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Department of Mathematical Sciences

# MATH1607 Dynamics I

Dynamics concerns evolution with time. In this course we study a model of time-development called "classical mechanics". This applies to the world around us and describes the motion of everyday objects via "forces". It was invented by Isaac Newton in the 17th century, when it stimulated revolutions in astronomy, physics and mathematics. Today it is a cornerstone of applied science.

This introductory course treats firstly the motion of point particles, and then the motion of a certain extended body - a flexible stretched string. Highlights include conservation laws and use of Fourier series.

We use what you have covered in Calculus I (ordinary differential equations, partial differentiation, Fourier series) and Linear Algebra I (vectors). It is vital to be familiar with this material!

The Dynamics course leads on naturally to the second-year courses Mathematical Physics II and Analysis in Many Variables II.

## Outline of course

Aim: to provide an introduction to classical mechanics applied to simple physical systems.

• Frames of reference, Newton’s laws in vector form, forces, mass, momentum, gravitational force, projectiles, Lorentz force and charged particles in constant electromagnetic fields.
• Concepts of energy and angular momentum.
• Simple harmonic motion and oscillations about a stable equilibrium. Damped oscillations and resonance.
• Central forces and the use of energy and angular momentum to study planetary motion.
• Waves and strings, including the derivation of the wave equation for small amplitude vibrations and its solution by separation of variables.

### Prerequisites

For details of prerequisites, corequisites, excluded combinations, teaching methods, and assessment details, please see the Faculty Handbook.