MTU Cork Library Catalogue

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Differential equations : with applications and historical notes / George F. Simmons.

By: Simmons, George Finlay, 1925-.
Material type: materialTypeLabelBookSeries: International series in pure and applied mathematics.Publisher: New York : McGraw-Hill, [1972]Description: xv, 465 p : ill. ; 24 cm. + hbk.ISBN: 0070573751.Subject(s): Differential equationsDDC classification: 515.3
Contents:
The nature of differential equations -- First order equations -- Second order linear equations -- Oscillation theory and boundary value problems -- Power series solutions and special functions -- Some special functions of mathematical physics -- Systems of first order equations -- Nonlinear equations -- The calculus of variations -- Laplace transforms -- The existence and uniqueness of solutions.

Enhanced descriptions from Syndetics:

A revision of a much-admired text distinguished by the exceptional prose and historical/mathematical context that have made Simmons' books classics. The Second Edition includes expanded coverage of Laplace transforms and partial differential equations as well as a new chapter on numerical methods.

Includes bibliographical references and index.

The nature of differential equations -- First order equations -- Second order linear equations -- Oscillation theory and boundary value problems -- Power series solutions and special functions -- Some special functions of mathematical physics -- Systems of first order equations -- Nonlinear equations -- The calculus of variations -- Laplace transforms -- The existence and uniqueness of solutions.

Table of contents provided by Syndetics

  • 1 The Nature of Differential Equations
  • 2 First Order Equations
  • 3 Second Order Linear Equations
  • 4 Qualitative Properties of Solutions
  • 5 Power Series Solutions and Special Functions
  • 6 Fourier Series and Orthogonal Functions
  • 7 Partial Differential Equations and Boundary Value Problems
  • 8 Some Special Functions of Mathematical Physics
  • 9 Laplace Transforms
  • 10 Systems of First Order Equations
  • 11 Nonlinear Equations
  • 12 The Calculus of Variations
  • 13 The Existence and Uniqueness of Solutions
  • 14 Numerical Methods

Reviews provided by Syndetics

CHOICE Review

Given this is the second edition of a respected text, it is important to examine what has changed and how the text has improved. Using an "algorithmic viewpoint," the authors explore the standard aspects of graph theory--complements, paths, walks, subgraphs, trees, cycles, connectivity, symmetry, network flows, digraphs, colorings, graph matchings, and planar graphs. The expanded topics include explorations of subgraph counting, graphs and symmetries via permutation groups, graph embeddings on topological surfaces such as the Klein bottle and the double torus, and the connections of graphs to linear programming, including the primal-dual algorithm and discrete considerations, where the integral variables are bounded. Other text changes include some proof corrections and meaningful content revisions. Each chapter section contains rich exercise sets, complemented by chapter notes and an extensive bibliography. The authors' claim is correct--their style is "rigorous, but informal," insightful, and it works. The text's algorithms are generic in style, and usable with any major language. In summary, aimed at computer science and mathematics students, this revised text on graph theory will both challenge upper-level undergraduates and provide a comprehensive foundation for graduate students. Summing Up: Recommended. Upper-division undergraduates and above; faculty and professionals. --Jerry Johnson, Western Washington University

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