Introduction to the Calculus of Variations (Classic Reprint) - Hardcover

William Elwood Byerly

Hardcover

ISBN 10: 0331684187 ISBN 13: 9780331684186

Publisher: Forgotten Books, 2018

Synopsis

Explore the foundations and applications of the calculus of variations in a clear, approachable way.

This classic introduction explains how to find the best shapes and paths that optimize quantities like length, time, and area. It builds from simple problems to general methods used in physics and geometry.

The book starts with the origin and core ideas, then moves through key techniques such as deriving the fundamental equations, using Lagrange’s method, and applying Hamilton’s principle. It includes concrete problems like the shortest line, curves of quickest descent, and surfaces of least area, along with extensions to multiple dependent variables and changing limits. The explanations emphasize intuition and practical steps, making the subject accessible to readers new to the topic.
What you’ll experience

• A guided progression from basic ideas to general extremum problems
• Step-by-step derivations of core equations and principles
• Worked examples that illustrate how the theory applies to geometry and physics
• Extensions to problems with several dependent variables and variable endpoints

Ideal for readers of mathematical physics and advanced calculus who want a solid, example-driven introduction to the calculus of variations.

Edition details

• Publisher: Forgotten Books
• Publication date: 2018
• Language: English
• ISBN 10: 0331684187
• ISBN 13: 9780331684186
• Binding: Hardcover
• Number of pages: 57