GATE Syllabus is based on the different stream according to the qualifying examination bu the maths section is common to all the branches. IIT Delhi has defined the GATE syllabus along with the official notification. The syllabus is a very important part of the examination as it informs the candidate regarding what must be studied for the examination. This article will give you complete information regarding the **GATE Engineering Mathematics Syllabus.**

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**GATE Engineering Mathematics Syllabus**

Engineering Mathematics holds 15 percentage weightage in GATE Exam. Below we discuss the GATE Engineering Mathematics Syllabus:

GATE Paper Code | GATE Engineering Mathematics Syllabus |
---|---|

Aerospace Engineering (AE) | Linear Algebra, Calculus, Differential Equations |

Agricultural Engineering (AG) | Linear Algebra, Calculus, Differential Equations, Vector Calculus, Probability, and Statistics, Numerical Methods |

Biotechnology (BT) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods |

Civil Engineering (CE) | Linear Algebra, Calculus, Ordinary Differential Equations (ODE), Partial Differential Equations (PDE), Probability and Statistics, Numerical Methods |

Chemical Engineering (CH) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables |

Computer Science and Information Technology (CS) | Linear Algebra, Calculus, Probability, and Statistics, Discrete Mathematics |

Electronics and Communication (EC) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Vector Analysis, Complex Analysis |

Electrical Engineering (EE) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables, Transform Theory |

Instrumentation Engineering (IN) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Analysis of Complex Variables |

Mechanical Engineering (ME) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables |

Metallurgical Engineering (MT) | Linear Algebra, Calculus, Differential Equations, Vector Calculus, Probability and Statistics, Numerical Methods |

Mining Engineering (MN) | Linear Algebra, Calculus, Differential Equations, Vector Calculus, Probability and Statistics, Numerical Methods |

Petroleum Engineering (PE) | Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables |

Production and Industrial Engineering (PI) | |

Textile Engineering and Fiber Science (TF) | |

Engineering Sciences (XE) | Linear Algebra, Calculus, Ordinary Differential Equations (ODE), Partial Differential Equations, Probability and Statistics, Numerical Methods, Vector Calculus, Complex Variables |

### Linear Algebra

Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvector, Diagonalisation of matrices; Cayley-Hamilton Theorem.

### Calculus

Functions of a single variable: Limit, continuity and differentiability; Mean value theorems, Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem, Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

Functions of two variables: Limit, continuity and partial derivatives; Directional derivative, Total derivative; Tangent plane and normal line; Maxima, minima and saddle points, Method of Lagrange multipliers; Double and triple integrals, and their applications.

Sequence and series: Convergence of sequence and series; Tests for convergence, Power series; Taylor’s series; Fourier Series; Half range sine and cosine series.

### Vector Calculus

Gradient, divergence and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs).

### Complex Variable

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.

### Ordinary Differential Equation

First-order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second-order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

### Partial Differential Equation

Classification of second-order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one-dimensional heat and wave equations.

### Probability

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

### Numerical Methods

The solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule and Gaussian quadrature rule; Numerical solutions of first-order differential equations by Euler’s method and 4th order Runge-Kutta method.

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