GATE

Here is the complete information regarding the GATE Engineering Mathematics Syllabus 2023.

## Introduction

According to the qualifying examination, GATE Syllabus is based on the different streams, but the maths section is common to all the branches. IIT Kharagpur 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.

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## GATE Engineering Mathematics Syllabus 2023

Engineering Mathematics holds 15 percentage weightage in GATE Exam. Here we are discussing 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) Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables
Textile Engineering and Fiber Science (TF) Linear Algebra, Calculus, Differential Equations, Probability and Statistics, Numerical Methods, Complex Variables
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.

## Conclusion

Mathematics is the most scoring subject in the GATE examination. Many students manage to score full marks. Do not mug the formulas directly, instead understand the concept first to retain them for a longer time. Practice regularly and take as many mock tests as possible.

It is important to analyze your preparation so that you can make appropriate changes in your strategy.

Keep working hard, and do not lose hope.

Good luck with all your future endeavours!

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Education is the passport to the future, for tomorrow belongs to those who prepare for it today.

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