A Friendly Introduction to Analysis
by Kosmala, Witold A.J.Edition: 2nd
Format: Paperback
Pub. Date: 2004-01-09
Publisher(s): Pearson
Other versions by this Author
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Summary
This book is designed to be an easily readable, intimidation-free guide to advanced calculus. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first book to cover both single and multivariable analysis in such a clear, reader-friendly setting.Chapter topics cover sequences, limits of functions, continuity, differentiation, integration, infinite series, sequences and series of functions, vector calculus, functions of two variables, and multiple integration.For individuals seeking math fun at a higher level.
Table of Contents
| Fundamentals | |
| Sets and Subsets | |
| Operations on Sets | |
| Sequences | |
| Properties of Integers | |
| Matrices | |
| Mathematical Structures | |
| Logic | |
| Propositions and Logical Operations | |
| Conditional Statements | |
| Methods of Proof | |
| Mathematical Induction | |
| Counting | |
| Permutations | |
| Combinations | |
| Pigeonhole Principle | |
| Elements of Probability | |
| Recurrence Relations | |
| Relations and Digraphs | |
| Product Sets and Partitions | |
| Relations and Digraphs | |
| Paths in Relations and Digraphs | |
| Properties of Relations | |
| Equivalence Relations | |
| Computer Representation of Relations and Digraphs | |
| Operations on Relations | |
| Transitive Closure and Warshall's Algorithm | |
| Functions | |
| Functions | |
| Functions for Computer Science | |
| Growth of Functions | |
| Permutation Functions | |
| Order Relations and Structures | |
| Partially Ordered Sets | |
| Extremal Elements of Partially Ordered Sets | |
| Lattices | |
| Finite Boolean Algebras | |
| Functions on Boolean Algebras | |
| Circuit Design | |
| Trees | |
| Trees | |
| Labeled Trees | |
| Tree Searching | |
| Undirected Trees | |
| Minimal Spanning Trees | |
| Topics in Graph Theory | |
| Graphs | |
| Euler Paths and Circuits | |
| Hamiltonian Paths and Circuits | |
| Transport Networks | |
| Matching Problems | |
| Coloring Graphs | |
| Semigroups and Groups | |
| Binary Operations, Revisited | |
| Semigroups | |
| Products and Quotients of Semigroups | |
| Groups | |
| Products and Quotients of Groups | |
| Languages and Finite-State Machines | |
| Languages | |
| Representations of Special Grammars and Languages | |
| Finite-State Machines | |
| Semigroups, Machines, and Languages | |
| Machines and Regular Languages | |
| Simplification of Machines | |
| Groups and Coding | |
| Coding of Binary Information and Error Detection | |
| Decoding and Error Correction | |
| Public Key Cryptology | |
| Algorithms and Pseudocode | |
| Additional Experiments in Discrete Mathematics | |
| Answers to Odd-Numbered Exercises | |
| Answers to Chapter Tests | |
| Index | |
| Table of Contents provided by Publisher. All Rights Reserved. |
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