Basic algebra and trigonometry
Transposition, simplification, quadratic equations, simultaneous equations, functions and identities.
Basic calculus
Derivative as slope and rate of change, standard derivatives; product, quotient and function of a function rules; integration
as reverse of differentiation, standard integrals, area under a curve; solution of simple differential equations by direct integration.
Complex numbers
Addition, subtraction, multiplication, complex conjugate and division in algebraic form. The Argand diagram. Polar form and
exponential form, with multiplication and division. De Moivre's theorem (powers and roots). Locus problems.
Calculus
Implicit, parametric and logarithmic differentiation. Maxima and minima. MacLaurin's series. Partial differentiation, first order change, analysis of errors, method of least squares. Integration techniques (substitution, partial fractions, by parts) and simple applications of integration.
Matrices and Determinants
Second and third order determinants, evaluation, properties, Cramer's Rule for solution of simultaneous equations; matrices, addition, subtraction, multiplication, transpose, inverse (via adjoint), solution of simultaneous linear equations by matrix inversion.
Vectors
Sum, difference, magnitude, components, Cartesian representation in three dimensions; scalar and vector products, angle between vectors, application to simple geometrical and physical problems.
Differential Equations
Solution of first order by separation of variables and integrating factor; second order with constant coefficients, auxiliary
equation, complementary function, particular integral by substitution.
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