AN 209 Engineering Mathematics syllabus and Books Recommended by Institution of Engineers (India)

AN 209 Engineering Mathematics syllabus and Books Recommended by Institution of Engineers (India)

  SYLLABUS

Group A

Calculus of functions of one variable: Successive differentiation, Leibnitz theorem, Roll’s and Mean value theorems. Taylor's and Maclaurin’s expansion theorems. Fundamental theorem of integral calculus. Elementary reduction formulae for integrals. Applications to length, area, volume, surface area of revolution, moments of centre of gravity. Infinite series-convergence, divergence ratio tests, etc.
Calculus of functions of several variables: Partial derivatives, gradient and directional derivatives.
Differentiation of implicit functions, exact differentials, tangents, normals, maxima; minima, saddle points. Method of Lagrange’s multiplier. Multiple integrals.
Vector Calculus: Scalar and vector fields. Line and surface integrals. Gradient and divergence. Green's and Stoke's theorems and their applications.
Linear Algebra: Vector spaces-linear independence and dependence of vectors, inner products, linear transformations. Matrices and determinants. Systems of linear equations¬ consistency and inconsistency. Gauss elimination, rank of a matrix, inverse of a matrix. . Eigen values and eigenvectors of a matrix, diagonalization of a matrix.

GROUP B

Ordinary Differential Equations (ODEs): Formation of ODEs, definition of order, degree and solutions. ODEs of first. order; separable variables, homogeneous. and non-homogeneous .equations, exactness and integrating factors, linear equations and Bernoulli's equations {general linear ODEs of nth order, solutions of homogeneous and non-homogeneous equations, operator method, methods of undetermined coefficients and variation of parameters). Solutions of simple simultaneous ODEs.
Partial differential equations and its applications. Transforms theory-Laplace, Fourier, etc.
Numerical Methods: Difference operators forward, backward, central, shift and average. operators, and relations. between them. Newton's forward and backward interpolations. Lagrange’s interpolation and the error formula for interpolation. Numerical differentiation and integration. Trapezoidal rule and Simpson's one-third rule, including error formulae.
Introduction to Probability and Statistics: Basic concepts, including introduction to probability theory, Venn diagrams., central limit theorem, mean, mode and median. Properties of Beta, Poisson, Exponential and Normal distributions. Correlation and regression, Students t-distribution test, Chi-square and F tests of significance.

Books Recommended by the Institution of Engineers (India):-

1. Advanced Engineering Mathematics by E Kreyszig.

2.  An Introduction to Linear Algebra by V Krishnamurthy, VP Maina, JL Arora.

3. Calculus and Analytical Geometry by GB Thomas and RL Finny.

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