A Course In Mathematical Analysis 2.2 (Differential Equations) by Edouard Goursat
Mathematical Analysis 2.2 (Differential Equations) - Table of Contents
1. Elementary Methods of Integration
I. Formation of Differential Equations
II. Equations of the First Order
III. Equations of Higher Order
2. Existence Theorems
I. Calculus of Limits
II. The Method of Successive Approximations (Cauchy–Lipschitz Method)
III. First Integrals; Multipliers
IV. Infinitesimal Transformations
3. Linear Differential Equations
I. General Properties; Fundamental Systems
II. Study of Some Particular Equations
III. Regular Integrals; Equations with Periodic Coefficients
IV. Systems of Linear Equations
4. Non-Linear Differential Equations
I. Exceptional Initial Values
II. Study of Some First-Order Equations
III. Singular Integrals
5. Partial Differential Equations of the First Order
I. Linear Equations of the First Order
II. Total Differential Equations
III. Equations of the First Order in Three Variables
IV. Simultaneous Equations
V. Generalities on Higher-Order Equations
What You Will Learn in Mathematical Analysis 2.2 (Differential Equations)
"A Course in Mathematical Analysis Volume 2 Part 2 (Differential Equations) by Édouard Goursat" is a classic text in "mathematical analysis" that provides a rigorous introduction to "differential equations". This volume focuses on both the theoretical foundations and practical methods, offering clear explanations and detailed proofs that make complex topics accessible to students and researchers alike.
The book covers first-order and higher-order differential equations, including both linear and non-linear types. Goursat explores "linear systems", singular solutions, existence theorems, and fundamental systems, providing a structured approach that helps readers understand the underlying principles and applications. Partial differential equations and methods of integration are also treated with precision, emphasizing both clarity and rigor.
Ideal for advanced undergraduates, graduate students, and professionals in mathematics, physics, or engineering, this work remains a foundational reference. Goursat’s careful treatment of theory, coupled with examples and applications, ensures that readers gain a solid understanding of "differential equations" and their role in broader "mathematical analysis". This volume continues to be highly regarded for its clarity, systematic approach, and lasting contribution to the study of mathematics.
Book Details & Specifications
Title:
A Course In Mathematical Analysis 2.2 (Differential Equations) by Edouard Goursat
Publisher:
Ginn & Company
Year:
1917
Pages:
330
Type:
PDF
Language:
English
ISBN-10 #:
0486605566
ISBN-13 #:
978-0486605562
License:
Public Domain Work
Amazon:
Amazon
About the Author: Edouard Goursat
The author Edouard Goursat
(1858–1936) was a prominent French mathematician known for his work in "mathematical analysis" and "complex analysis". He developed rigorous methods for studying "differential equations", analytic functions, and higher mathematics, making complex concepts clear and structured. Goursat taught at the University of Paris and authored the multi-volume "A Course in Mathematical Analysis", a classic reference for students and researchers. His works emphasize precise proofs, logical organization, and practical applications, continuing to influence the study of "differential equations" and "complex analysis" in mathematics education and research.
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