# 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.

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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