Lecture Notes and Handouts

This page contains lecture notes, handouts and problem sheets for the courses Dynamics from Part IA of the Mathematical Tripos, Computational Projects (otherwise known as CATAM) from Parts IB and II of the Mathematical Tripos and Mathematical Methods II for Part IB of the Natural Sciences Tripos at the University of Cambridge.

These are not guaranteed to be complete: indeed, all the diagrams are missing (as they are hand-drawn in the originals). Furthermore, the files date back to the last time I lectured the course in question: 2007 in the cases of Dynamics and Computational Projects, and 2002 for Mathematical Methods II.

Material in small type within the notes (separated from the main text by horizontal rules) indicates advanced or non-examinable topics.

For my other courses (Acoustics and Stability, a postgraduate course, and Complex Methods, an undergraduate course aimed at applied mathematicians, scientists and engineers), please contact me directly.

Each file may be downloaded as a PDF. All are © 2000–23 Dr R. E. Hunt, and may not be copied or reproduced without permission. I welcome feedback of any form via email.

Dynamics (Mathematical Tripos, Part IA)

• Summary of Required Results from Other Courses
• Chapter 1: Basic Concepts
  • Lecture Notes for Chapter 1
• Chapter 2: Dynamical Examples
  • Lecture Notes for Chapter 2
  • Worked Example: A Forced Damped Harmonic Oscillator
  • Worked Example: A Particle Moving under Gravity with Quadratic Friction
  • Worked Example: A Struck Pendulum
  • Worked Example: A Rocket with Linear Friction
• Chapter 3: Dimensional Analysis
  • Lecture Notes for Chapter 3
  • Worked Example: Dimensional Analysis of Oil Flow
• Chapter 4: Energy and Stability
  • Lecture Notes for Chapter 4
  • Worked Example: Small Oscillations with Elasticity
  • Worked Example: The Speed of a Charged Particle in an Electromagnetic Field
  • Worked Example: Small Oscillations with One Degree of Freedom
• Chapter 5: Impulses and Collisions
  • Lecture Notes for Chapter 5
  • Worked Example: Three Balls Colliding in One Dimension
  • Worked Example: A Ping-Pong Ball Bouncing on a Plane
• Chapter 6: Central Forces
  • Lecture Notes for Chapter 6
  • Worked Example: A Particle Moving Under a Central Force
• Chapter 7: Rotating Frames
  • Lecture Notes for Chapter 7
  • Worked Example: A Bead on a Rotating Wire Hoop
  • Worked Example: Deflection of a Projectile due to the Earth's Rotation
• Chapter 8: Orbits
  • Lecture Notes for Chapter 8
  • Worked Example: The Orbit of a Comet
• Chapter 9: Systems of Particles
  • Lecture Notes for Chapter 9
• Chapter 10: Rigid Bodies
  • Lecture Notes for Chapter 10
  • Worked Example: A Cylinder Rolling Down a Slope
  • Worked Example: A Sphere Thrown Along a Rough Surface
  • Worked Example: A Bead Sliding on a Rotating Rod
  • Worked Example: A Rod Sliding Inside a Wire Loop
• Chapter 11: Phase-Plane Techniques
  • Lecture Notes for Chapter 11
• Problem Sheets
  • Example Sheet 1
  • Example Sheet 2
  • Example Sheet 3
  • Example Sheet 4

Computational Projects (Mathematical Tripos, Parts IB and II)

A (fairly elementary) handout on complexity calculations

Mathematical Methods II (Natural Sciences Tripos, Part IB)

• Summary of Results from Previous Courses
• Chapter 1: Variational Methods
  • Lecture Notes for Chapter 1
  • 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 for Chapter 2
  • 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 for Chapter 3
  • 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 for Chapter 4
  • 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 for Chapter 5
  • 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: Solving Differential Equations using the Laplace Transform and its Inverse
  • Summary of Results from Chapter 5
• Problem Sheets, Hints and Solutions
  • Problem Sheet 1: Variational Methods
  • Hints and Solutions for Problem Sheet 1
  • Problem Sheet 2: Poisson's Equation
  • Hints and Solutions for Problem Sheet 2
  • Problem Sheet 3: Cartesian Tensors
  • Hints and Solutions for Problem Sheet 3
  • Problem Sheet 4: Complex Analysis, Contour Integration and Transform Theory
  • Hints and Solutions for Problem Sheet 4