF x OR OF $$x+h$$ INTO ENTIRE FUNCTIONS OF x OR OF h TO WHICH WE APPEND DEFINITE INTEGRALS. EQUIVALENT EXPRESSIONS TO THESE SAME INTEGRALS," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 197-202, Springer.
- Dennis M. Cates, 2019. "Theorems Of Taylor And Of Maclaurin. Extension Of These Theorems To Functions Of Several Variables," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 203-207, Springer.
- Dennis M. Cates, 2019. "Rules On The Convergence Of Series. Application Of These Rules To The Series Of Maclaurin," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 209-213, Springer.
- Dennis M. Cates, 2019. "Imaginary Exponentials And Logarithms. Use Of These Exponentials And Of These Logarithms In The Determination Of Definite Or Indefinite Integrals," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 215-219, Springer.
- Dennis M. Cates, 2019. "Integration By Series," Springer Books, in: Cauchy's Calcul Infinitésimal, chapter 0, pages 221-226, Springer.
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