Cauchy's Calcul Infinitésimal
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Published By Springer International Publishing

9783030110352, 9783030110369

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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.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_7 ◽

2019 ◽

pp. 31-35

Author(s):

Dennis M. Cates

Keyword(s):

Finite Differences ◽

Indeterminate Form ◽

Derived Function

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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 $$\frac{0}{0}$$ .

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_6 ◽

2019 ◽

pp. 27-30

Author(s):

Dennis M. Cates

Keyword(s):

Single Variable

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DIFFERENTIALS OF FUNCTIONS OF A SINGLE VARIABLE.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_4 ◽

2019 ◽

pp. 17-20

Author(s):

Dennis M. Cates

Keyword(s):

Single Variable

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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.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_36 ◽

2019 ◽

pp. 197-202

Author(s):

Dennis M. Cates

Keyword(s):

Entire Functions ◽

Definite Integrals ◽

Equivalent Expressions

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OF DEFINITE INTEGRALS WHOSE VALUES ARE INFINITE OR INDETERMINATE. PRINCIPAL VALUES OF INDETERMINATE INTEGRALS.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_24 ◽

2019 ◽

pp. 129-132

Author(s):

Dennis M. Cates

Keyword(s):

Definite Integrals

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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 SAME SIGN.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_23 ◽

2019 ◽

pp. 123-127

Author(s):

Dennis M. Cates

Keyword(s):

Geometric Representation ◽

Definite Integral ◽

Definite Integrals ◽

Two Factors

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THEOREM OF HOMOGENEOUS FUNCTIONS. MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_10 ◽

2019 ◽

pp. 49-52

Author(s):

Dennis M. Cates

Keyword(s):

Homogeneous Functions ◽

Several Variables

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USE OF PARTIAL DERIVATIVES IN THE DIFFERENTIATION OF COMPOSED FUNCTIONS. DIFFERENTIALS OF IMPLICIT FUNCTIONS.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_9 ◽

2019 ◽

pp. 43-47

Author(s):

Dennis M. Cates

Keyword(s):

Implicit Functions ◽

Partial Derivatives ◽

Composed Functions

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IMAGINARY EXPONENTIALS AND LOGARITHMS. USE OF THESE EXPONENTIALS AND OF THESE LOGARITHMS IN THE DETERMINATION OF DEFINITE OR INDEFINITE INTEGRALS.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_39 ◽

2019 ◽

pp. 215-219

Author(s):

Dennis M. Cates

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RULES ON THE CONVERGENCE OF SERIES. APPLICATION OF THESE RULES TO THE SERIES OF MACLAURIN.

Cauchy's Calcul Infinitésimal ◽

10.1007/978-3-030-11036-9_38 ◽

2019 ◽

pp. 209-213

Author(s):

Dennis M. Cates

Keyword(s):

Convergence Of Series

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