Browse Hierarchy MED3001: Mathematics I

"This module covers mathematical topics such as algebra, functions, geometry and trigonometry, and an introduction to the techniques of calculus. Algebra: Review of theory of indices, logarithms, quadratic equations and quadratic functions, logarithmic and exponential equations. Polynomials: the remainder and factor theorems, identical polynomials. Principle of undetermined coefficients, factorisation. Partial fractions. Inequalities involving the modulus sign. Functions: The set-theoretical definition of a function; composite functions; inverse functions. The modulus of a function. Determination of the range or image set of a function. Odd and even functions; periodic functions, rational functions. Limits and asymptotes of functions. The algebraically-defined exponential and logarithmic functions. Coordinate Geometry: Review of some of the theorems of circle geometry, properties of tangents to a circle and circular measure. Loci: the standard equations of conic sections, standard and parametric equation of curves. The standard and general equation of a circle. Trigonometry: definition of the functions for an acute angle and extension to an angle of any sign and magnitude. Graphical representation of the functions. Basic relationships between trigonometric functions. Inverse trigonometric functions. Compound angle, multiple and submultiple angles. Trigonometric identities. The solution of trigonometric equations and equations involving factor formulae over a restricted domain of the angle. Graphical solution of trigonometric equations. General solution of trigonometric equations. Calculus: Fundamental elements of differential calculus; the derivative of a function, gradient at a point on a curve, the general gradient function, instantaneous rate of change. Second and higher order derivatives. Methods of differentiation: differentiation of powers, function of functions, products, quotients, trigonometric, logarithmic and exponential functions. Differentiation involving parameters. Application of differentiation: equations of the tangent and normal to a curve, maximum, minimum and turning points, simple rates of change. Elements of integral calculus: standard integrals; differentiation reversed. Definite integrals; area under the curve involving standard integrals."