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Engineering Mathematics Hand Notes For GATE

Engineering Mathematics Hand Notes For GATE



Graduate Aptitude Test In Engineering (GATE) is organized by various Indian Institute Of Technology (IITs). 

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Syllabus Of Engineering Mathematics For GATE:

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, local maxima and minima, Taylor and Maclaurin series; Evaluation of definite
and indefinite integrals, application of definite integral to obtain area and volume; Partial
derivatives; Total derivative; Gradient, Divergence and Curl, Vector identities, Directional
derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher
order linear equations with constant coefficients; Euler-Cauchy equations; Laplace
transform and its application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of onedimensional diffusion equation; first and second order one-dimensional wave equation
and two-dimensional Laplace equation.

Probability and Statistics: Definitions of probability and sampling theorems; Conditional
probability; Discrete Random variables: Poisson and Binomial distributions; Continuous
random variables: normal and exponential distributions; Descriptive statistics - Mean,
median, mode and standard deviation; Hypothesis testing.

Numerical Methods: Accuracy and precision; error analysis. Numerical solutions of linear
and non-linear algebraic equations; Least square approximation, Newton’s and
Lagrange polynomials, numerical differentiation, Integration by trapezoidal and Simpson’s
rule, single and multi-step methods for first order differential equations.

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