A Treatise on the Integral Calculus with Applications, Examples and Problems

✍ Scribed by Joseph Edwards

• Publisher: Chelsea Publishing Co.
• Year: 1954
• Tongue: English
• Leaves: 1009
• Edition: Reprint 1954
• Category: Library

✦ Table of Contents

Title Page
Preface
Table of Contents
CHAPTER XXIII - CHANGE OF THE VARIABLES IN A MULTIPLE INTEGRAL.
CHAPTER XXIV - EULERIAN INTEGRALS, GAUSS' Pi(x,µ) FUNCTION.
CHAPTER XXV - LEJEUNE-DIRICHLET INTEGRALS, LIOUVILLE INTEGRALS.
CHAPTER XXVI - DEFINITE INTEGRALS (I.).
CHAPTER XXVII - DEFINITE INTEGRALS (II.).LOGARITHMIC AND EXPONENTIAL FUNCl'IONS INVOLVED.
CHAPTER XXVIII - DEFINITE INTEGRALS (IlI.).
CHAPTER XXIX - THE COMPLEX VARIABLE. VECTORS. CONFORMAL REPRESENTATION.
CHAPTER XXX - INTEGRATION. CONTOUR INTEGRATION. TAYLOR'S THEOREM.
CHAPTER XXXI - ELLIPTIC INTEGRALS AND FUNCTIONS.
CHAPTER XXXII - ELLIPl'IC INTEGRALS. THE WEIERSTRASSIAN FORMS.
CHAPTER XXXIII - ELLIPTIC FUNCTIONS. REDUCTION TO STANDARD FORMS.
CHAPTER XXXIV - (SECTION I.) CALCULUS OF VARIATIONS.
CHAPTER XXXIV - (SECTION II.) DOUBLE INTEGRALS. CULVERWELL'S METHOD OF DISCRIMINATION.
CHAPTER XXXV - (SECTION I.) FORMULAE OF LAGRANGE AND FOURIER.
CHAPTER XXXV - (SECTION II.) DIRICHLET'S INVESTIGATION.
CHAPTER XXXVI - MEAN VALUES.
CHAPTER XXXVII - CHANCE.
CHAPTER XXXVIII - UNCERTAINTIES OF OBSERVATION.
CHAPTER XXXIX - THEOREMS OF STOKES AND GREEN. HARMONIC ANALYSIS.
CHAPTER XL.- SUPPLEMENTARY NOTES.
A. RIEMANN'S Definition and Theorem
B. Convergence of an Infinite Integral
C. Strict Accuracy of Standard Forms
D. HERMITE'S Method for Rational Fractions
E. LEGENDRE'S Transformation applied to Form Int(1/(X*Sqrt(Y)), dx)
F. Continuity of a Function of two IndependentVariables. Differentiation of a Definite Integral. Double Integrals
G. Uniform Convergence. Double Limits
H. Unicursal Curves
I. GENERAL REVIEW
ANSWERS TO EXAMPLES AND PROBLEMS.
INDEX
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