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Engineering Mathematics Syllabus

This document outlines the topics covered in the Engineering Mathematics course required for all candidates in the XE program. It includes 8 sections covering topics such as linear algebra, calculus, vector calculus, complex variables, ordinary and partial differential equations, probability and statistics, and numerical methods. Some of the major concepts covered are systems of linear equations, eigenvalues and eigenvectors, limits, derivatives, integrals, sequences and series, differential equations, and numerical integration techniques.

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Subradip debnath
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125 views1 page

Engineering Mathematics Syllabus

This document outlines the topics covered in the Engineering Mathematics course required for all candidates in the XE program. It includes 8 sections covering topics such as linear algebra, calculus, vector calculus, complex variables, ordinary and partial differential equations, probability and statistics, and numerical methods. Some of the major concepts covered are systems of linear equations, eigenvalues and eigenvectors, limits, derivatives, integrals, sequences and series, differential equations, and numerical integration techniques.

Uploaded by

Subradip debnath
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© © All Rights Reserved
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XE - A Engineering Mathematics(Compulsory for all XE Candidates)

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 2π.

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.

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