Questionbanks  MATHSI 
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MODULE1 1. Powers and Roots of Exponential and Trigonometric Functions. (Given any Numerical) 2. Expansion of sinn θ, cosn θ in terms of sines and cosines of multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ. (Given any Numerical) 3. Separation of real and imaginary parts of all types of Functions. (Given any Numerical) 4. Circular functions of complex number and Hyperbolic functions OR Inverse Circular and Inverse Hyperbolic functions. (Given any Numerical) MODULE2 1. Logarithmic functions, Separation of real and Imaginary parts of Logarithmic Functions. (Given any Numerical) 2. Successive differentiation: nth derivative of standard functions. (Given any Numerical) 3. Leibnitz’s Theorem (without proof) and problems. (Given any Numerical) MODULE3 1. Types of Matrices (symmetric, skew‐ symmetric, Hermitian, Skew Hermitian, Unitary, Orthogonal Matrices and properties of Matrices). (Given any Numerical) 2. Rank of a Matrix using Echelon forms (Given any Numerical) 3. Reduction to normal form (Given any Numerical) 4. PAQ in normal form (Given any Numerical) 5. System of homogeneous and non – homogeneous equations, their consistency and solutions (Given any Numerical) 6. Linear dependent and independent vectors. Application of inverse of a matrix to coding theory. (Given any Numerical) MODULE4 1. Partial derivatives of first and higher order. (Given any Numerical) 2. Total differentials, differentiation of composite and implicit functions. (Given any Numerical) 3. Euler’s Theorem on Homogeneous functions with two and three independent variables (with proof). Deductions from Euler’s Theorem (Given any Numerical) MODULE5 1. Maxima and Minima of a function of two independent variables (Given any Numerical) 2. Jacobian (Given any Numerical) 3. Taylor’s Theorem (Statement only) and Taylor’s series (Given any Numerical) 4. Maclaurin’s series (Statement only) (Given any Numerical) 5. Expansion of 𝑒𝑥 , sin(x), cos(x), tan(x), sinh(x), cosh(x), tanh(x), log(1+x), 𝑠𝑖𝑛−1(𝑥),𝑐𝑜𝑠−1(𝑥),𝑡𝑎𝑛−1(𝑥) (Given any Numerical) 6. Binomial series (Given any Numerical) MODULE6 1. Indeterminate forms (Given any Numerical) 2. L‐ Hospital Rule, problems involving series. (Given any Numerical) 3. Solution by Newton Raphson method and Regula–Falsi Equation. (Given any Numerical) 4. Solution of system of linear algebraic equations, by (1) Gauss Elimination Method, (2) Gauss Jacobi Iteration Method, (3) Gauss Seidal Iteration Method. (Scilab programming for above methods is to be taught during lecture hours) (Given any Numerical) 
