GATE 2021 syllabus for Engineering Mathematics (XE-A) gives you details of the latest GATE syllabus for the subject release by the official gate organizing institute IIT Bombay for the year 2021. We also created an easy to use ad-free mobile app for GATE syllabus, previous year papers with keys, gate calculator, virtual calculator, and more. **Download iStudy App for all GATE preparation needs.**

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## GATE 2021 Syllabus – Engineering Mathematics (XE-A)

#### 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’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 2n.

#### 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.

#### GENERAL APTITUDE (Common for all branches)

**Verbal Aptitude**

*Basic English Grammar*

Tenses, articles, adjectives, prepositions, conjunctions, verb-noun agreement, and other parts of speech

*Basic Vocabulary*

Words, idioms, and phrases in context

*Reading and Comprehension*

*Narrative Sequencing*

**Quantitative Aptitude**

*Data Interpretation*

Data graphs (bar graphs, pie charts, and other graphs representing data), 2- and 3-dimensional plots, maps, and tables

*Numerical Computation and Estimation*

Ratios, percentages, powers, exponents and logarithms, permutations and combinations, and series

*Mensuration and Geometry*

*Elementary Statistics and Probability*

**Analytical Aptitude**

*Logic*

Deduction and Induction

*Analogy*

*Numerical Relations and Reasoning*

**Spatial Aptitude**

*Transformation of Shapes*

Translation, rotation, scaling, mirroring, assembling, and grouping

Paper folding, cutting, and patterns in 2 and 3 dimensions

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