**Linear Algebra:**

Linear Algebra: Finite dimensional vector spaces; Linear transformations and their matrix representations, rank; systems of linear equations, eigenvalues and eigenvectors, minimal polynomial, Cayley-Hamilton Theorem, diagonalization, Hermitian, Skew-Hermitian and unitary matrices; Finite dimensional inner product spaces, Gram-Schmidt orthonormalization process, self-adjoint operators.

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**Fourier Series :**

Fourier series

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**Probability and statistics:**

Sampling theorems, Conditional probability, Mean, median, mode and standard deviation, Random variables, Discrete and continuous distributions, Poisson, Normal and Binomial distribution, Correlation and regression analysis

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**Calculus:**

Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial derivatives, Maxima and Minima, Multiple Integrals.

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**Numerical Methods:**

Solutions of non-linear algebraic equations, single and multi-step methods for differential equations.

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**Differential equations:**

First order equation (linear and non-linear), Higher order linear differential equations with constant coefficients, methods of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and Variable separable method.

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**Complex variables:**

Analytic functions, Cauchy’s integral theorem, and integral formula, Taylors and Laurent’s series, Residue theorem, Solution integrals.

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**Vector Calculus:**

Vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green’s theorems.

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**Laplace Transforms:**

Linear Property, First shifting theorem, change of scale property, second shifting theorem, multiplication by ‘t’, division by ‘t’, Laplace transform of integral, inverse Laplace transform, Convolution theorem.

**GATE Mathematics **weightage** analysis branch wise.**

Branch | 1Marck | 2Mark |

Electronics and Communications Engineering | 5 | 4 |

Civil Engineering | 3 | 5 |

Electrical Engineering | 3 | 3 |

Chemical Engineering | 4 | 2 |

Computer Science and Information Technology | 5 | 6 |

Mechanical Engineering | 5 | 4 |