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# GATE Engineering Mathematics (XE) Syllabus 2023

Organisation : Graduate Aptitude Test In Engineering GATE
Exam Name : GATE Engineering Mathematics (XE) Exam
Announcement : GATE Engineering Mathematics (XE) Syllabus 2023
Website : https://gate.iitk.ac.in

## GATE Engineering Mathematics (XE) Syllabus

In each of the following subjects the topics have been divided into two categories – Core Topics and Special Topics. The corresponding sections of the question paper will contain 90% of their questions on Core Topics and the remaining 10% on Special Topics.

Related / Similar Syllabus : Joint Admission Test JAM Mathematics (MA) Syllabus 2022 ## Engineering Mathematics (XE) Syllabus

Section 1: Linear Algebra
Algebra of real matrices: Determinant, inverse and rank of a matrix; System of linear equations (conditions for unique solution, no solution and infinite number of solutions); Eigenvalues and eigenvectors of matrices; Properties of eigenvalues and eigenvectors of symmetric matrices, diagonalization of matrices; Cayley-Hamilton Theorem.

Section 2: Calculus

Functions of Single Variable:
Limit, indeterminate forms and L’Hospital’srule; Continuity and differentiability; Mean value theorems; Maxima and minima; Taylor’s theorem; Fundamental theorem and mean value theorem of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes (rotation of a curve about an axis).

Functions of Two Variables:
Limit, continuity and partial derivatives; Directional derivative; Total derivative; Maxima, minima and saddle points; Method of Lagrange multipliers; Double integrals and their applications.

Sequences and Series:
Convergence of sequences and series; Tests of convergence of series with non-negative terms (ratio, root and integral tests); Power series; Taylor’s series; Fourier Series of functions of period 2π.

Section 3: Vector Calculus
Gradient, divergence and curl; Line integrals and Green’s theorem.

Section 4: Complex Variables
Complex numbers, Argand plane and polar representation of complex numbers; De Moivre’s theorem; Analytic functions; Cauchy-Riemann equations.

Section 5: Ordinary Differential Equations
First order equations (linear and nonlinear); Second order linear differential equations with constant coefficients; Cauchy-Euler equation; Second order linear differential equations with variable coefficients; Wronskian; Method of variation of parameters; Eigenvalue problem for second order equations with constant coefficients; Power series solutions for ordinary points.

Section 6: Partial Differential Equations
Classification of second order linear partial differential equations; Method of separation of variables: One dimensional heat equation and two dimensional Laplace equation.

Section 7: Probability and Statistics
Axioms of probability; Conditional probability; Bayes’ Theorem; Mean, variance and standard deviation of random variables; Binomial, Poisson and Normal distributions; Correlation and linear regression.

Section 8: Numerical Methods
Solution of systems of linear equations using LU decomposition, Gauss elimination method; Lagrange and Newton’s interpolations; Solution of polynomial and transcendental equations by Newton- Raphson method; Numerical integration by trapezoidal rule and Simpson’s rule; Numerical solutions of first order differential equations by explicit Euler’s method. 