GATE 2016 Syllabus For Engineering Mathematics (XE-A), Download gate 2016 syllabi pdf, Graduate Aptitude Test in Engineering 2016 Syllabus For Engineering Mathematics.

### GATE 2016 Syllabus For Engineering Mathematics

Gate 2016 New Syllabus available For all 23 papers. Read & Download your branch Syllabus that is Engineering Mathematics below.

Graduate Aptitude Test in Engineering (GATE) is an all India examination that primarily tests the comprehensive understanding of the candidates in various undergraduate subjects in Engineering/Technology/Architecture and post-graduate level subjects in Science.

GATE 2016 Organizing By Indian Institute of Science. IIS has been released the Gate 2016 Syllabus For Engineering Mathematics. Students those who want GATE 2016 XE-A Syllabus PDF to Download from below Link.

**Note :**

1. GATE Online Application Processing System (GOAPS) Website Opens for Enrolment, Application Filling, Application Submission – **September 1, 2015 (Tuesday)**

2. GATE 2016 Online Examination Forenoon: 9.00 AM to 12.00 Noon Afternoon: 2.00 PM to 5.00 PM (On Saturdays and Sundays only) – **January 30 to February 07, 2016.**

**XE -A Engineering Mathematics Syllabus**

General Aptitude (GA) Syllabus : Common in all papers – Download Here

**XE-A (Compulsory for all XE candidates) Engineering Mathematics:**

**Section 1: Linear Algebra**

Algebra of matrices; Inverse and rank of a matrix; System of linear equations; Symmetric, skew-symmetric and orthogonal matrices; Determinants; Eigenvalues and eigenvectors; Diagonalisation of matrices; Cayley-Hamilton Theorem.

**Section 2: Calculus**

** Functions of single variable:** Limit, continuity and differentiability; Mean value theorems; Indeterminate forms and L’Hospital’s rule; Maxima and minima; Taylor’s theorem; Fundamental theorem and mean value-theorems of integral calculus; Evaluation of definite and improper integrals; Applications of definite integrals to evaluate areas and volumes.

**Functions of two variables:** Limit, continuity and partial derivatives; Directional derivative; Total derivative; Tangent plane and normal line; Maxima, minima and saddle points; Method of Lagrange multipliers; Double and triple integrals, and their applications.

**Sequence and series:** Convergence of sequence and series; Tests for convergence; Power series; Taylor’s series; Fourier Series; Half range sine and cosine series. Section 3: Vector Calculus Gradient, divergence and curl; Line and surface integrals; Green’s theorem, Stokes theorem and Gauss divergence theorem (without proofs).

**Section 3: Complex variables**

Analytic functions; Cauchy-Riemann equations; Line integral, Cauchy’s integral theorem and integral formula (without proof); Taylor’s series and Laurent series; Residue theorem (without proof) and its applications.

**Section 4: Ordinary Differential Equations**

First order equations (linear and nonlinear); Higher order linear differential equations with constant coefficients; Second order linear differential equations with variable coefficients; Method of variation of parameters; Cauchy-Euler equation; Power series solutions; Legendre polynomials, Bessel functions of the first kind and their properties.

**Section 5: Partial Differential Equations **

Classification of second order linear partial differential equations; Method of separation of variables; Laplace equation; Solutions of one dimensional heat and wave equations.

**Section 6: Probability and Statistics **

Axioms of probability; Conditional probability; Bayes’ Theorem; Discrete and continuous random variables: Binomial, Poisson and normal distributions; Correlation and linear regression.

**Section 7: Numerical Methods **

Solution of systems of linear equations using LU decomposition, Gauss elimination and Gauss-Seidel methods; Lagrange and Newton’s interpolations, Solution of polynomial and transcendental equations by Newton-Raphson method; Numerical integration by trapezoidal rule, Simpson’s rule and Gaussian quadrature rule; Numerical solutions of first order differential equations by Euler’s method and 4th order Runge-Kutta method.

Download GATE 2016 Engineering Mathematics Syllabus

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