This module provides a solid foundation in differential and integral calculus. It shows the learner how to test simple series and sequences for convergence. An introduction to linear algebra including matrices is covered. Complex numbers, in their various forms, are introduced.
*Curricular information is subject to change
Calculus
- Rules and techniques of differentiation – product rule, quotient rule, chain rule. Maxima and minima. Inverse functions including trigonometric functions. Applications to applied physics problems.
- Integral Calculus: Methods of integration – substitution, by parts, using partial fractions. Areas. Applications to applied physics problems.
Sequences and Series
- The Binomial Theorem: Factorial notation, combinations, the expansion of the General Binomial Theorem.
- Convergence of sequences. Convergence of series. Tests for convergence. Power series.
Complex Numbers
- The imaginary unit i, addition, multiplication and division of complex numbers, geometric representation, conjugate and modulus, polar and exponential form. De Moivre’s Theorem; Complex polynomials, roots, the remainder and factor theorems.
Linear Algebra
- Linear Equations: Introduction to systems of linear equations. Various methods of solving.
- Introduction to matrices. Matrix Algebra. Row operations and elementary matrices. Row equivalent matrices. Transpose of a matrix. Matrix inverse and its evaluation. Use of matrix inverses in the solution of linear equations.
Lectures supported by tutorials and problem sheets which may be supplemented by online materials and the use of mathematical software packages.
| Module Content & Assessment | |
|---|---|
| Assessment Breakdown | % |
| Formal Examination | 70 |
| Other Assessment(s) | 30 |