Introduction to Mathematical Methods 1

Wedi cwblhau'r modiwl dylai'r myfyrwyr fedru:

1. 1. Solve mathematical problems by using algebraic techniques.
2. 2. Identify linear, quadratic, trigonometric, exponential and logarithmic functions and recall fundamental relations between them.
3. 3. Manipulate with vectors.
4. 4. Examine complex numbers and use them to solve simple problems.
5. 5. Solve simple questions on differentiation and recognise the relation between dy/dx and the gradient of the curve y(x).

This module introduces the student to some of the basic mathematical tools commonly used in the physical sciences. Topics covered include algebraic techniques, logarithms, trigonometry, an introduction to vectors and differentiation. Particular emphasis is placed on the use of mathematical techniques to solve physics problems.

Number: Fractions, decimal system, different bases, indices and logarithms.

Algebraic techniques: linear and quadratic equations, factorisation, transposition of formulae, equations involving fractions, simultaneous equations. Indicial, exponential and logarithmic equations.

Trigonometry: Sine and cosine rules. Unit circle representation. Graphs of trigonometrical functions. Trigonometric equations and identities including addition and double angle formulae.

Vectors: Vector representation, unit vectors, position vectors, vector components, vector addition, scalar product.

Complex Numbers: Introduction to complex numbers, multiplication and division in polar form, de Moivre's theorem, powers and roots of complex numbers.

Differentiation and its applications: Gradient of a curve, equation of a straight line, tangents and normals, rates of change, stationary values and turning points, curve sketching.

Mae'r modiwl hwn yn cydymffurfio a FfCChC Lefel 3