Mathematics (MATH)
6 units: Vectors, Three-Dimensional Geometry, Integrals, Applications of the Integrals, Differential Equations.
Detailed syllabus
Unit 1: Vectors (10 hours, 5 marks)
Magnitude and direction, direction cosines and ratios, types of vectors, position vectors, components, addition, scalar multiplication, section formula, scalar (dot) and vector (cross) products and their applications.
Unit 2: Three-Dimensional Geometry (20 hours, 10 marks)
Coordinate axes and planes, distance between two points, direction cosines and ratios of a line, Cartesian and vector equations of a line, skew lines, shortest distance between two lines, angle between two lines.
Unit 3: Integrals (20 hours, 9 marks)
Integration as the inverse of differentiation, substitution, partial fractions and integration by parts, standard integrals, fundamental theorem of calculus, properties and evaluation of definite integrals.
Unit 4: Applications of the Integrals (10 hours, 6 marks)
Area under simple curves: lines, circles, parabolas and ellipses in standard form.
Unit 5: Differential Equations (10 hours, 5 marks)
Order and degree, general and particular solutions, variables separable, homogeneous equations of first order and first degree, linear equations dy/dx + Py = Q and dx/dy + Px = Q.
Unit 6: Linear Programming (10 hours, 5 marks)
Constraints, objective function, optimisation, graphical solution in two variables, feasible and infeasible regions, optimal feasible solutions (up to three non-trivial constraints).
Source: official document