GATE XE Engineering Mathematics Syllabus
Complete section-wise syllabus for GATE XE Engineering Mathematics section. This syllabus is prepared based on the latest official GATE notification and is regularly updated to reflect any changes announced by the exam authorities. Each section includes a detailed list of topics that candidates should study to prepare effectively for the exam.
8TopicsA Section Code15 Marks
Engineering Mathematics (A) is mandatory for all Engineering Sciences (XE) candidates regardless of the optional subject chosen. It is always tested in the exam.
- 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)
- Eigen values and eigen vectors of matrices; Properties of eigen values and eigen vectors of symmetric matrices, diagonalization of matrices; Cayley-Hamilton Theorem
- Functions of Single Variable: Limit, indeterminate forms and L'Hospital's rule; 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
- Gradient, divergence and curl; Line integrals and Green's theorem
- Complex numbers, Argand plane and polar representation of complex numbers; De Moivre's theorem; Analytic functions; Cauchy-Riemann 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; Eigen value problem for second order equations with constant coefficients; Power series solutions for ordinary points
- Classification of second order linear partial differential equations; Method of separation of variables: One-dimensional heat equation and two-dimensional Laplace equation
- Axioms of probability; Conditional probability; Bayes' Theorem; Mean, variance and standard deviation of random variables
- Binomial, Poisson and Normal distributions; Correlation and linear regression
- 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