Introduces analysis, presenting analytical proofs backed by geometric intuition and placing minimum reliance on geometric argument. This edition separates continuity and differentiation and expands coverage of integration to include discontinuous functions. The discussion of differentiation of a vector function of a vector variable has been modernized by defining the derivative to be the Jacobian matrix; and, the general form of the chain rule is given, as is the general form of the implicit transformation theorem.
CALCULUS OF ONE VARIABLE.
The Number System.
Functions, Sequences, and Limits.
Continuity and More Limits.
The Elementary Transcendental Functions.
Vectors and Curves.
Functions of Several Variables.
Limits and Continuity.
The Inversion Theorem.
Line and Surface Integrals.
THEORY OF CONVERGENCE.
Sequence and Series of Functions.
The Taylor Series.
Integral Representations of Functions.
Gamma and Beta Functions.
Laplace's Method and Stirling's Formula.
Elementary Differentiation and Integration Formulas.
Answers, Hints, and Solutions.
Tertiary; University or College
Number Of Pages: 752
Published: 5th January 2016
Country of Publication: US
Dimensions (cm): 23.45 x 17.15
Weight (kg): 1.19
Edition Number: 1
Edition Type: Revised