Title Engineering Maths WB.pdf ✅

GATE Syllabus Electronics & Communication (EC) : Linear Algebra : Vector space, basis, linear dependence and independence, matrix algebra, Eigen values and Eigen vectors, rank, solution of linear equations – existence and uniqueness. Calculus : Mean value theorems, theorems of integral calculus, evaluation of definite and improper integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume integrals, Taylor series. Differential Equations : First order equations (linear and nonlinear), higher order linear differential equations, Cauchy's and Euler's equations, methods of solution using variation of parameters, complementary function and particular integral, partial differential equations, variable separable method, initial and boundary value problems. Vector Analysis : Vectors in plane and space, vector operations, gradient, divergence and curl, Gauss's, Green's and Stoke's theorems. Complex Analysis : Analytic functions, Cauchy's integral theorem, Cauchy's integral formula; Taylor's and Laurent's series, residue theorem. Numerical Methods : Solution of nonlinear equations, single and multistep methods for differential equations, convergence criteria. Probability and Statistics : Mean, median, mode and standard deviation; combinatorial probability, probability distribution functions -binomial, Poisson, exponential and normal; Joint and conditional probability; Correlation and regression analysis. Electrical Engineering (EE) : Linear Algebra : Matrix Algebra, Systems of linear equations, Eigen values, Eigen vectors. Calculus : Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, Green’s theorem. Differential equations : First order equations (linear and non-linear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of variables. Complex variables : Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, Solution integrals. Probability and Statistics : Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, Regression analysis. Numerical Methods : Solutions of non-linear algebraic equations, Single and Multi-step methods for differential equations. Transform Theory : Fourier Transform, Laplace Transform, Z-Transform. Mechanical Engineering (ME) : Linear Algebra : Matrix algebra, systems of linear equations, Eigen values and Eigen vectors. Calculus : Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems. Differential equations : First order equations (linear and non-linear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and