Note :
i. The Questions paper will consist of four Units.
ii. Examiner will set total of NINE questions comprising TWO questions from each Unit and ONE compulsory question of short answer type covering whole syllabi.
iii. The students are required to attempt ONE question from each unit and compulsory question.
iv. All questions carry equal marks unless specified.
v.The students can use only basic type of calculator.
vi.Log tables are allowed. The same may be provided to the students for computation.
Unit - 1
Introduction to differentiation, intergration and matrix algebra.
Data representation and computer arithmetic : Introduction, Concept of Exact and approximate numbers, concept of significant digits, Representation of numbers in Memory, strorage of interger numbers: signed representation, 1's Complement Representatio, 2's complement representation,floating point numbers and their storage, floating point arithmetic normalization and their consequences, errors, measures of accuracy: Absolute error, relatives error and percentage error, error types: Data errors, Truncation errors, Round-off errors, Computational error, Rules, Computational error propagation: Error Propagation in Addition Operation, Subtration operation, Multipilication operation and Division Operation.
Unit - 2
Solution of non-linear equations : introduction, types of non-linear equations: polynomial equations, Transcendental equations, methods of finding solutions of non-iterative methods: Direct method, Iterative method.
Iterative methods : Bisection method, false-position method, Secant method, newton - rasphson methods, Zeros of a polynomial using birge - vieta method. Convergence of iterative methods, Comparison between iterative methods.
Simultaneous Linear equations : Solution of Simultaneaus linear equations using direct and iterative methods: Direct methods : Gauss - Elimination method, gauss-Jordan method, Concept of Pivoting, Iterative method : Gauss - Seidal method.
Unit - 3
Interpolation : Introduction, lagrange interpolation, inverse interpolation, Finite differences: Forward differences, Backward difference table, divided difference table, observations regarding difference tables, Newton's method of interpolation : newton's forward difference interpolation formula, Newton's backward difference interpolation formula, newton's divided difference interpolation formula.
Numerical integration : introduction, newton-cotes intergration formulae: trapezoidal rule, simpson's 1/3rd rule, Simpson's 3/8th rule.
Unit - 4
Approximation : Approximation of Functions: Taylor series representation, Chebyshev polynomials.
Solution of Ordinary differential equations : Introduction, Euler's method, Runga-kutta methods: 2nd order & 4th order, Predictor corrector methods: Euler's method.
