Linear Algebra: In linear algebra, the aspirants should focus on rank & determinant of matrices, Eigen values & vectors, and systems of linear equations. Topics such as basis vectors and span of basis vectors to form an n-dimensional space are not being covere
Calculus: Calculus is essential. All the aspirants should focus on maxima & minima in single variable calculus. Vector calculus which plays a significant role covers Gradient, Divergence, Curl as well as Vector Integral Theorems. Aspirants are advised to practice limits as well.
Differential Equations: Finding the solution of differential equations is extremely important. Focusing on higher order differential equations is a must along with first order equations. Bernoulli’s Equation and Euler Differential Equation should also be paid attention to.
Probability and statistics: Bayes’ Theorem will cover most of the questions. Question from Random Variables like Poisson’s Distribution, statistics, mean, median and mode as well as the coefficient of correlation have a high probability of appearing in GATE.
Complex Analysis (Excluding CS): Cauchy-Riemann Equations, Residue Method of Integration and Taylor series have to be practiced well. It looks small, but each of the subtopics is extremely large by themselves.
Numerical Methods (Excluding CS): Making a note of important formulae for Trapezoidal Rule and Simpson’s Rule is a must. Aspirants must practice as many questions as possible on solving equations using the Newton-Raphson method, Bisection method, and numerical integration techniques.
Transform Theory (For EE and ME ONLY): Laplace and inverse Laplace transforms are the topics to be practiced well.
Discrete Mathematics (For CS ONLY): Graph connectivity and colouring, relations and functions and mathematical logic (Propositions, and Predicate logic). Discrete Mathematics – tautology, satisfiability, equivalences of given propositional statements. Finding the number of edges, vertices, or components for the given connected or disconnected graph, Euler circuit, checking isomorphism, Hamiltonian cycle for given graphs as well as simple properties of various graphs such as complete graph, bipartite graph, regular graph, cycle graph, and line graph.
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