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# GATE Syllabus 2020 for Engineering Mathematics – GATE Exam Syllabus

## GATE Exam Syllabus 2020 for Engineering Mathematics

### EngineeringMathematics (XE-A)

GATE Engineering Mathematics Syllabus: The Graduate Aptitude Test in Engineering (GATE), an all India level examination administered and conducted in eight zones across the country by the GATE Committee. Here we bring you the Gate 2020 Exam Syllabus for Engineering Mathematics subject. Check out the GATE Syllabus for Engineering Mathematics and other important aspects of the GATE Exam Engineering Mathematics Syllabus.

### 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.