Lecture Notes and Example Sheets

This page contains handouts and lecture notes for the course Mathematical Methods II from Part IB of the Natural Sciences Tripos. These are not guaranteed to be complete: indeed, all the diagrams are missing (as they are hand-drawn in the originals), and chunks of text are missing from the lecture notes (since students are required to write these in by hand during the lectures).

All files are in PostScript format.

Example Sheets and Hints & Solutions

Lecture Notes

• Summary of Results from Previous Courses
• Chapter 1: Variational Methods
  • Lecture Notes
  • Worked Example: Constrained Maximization
  • Worked Example: Geodesics on the Surface of a Sphere
  • Worked Example: The Catenary
  • Worked Example: The Rayleigh-Ritz Method
  • Summary of Results from Chapter 1
• Chapter 2: Poisson's Equation
  • Lecture Notes
  • Worked Example: Steady-State Temperature Distribution in a Cylinder
  • Worked Example: Diffusion of a Solute past a Solid Sphere
  • Worked Example: Heat Source near an Insulated Wall
  • Worked Example: Electrostatics: Using the Integral Solution of Poisson's Equation
  • Worked Example: Solution of Laplace's Equation in a 3D Half-Space
  • Summary of Results from Chapter 2
• Chapter 3: Cartesian Tensors
  • Lecture Notes
  • Worked Example: Decomposition of Second Rank Tensors
  • Worked Example: Evaluation of an Isotropic Integral
  • Worked Example: Proving Vector Differential Identities
  • Summary of Results from Chapter 3
• Chapter 4: Complex Analysis
  • Lecture Notes
  • Worked Example: Calculating Residues
  • Worked Example: Branch Cuts for Multiple Branch Points
  • Summary of Results from Chapter 4
• Chapter 5: Contour Integration and Transform Theory
  • Lecture Notes
  • Worked Example: Contour Integration: Integrals of Trigonometric Functions
  • Worked Example: Contour Integration: Integration Round a Branch Cut
  • Worked Example: Contour Integration: Inverse Fourier Transforms
  • Worked Example: Contour Integration: Singular Point on the Real Axis
  • Worked Example [extra]: Contour Integration: Using the Residue at Infinity
  • Worked Example: Solving Differential Equations using the Laplace Transform and its Inverse
  • Summary of Results from Chapter 5

Feedback is welcomed and should be addressed to the lecturer.

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