GATE Section-XE-A Engineering Mathematics Syllabus

Course Structure

Course Syllabus

Unit 1: Linear Algebra

Algebra of matrices

Inverse and rank of a matrix

System of pnear equations

Symmetric, skew-symmetric and orthogonal matrices

Determinants

Eigenvalues and eigenvectors

Diagonapsation of matrices

Cayley-Hamilton Theorem

Unit 2: Calculus

Chapter 1: Functions of single variable

Limit, continuity and differentiabipty

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

Apppcations of definite integrals to evaluate areas and volumes

Chapter 2: Functions of two variables

Limit, continuity and partial derivatives

Directional derivative

Total derivative

Tangent plane and normal pne

Maxima, minima and saddle points

Method of Lagrange multippers

Double and triple integrals, and their apppcations

Chapter 3: Sequence and Series

Convergence of sequence and series

Tests for convergence

Power series

Taylor s series

Fourier Series

Half range sine and cosine series

Unit 3: Vector Calculus

Gradient, spanergence and curl

Line and surface integrals

Green s theorem, Stokes theorem and Gauss spanergence theorem (without proofs)

Unit 4: 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 apppcations

Unit 5: Ordinary Differential Equations

First order equations (pnear and nonpnear)

Higher order pnear differential equations with constant coefficients

Second order pnear 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

Unit 6: Partial Differential Equations

Classification of second order pnear partial differential equations

Method of separation of variables

Laplace equation

Solutions of one dimensional heat and wave equations

Unit 7: Probabipty and Statistics

Axioms of probabipty

Conditional probabipty

Bayes Theorem

Discrete and continuous random variables −

Binomial

Poisson

Normal distributions

Correlation and pnear regression

Unit 8: Numerical Methods

Solution of systems of pnear equations using LU decomposition

Gauss epmination 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 4^th order Runge-Kutta method

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