Includes study material for understanding sets and functions, continuity, intergration, convergence, differentiation and other functions of advanced calculus.
Author(s): Robert Creighton Buck, Ellen F. Buck
Edition: 3
Publisher: McGraw-Hill College
Year: 1978
Language: English
Commentary: Worse copy at https://library.bz/main/uploads/463B84D4F6EC700647EE6083E56B9199
Pages: 622
1 SETS AND FUNCTIONS
1.1 Introduction
1.2 R and R*
1.3 Distance
1.4 Functions
1.5 Topological Terminology
1.6 Sequences
1.7 Consequences of the Monotonic-Sequence Property
1.8 Compact Sets
2 CONTINUITY
2.1 Preview
2.2 Basic Definitions
2.3 Uniform Continuity
2.4 Implications of Continuity
2.5 Limits of Functions
2.6 Discontinuities
2.7 Inverses for Functions of One Variable
3 DIFFERENTIATION
3.1 Preview
3.2 Mean Value Theorems and L'Hospital's Rule
3.3 Derivatives for Functions on R^n
3.4 Differentiation of Composite Functions
3.5 Taylor's Theorem
3.6 Extremal Problems
4 INTEGRATION
4.1 Preview
4.2 The Definite Integral
4.3 Evaluation of Definite Integrals
4.4 Substitution in Multiple Integrals
4.5 Improper Integrals
5 SERIES
5.1 Preview
5.2 Infinite Series
5.3 Conditionally Convergent Series
5.4 Double Series
5.5 Some Sums
6 UNIFORM CONVERGENCE
6.1 Preview
6.2 Series and Sequences of Functions
6.3 Power Series
6.4 Improper Integrals with Parameters
6.5 The Gamma Function
6.6 Fourier Series
7 DIFFERENTIATION OF TRANSFORMATIONS
7.1 Preview
7.2 Transformations
7.3 Linear Functions and Transformations
7.4 Differentials of Transformations
7.5 Inverses of Transformations
7.6 The Implicit Function Theorems
7.7 Functional Dependence
8 APPLICATIONS TO GEOMETRY AND ANALYSIS
8.1 Preview
8.2 Set Functions
8.3 Transformations of Multiple Integrals
8.4 Curves and Arc Length
8.5 Surfaces arid Surface Area
8.6 Integrals over Curves and Surfaces
9 DIFFERENTIAL GEOMETRY AND VECTOR CALCULUS
9.1 Preview
9.2 Differential Forms
9.3 Vector Analysis
9.4 The Theorems of Green, Gauss, and Stokes
9.5 Exact Forms and Closed Forms
9.6 Applications
10 NUMERICAL METHODS
10.1 Preview
10.2 Locating Zeros
10.3 Fixed-Point Methods
10.4 Extremal Problems
10.5 Miscellaneous Approximation Methods
Back Matter
APPENDIXES
1 Logic and Set Theory
2 Foundations of the Real Number System
3 Linear Algebra
4 Applications of Mathematics
5 Introduction to Complex Analysis
6 Further Topics in Real Analysis
SUGGESTED READING
HINTS AND ANSWERS
LIST OF SYMBOLS
INDEX
Back Cover
