Brief description
Problem solving and numeracy are fundamental requirements in Physics and highly valued skills in the work place. This module is aimed at enabling students to solve numerical problems and to perform basic operations in calculus. Provision will be through lectures, weekly example sheets and problem solving seminars based on the applications of elementary vectors, complex numbers, trigonometry, calculus and differential equations encountered in Part 1 Physics.

Learning outcomes
After taking this module students should be able to:

• Understand the utility of elementary vectors, complex numbers, trigonometry, calculus and differential equations for analysis in Physics.
• Apply the mathematical problem solving techniques developed to treat a range of simple physical systems.
• Answer straight forward numerical and calculus related problems in Physics.

Additional learning activities
None

Outline syllabus
(a) Differential Equations
Introduction and definition of terms Solving simple DEs by direct integration
Linear first order DEs, both homogeneous and inhomogeneous solved by three methods:
i) The method of separation of variables.
ii) The integrating factor method.
iii) Direct integration by product rule.

Second order linear DEs with constant coefficients. Defining the auxiliary equation
Homogeneous case - forcing function = 0. Inhomogeneous case - solutions if forcing function is:
i) polynomial.
ii) exponential.
iii) sinusoidal.
(Introduction to Partial Differentiation)

(b) Vectors
Scalar and vector quantities. Vector notation and unit vectors. Vector addition, scalar and vector products, rates of change of vectors

(c) Complex Numbers
Real and imaginary numbers. Complex numbers and their operations.
Graphical representation of complex numbers: the Argand diagram and polar form. Elementary functions of a complex variable: Euler's formula, trigonometric, hyperbolic and logarithmic functions.
Powers and roots of a complex number - de Moivre's theorem.
Phasors.