JELET Syllabus Engineering Mathematics:
Matrix & Vector:
Matrix – definition – order of a matrix – leading element – principal diagonal. Types of matrices – Null matrix – Square matrix – identity matrix – upper and lower triangular matrix – symmetric matrix
Determinant of a square matrix – minors and cofactors – procedures for evaluation – properties of determinants (no deduction) – evaluation of determinant by Ohio’s method (4th order) – problems
Concept of vector – addition and subtraction of vectors – multiplication of a vector by a scalar – position vector of a point – ratio formula – rectangular resolution of a vector – dot and cross product – geometrical interpretation – distributive law – applications.
Meaning of interpolation – difference table – Newton’s forward interpolation formula (no deduction) – problems
Numerical solution of non – linear equations – formula for Newton – Raphson method (no deduction) – problems
Numerical Solution of system of linear equation – Gauss – Elimination Method (No Deduction) – Problems
Definition – order and degree of a differential equation – differential equations of 1st order and 1st degree – Separation of variables – problems
Homogeneous differential equations – equations reducible to the homogeneous form – problems
Exact differential equations – equations reducible to the exact form – problems. Linear equations – Bernoulli’s equations.
Differential equation of 2nd order with constant co – efficient – Complementary function and particular integral – problems
Function of two or more variables – definition and meaning of partial derivatives (1st order ) . homogeneous functions – Euler’s theorem on homogeneous functions ( no deduction) problems.
Probability and Statistics:
Introduction – random experiment – Sample space – events. Classical and axiomatic definition of probability multiple theorem – related problems.
Statistics – Frequency distribution
Measure of central tendency – Mean – Median – Mode – Standard Deviation – Simple problems