Advanced Programme Mathematics

Notes and examples on Absolute values ( basics, inequalities, graphs, and equations.)

Complex numbers, argand diagrams, argument of z, complex numbers equations, quadratic equations, roots, inspection, finding the equation of an unknown.

First principles, fundamental rules (general, product, quotient, chain), slope at a point, use of trig and examples.

Basic finance, bank transactions, sinking fund, balance outstanding, depreciation, annuities, investment decrease, lump sum payment ,% paid to capital, appreciation, deferred annuities .

Steps and examples on piece-wise functions. fog,gof, rational functions interpretation and sketching.

the definite integral, Riemann sums, open integral, closed integral, areas integration, integration by substitution, use of double and compound angles, integration by parts, chain rule.

Included in this document : 1. Mathematical Induction 2. Implicit Differentiation 3. Finding the Derivative of Ln 4. Trig Differentiation 5. Trig Integration 6. Functions

Logs, log laws, deductions, equations, the number e, graphs with e, natural logs, examples.

Matrices rules and properties, determinant, inverse, transpose and trace, gauss elimination, system of equations, linear equations, nature of solutions linear matrix, solutions in 3d space, transformations, gauss Jordan reduction.