3rd Year Honours and Diploma Mathematical Physics
Mathematical Methods --Part II

Brian Dolan

This material is available on the web at www.thphys.may.ie/thphys/staff/bdolan/teaching.html

Textbooks:

1. Kreider, Kuller Ostberg and Perkins, An Introduction to Linear Analysis
2. Arfken, Mathematical Methods for Physicists
3. Morse and Feshbach, Methods of Mathematical Physics (2 vols.)
4. Courant and Hilbert, Methods of Mathematical Physics, Vol. 1

Topics:

1. Review of second order linear ordinary differential equations
   • Harmonic oscillator equation
   • Legendre's equation
   • Laguerre's equation
   • Hermite's equation
   • Bessel's equation
2. Linear independence of functions and Wronskian's
3. Orthogonal function expansions and Sturm-Liouville theory
   • Self-adjointness
   • Orthogonality
   • Linear independence
   • Completeness
   • Applications to inhomogeneous differential equations
4. Partial differential equations and separation of variables
   • Heat equation
   • Laplace's equation
5. Complex analysis in one variable and complex integration
6. Fourier Transforms
   • Applications of Fourier transforms to partial differential equations
   • The convolution theorem

Here are problem sheets for part II of the mathematical methods course, in PDF format:

• Problems 1, (PDF)

• Problems 2, (PDF)

• Problems 3, (PDF)

• Problems 4, (PDF)

Here are lecture notes for part II of the mathematical methods course, in both Postscript and PDF format:

• Lecture Notes (PDF); (Postscript)

Previous exam questions for Mathematics Methods, part II

Exam paper, Summer 2007
Exam paper, Autumn 2007

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