Cauchy's Calcul Infinitésimal
Dennis M. Cates ()
in Springer Books from Springer
Date: 2019
ISBN: 978-3-030-11036-9
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Chapters in this book:
- Ch Chapter 1 OF VARIABLES, THEIR LIMITS, AND INFINITELY SMALL QUANTITIES
- Dennis M. Cates
- Ch Chapter 10 THEOREM OF HOMOGENEOUS FUNCTIONS. MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES
- Dennis M. Cates
- Ch Chapter 11 USE OF INDETERMINATE FACTORS IN THE STUDY OF MAXIMA AND MINIMA
- Dennis M. Cates
- Ch Chapter 12 DIFFERENTIALS AND DERIVATIVES OF VARIOUS ORDERS FOR FUNCTIONS OF A SINGLE VARIABLE. CHANGE OF THE INDEPENDENT VARIABLE
- Dennis M. Cates
- Ch Chapter 13 DIFFERENTIALS OF VARIOUS ORDERS FOR FUNCTIONS OF SEVERAL VARIABLES
- Dennis M. Cates
- Ch Chapter 14 METHODS THAT WORK TO SIMPLIFY THE STUDY OF TOTAL DIFFERENTIALS FOR FUNCTIONS OF SEVERAL INDEPENDENT VARIABLES. SYMBOLIC VALUES OF THESE DIFFERENTIALS
- Dennis M. Cates
- Ch Chapter 15 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
- Dennis M. Cates
- Ch Chapter 16 USE OF DIFFERENTIALS OF VARIOUS ORDERS IN THE STUDY OF MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES
- Dennis M. Cates
- Ch Chapter 17 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
- Dennis M. Cates
- Ch Chapter 18 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
- Dennis M. Cates
- Ch Chapter 19 USE OF DERIVATIVES AND DIFFERENTIALS OF VARIOUS ORDERS IN THE EXPANSION OF ENTIRE FUNCTIONS
- Dennis M. Cates
- Ch Chapter 2 OF CONTINUOUS AND DISCONTINUOUS FUNCTIONS. GEOMETRIC REPRESENTATION OF CONTINUOUS FUNCTIONS
- Dennis M. Cates
- Ch Chapter 20 DECOMPOSITION OF RATIONAL FRACTIONS
- Dennis M. Cates
- Ch Chapter 21 DEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 22 FORMULAS FOR THE DETERMINATION OF EXACT OR APPROXIMATE VALUES OF DEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 23 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
- Dennis M. Cates
- Ch Chapter 24 OF DEFINITE INTEGRALS WHOSE VALUES ARE INFINITE OR INDETERMINATE. PRINCIPAL VALUES OF INDETERMINATE INTEGRALS
- Dennis M. Cates
- Ch Chapter 25 SINGULAR DEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 26 INDEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 27 VARIOUS PROPERTIES OF INDEFINITE INTEGRALS. METHODS TO DETERMINE THE VALUES OF THESE SAME INTEGRALS
- Dennis M. Cates
- Ch Chapter 28 ON INDEFINITE INTEGRALS WHICH CONTAIN ALGEBRAIC FUNCTIONS
- Dennis M. Cates
- Ch Chapter 29 ON THE INTEGRATION AND THE REDUCTION OF BINOMIAL DIFFERENTIALS AND OF ANY OTHER DIFFERENTIAL FORMULAS OF THE SAME TYPE
- Dennis M. Cates
- Ch Chapter 3 DERIVATIVES OF FUNCTIONS OF A SINGLE VARIABLE
- Dennis M. Cates
- Ch Chapter 30 ON INDEFINITE INTEGRALS WHICH CONTAIN EXPONENTIAL, LOGARITHMIC, OR CIRCULAR FUNCTIONS
- Dennis M. Cates
- Ch Chapter 31 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
- Dennis M. Cates
- Ch Chapter 32 ON THE TRANSITION OF INDEFINITE INTEGRALS TO DEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 33 DIFFERENTIATION AND INTEGRATION UNDER THE $$\int $$ SIGN. INTEGRATION OF DIFFERENTIAL FORMULAS WHICH CONTAIN SEVERAL INDEPENDENT VARIABLES
- Dennis M. Cates
- Ch Chapter 34 COMPARISON OF TWO TYPES OF SIMPLE INTEGRALS WHICH RESULT IN CERTAIN CASES FROM A DOUBLE INTEGRATION
- Dennis M. Cates
- Ch Chapter 35 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
- Dennis M. Cates
- Ch Chapter 36 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
- Dennis M. Cates
- Ch Chapter 37 THEOREMS OF TAYLOR AND OF MACLAURIN. EXTENSION OF THESE THEOREMS TO FUNCTIONS OF SEVERAL VARIABLES
- Dennis M. Cates
- Ch Chapter 38 RULES ON THE CONVERGENCE OF SERIES. APPLICATION OF THESE RULES TO THE SERIES OF MACLAURIN
- Dennis M. Cates
- Ch Chapter 39 IMAGINARY EXPONENTIALS AND LOGARITHMS. USE OF THESE EXPONENTIALS AND OF THESE LOGARITHMS IN THE DETERMINATION OF DEFINITE OR INDEFINITE INTEGRALS
- Dennis M. Cates
- Ch Chapter 4 DIFFERENTIALS OF FUNCTIONS OF A SINGLE VARIABLE
- Dennis M. Cates
- Ch Chapter 40 INTEGRATION BY SERIES
- Dennis M. Cates
- Ch Chapter 5 THE DIFFERENTIAL OF THE SUM OF SEVERAL FUNCTIONS IS THE SUM OF THEIR DIFFERENTIALS. CONSEQUENCES OF THIS PRINCIPLE. DIFFERENTIALS OF IMAGINARY FUNCTIONS
- Dennis M. Cates
- Ch Chapter 6 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 $$\frac{0}{0}$$
- Dennis M. Cates
- Ch Chapter 7 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
- Dennis M. Cates
- Ch Chapter 8 DIFFERENTIALS OF FUNCTIONS OF SEVERAL VARIABLES. PARTIAL DERIVATIVES AND PARTIAL DIFFERENTIALS
- Dennis M. Cates
- Ch Chapter 9 USE OF PARTIAL DERIVATIVES IN THE DIFFERENTIATION OF COMPOSED FUNCTIONS. DIFFERENTIALS OF IMPLICIT FUNCTIONS
- Dennis M. Cates
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DOI: 10.1007/978-3-030-11036-9
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