XE0 Engineering Mathematics (15M, compulsory) — GATE Engineering Scie…
XE0 Engineering Mathematics (15M, compulsory) for GATE Engineering Sciences (XE): all 10 topics, with study resources and previous year questions for each.
Topics in XE0 Engineering Mathematics (15M, compulsory)
- Linear Algebra (GATE XE) — Algebra of real matrices: Determinant, inverse and rank of a matrix; System of linear equations (conditions for unique solution, no solution and infinite numbe…
- Functions of Single Variable (GATE XE) — Functions of Single Variable: Limit, indeterminate forms and L'Hospital's rule; Continuity and differentiability; Mean value theorems; Maxima and minima; Taylo…
- Functions of Two Variables (GATE XE) — Functions of Two Variables: Limit, continuity and partial derivatives; Directional derivative; Total derivative; Maxima, minima and saddle points; Method of La…
- Sequences and Series (GATE XE) — Sequences and Series: Convergence of sequences and series; Tests of convergence of series with non-negative terms (Cauchy Condensation Test, Ratio, Root and in…
- Vector Calculus (GATE XE) — Gradient, divergence and curl; Line integrals and Green's theorem.
- Complex variables (GATE XE) — Complex numbers, Argand plane and polar representation of complex numbers; De Moivre’s theorem; Definition and examples of Analytic functions; Cauchy-Riemann e…
- Ordinary Differential Equations (GATE XE) — First order equations (linear and nonlinear); Second order linear differential equations with constant coefficients; Cauchy-Euler equation; Second order linear…
- Partial Differential Equations (GATE XE) — Classification of second order linear partial differential equations, One dimensional heat and wave equations, two dimensional Laplace equation, Method of sepa…
- Probability and Statistics (GATE XE) — Axioms of probability; Conditional probability; Total probability theorem, Bayes' Theorem; Mean, variance and standard deviation of random variables; Binomial,…
- Numerical Methods (GATE XE) — Solution of systems of linear equations using LU decomposition, Gauss elimination method; Lagrange and Newton's interpolations; Solution of polynomial and tran…
Other GATE Engineering Sciences (XE) sections
- General Aptitude (10Q/15M)
- XE1 Fluid Mechanics (35M, choose any two)
- XE2 Materials Science (35M, choose any two)
- XE3 Solid Mechanics (35M, choose any two)
- XE4 Thermodynamics (35M, choose any two)
- XE5 Polymer Science and Engineering (35M, choose any two)
- XE6 Food Technology (35M, choose any two)
- XE7 Atmospheric and Oceanic Sciences (35M, choose any two)
- XE8 Energy Science (35M, choose any two)
- XE9 Textile Engineering and Fibre Science (35M, choose any two)