NMCV(Numerical Methods and Complex Variables), 2-1 SEMESTER Previous year Question paper, R23 regulation

 

NMCV 2-1 SEMESTER Previous Year Question Paper R23 Regulation 

  Hi, here we have the NMCV 2-1 SEMESTER PYQ (Previous Year Question Paper). The 2-1 SEMESTER exam mainly focuses on five units:

➡️ Iterative Methods
➡️ Numerical Integration, Solution of Ordinary Differential Equations with Initial Conditions
➡️ Functions of a Complex Variable and Complex Integration
➡️ Series Expansions and Residue Theorem
➡️ Conformal Mapping

Now, let's first look at the concepts covered in each unit.

UNIT	DETAILS
I	Iterative Methods: Introduction, Solutions of algebraic and transcendental equations: Bisection method, Secant method, Method of false position, General Iteration method, Newton-Raphson method (Simultaneous Equations).  Interpolation: Newton’s forward and backward formulae for interpolation with unequal intervals, Lagrange’s interpolation formula.
II	Numerical integration, Solution of ordinary differential equations with initial conditions: Trapezoidal rule, Simpson’s 1/3rd and 3/8th rule, Solution of initial value problems by Taylor’s series, Picard’s method of successive approximations, Euler’s method, Runge - Kutta method (second and fourth order), Milne’s Predictor and Corrector Method.
III	Functions of a complex variable and Complex integration: Introduction: Continuity, Differentiability, Analyticity, Cauchy-Riemann equations in Cartesian and polar coordinates, Harmonic and conjugate harmonic functions, Milne –Thompson method. Complex integration: Line integral, Cauchy’s integral theorem, Cauchy’s integral formula, Generalized integral formula (all without proofs) and problems on above theorems.
IV	Series expansions and Residue Theorem: Radius of convergence, Expansion of function in Taylor’s series, Maclaurin’s series and Laurent series. Types of Singularities: Isolated, Essential singularities, Pole of order m, Residues, Residue theorem (without proof), Evaluation of real integral of the types -∞fxdx or cc+2πfcosθ,sinθdθ.
V	Conformal mapping: Transformation by ez,lnz,z2,zn(n positive integer), sin(z), cos(z), z+az , Translation , rotation, inversion and bilinear transformation, fixed point cross ratio, properties, inversion of circles and cross ratio determination of bilinear transformation mapping given 3 points.

📜Mid-1 Paper Overview

Part-A (20 Marks):

It contains 10 short questions, each carrying 2 marks.

Part-B (50 Marks):

It contains 5 sets of questions. Each set has 4 questions, out of which 2 questions must be answered. Each set carries 10 marks.