Mathematical Physics with Differential Equations

Yisong Yang, Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University

Yisong Yang is a Professor of Mathematics at New York University's Polytechnic School of Engineering and an Affiliated Professor of Mathematics at NYU Shanghai. He received his Ph.D. in Mathematics from the University of Massachusetts at Amherst in 1988.

Preface
Notation and Convention
1. Hamiltonian Systems and Applications
2. Schrödinger Equation and Quantum Mechanics
3. Maxwell Equations, Dirac Monopole, and Gauge Fields
4. Special Relativity
5. Abelian Gauge Field Equations
6. Dirac Equations
7. GinzburgDSLandau Equations for Superconductivity
8. Magnetic Vortices in Abelian Higgs Theory
9. Non-Abelian Gauge Field Equations
10. Einstein Equations and Related Topics
11. Charged Vortices and ChernDSSimons Equations
12. Skyrme Model and Related Topics
13. Strings and Branes
14. BornDSInfeld Theory of Electromagnetism
15. Canonical Quantization of Fields
Appendices
Bibliography
Index