Mathematical Physics II by Boris Dubrovin
Mathematical Physics II - Table of Contents
0. Singular Points of Solutions to Analytic Differential Equations
1. Differential Equations in the Complex Domain: Basic Results
2. Analytic Continuation of Solutions. Movable and Fixed Singularities
3. Singularities for Differential Equations not Resolved with Respect to the Derivative. Weierstrass Elliptic Function
4. Poincar´e Method of Small Parameter
5. Method of Small Parameter Applied to Painlev´e Classification Problem
6. Monodromy of Linear Differential Operators with Rational Coefficients
7. Solutions to Linear Systems with Rational Coefficients: the Local Theory
8. Gauss Equation and Hypergeometric Function
What You Will Learn in Mathematical Physics II
"Mathematical Physics II" is a rigorous yet inspiring set of advanced lecture notes by Russian mathematician Boris Dubrovin, aimed at graduate students and researchers in mathematical physics. It explores "complex differential equations", focusing on how singularities form and behave in analytic solutions, and how the "monodromy" (behavior around singular points) reveals deep structure in systems with rational coefficients. The material blends "analysis, complex variables, and geometric insight" to deepen understanding of core phenomena in physics and mathematics.
The first part of the book examines the "singular points of analytic differential equations", covering analytic continuation, movable and fixed singularities, elliptic functions, and perturbation methods. The second part focuses on "linear operators", detailing local solutions around singularities, Fuchsian systems, and classic equations like the hypergeometric equation. Throughout, Dubrovin balances rigorous proofs with geometric intuition, making the notes a valuable resource for anyone studying "integrable systems" or advanced mathematical methods.
Dubrovin’s teaching legacy shines through in this text: it is not a standard textbook but a "conceptual guide" into complex systems where mathematics and physics meet. His work has influenced research in integrable systems, monodromy theory, and the mathematical foundations of physical laws.
Book Details & Specifications
Title:
Mathematical Physics II by Boris Dubrovin
Publisher:
SISSA
Year:
2008
Pages:
78
Type:
PDF
Language:
English
ISBN-10 #:
3832537198
ISBN-13 #:
978-3832537197
License:
University Educational Resource
Amazon:
Amazon
About the Author: Boris Dubrovin
The author Boris Dubrovin
, born in "Moscow, Russia" in 1950, was a renowned "mathematician" and "mathematical physicist". He studied at "Moscow State University", earning his doctorate in 1984, and later became a professor at "SISSA, Italy". Dubrovin made significant contributions to "integrable systems", bridging deep mathematics with theoretical physics. His expertise included "Frobenius manifolds", "Gromov–Witten invariants", and "nonlinear PDEs", influencing both geometry and quantum theory. Known for his innovative approach, Dubrovin’s work continues to inspire researchers in "mathematical physics" and advanced geometry, leaving a lasting legacy in modern theoretical mathematics.
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