A Course in Mathematical Analysis Volume 3: Variation of Solutions; Partial Differential Equations of the Second Order; Integral Equations; Calculus of Variations (Dover Books on Mathematics) - Hardcover

Edouard Goursat

Hardcover

ISBN 10: 0486446522 ISBN 13: 9780486446523

Publisher: Dover Publications, 2013

Synopsis

Edouard Goursat's three-volume A Course in Mathematical Analysis remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition. The first volume in this series addresses derivatives and differentials, definite integrals, expansion in series, and applications to geometry; the succeeding volume explores functions of a complex variable and differential equations. This, the third and final volume, examines variation of solutions and partial differential equations of the second order in its first part. The second part investigates integral equations and calculus of variations.
Topics related to variations of solutions and partial differential equations of the second order include equations of Monge-Ampère; linear equations in n variables; linear equations of the hyperbolic and elliptic types; and harmonic functions in three variables. Subjects relevant to integral equations and calculus of variations include the solution of integral equations by successive approximations; Fredholm's equation; the fundamental functions; applications of integral equations; and the calculus of variations. The text concludes with a note on conformal representation by Paul Montel.

Edition details

• Publisher: Dover Publications
• Publication date: 2013
• Language: English
• ISBN 10: 0486446522
• ISBN 13: 9780486446523
• Binding: Hardcover
• Number of pages: 752