Features

• Aimed at graduate students and professionals in both mathematics and computer science

• The first book of its kind devoted to the topic

• Authored by a noted authority in crossing numbers

Summary

Crossing Numbers of Graphs is the first book devoted to the crossing number, an increasingly popular object of study with surprising connections. The field has matured into a large body of work, which includes identifiable core results and techniques. The book presents a wide variety of ideas and techniques in topological graph theory, discrete geometry, and computer science.

Table of Contents

1. Introduction and History

Part I: The Crossing Number

2. Crossing Number

3. Crossing Number and other Parameters

4. Computational Complexity

5. Algorithms

Part II: Crossing Number Variants

6. Rectilinear Crossing Number

7. Local Crossing Number

8. Monotone and Book crossing numbers

9. Pair Crossing Number

10. k-planar Crossing Number

11. Independent Odd Crossing Number

12. Maximum Crossing Numbers

Part III: Applications

13. Crossing Minimization

14. Geometric Configurations

Appendix

A Topological Graph Theory Basics

B Complexity Theory

Features

• Gives students the necessary theoretical foundation and practical experience for solving analytical problems
• Presents a variety of solution methods, including the separation of variables, eigenfunction expansion, Fourier and Laplace transformations, Green’s functions, and asymptotic techniques
• Includes Mathematica^® code that enables students to check the accuracy of their work without interfering with the solution procedure
• Contains a wealth of worked examples and exercises—both computational exercises and standard problems not requiring a software package

A solutions manual and PDF projector files are available upon qualifying course adoption.

Summary

Solution Techniques for Elementary Partial Differential Equations, Third Editionremains a top choice for a standard, undergraduate-level course on partial differential equations (PDEs). Making the text even more user-friendly, this third edition covers important and widely used methods for solving PDEs.

New to the Third Edition

• New sections on the series expansion of more general functions, other problems of general second-order linear equations, vibrating string with other types of boundary conditions, and equilibrium temperature in an infinite strip
• Reorganized sections that make it easier for students and professors to navigate the contents
• Rearranged exercises that are now at the end of each section/subsection instead of at the end of the chapter
• New and improved exercises and worked examples
• A brief Mathematica^® program for nearly all of the worked examples, showing students how to verify results by computer

This bestselling, highly praised textbook uses a streamlined, direct approach to develop students’ competence in solving PDEs. It offers concise, easily understood explanations and worked examples that allow students to see the techniques in action.