Engineering Mathematics - I

Subject Overview
  code: HS01U7101
  Level: Under Graduate
  School/Faculty BTECH
  Semester Offered: I
  Credit Value: 4
  Subject Queries: 0863-2118302
  Subject Outline:  

Objectives

Without mathematics not a single day of an engineer will pass! Thus all the topics of this course are relevant to all branches of engineering. For instance, differentiation and integration is used almost everywhere. When data is given at only a few points, we use numerical methods for finding the functional values at other places and for finding derivatives, maxima-minima and integration. Laplace transformations are used, for example, for conversion of domains, from time domain to frequency domain. These are also used to solve differential equations. Differential equations are used in various places. Matrices are used in many places, like digital image processing, algorithms etc. They are used in coding theory

Syllabus

S.no Details of the Unit No. of Teaching Hours Ref. Book Number
1

Ordinary Differential Equations Revision of integral formulae, Formation of ordinary differential equations, Differential equations of first order and first degree – linear and Bernoulli. Applications to Newton’s Law of cooling, Law of natural growth and decay, Orthogonal trajectories. Non-homogeneous linear differential equations of second and higher order with constant coefficients with RHS term of the type e , Sin ax, Cos ax, polynomials in x, method of variation of parameters

12 1,4
2

Laplace Transformations Definitions and properties, Laplace transform of standard functions, Inverse transform, first shifting Theorem, Transforms of derivatives and integrals, Unit step function, second shifting theorem, Dirac’s delta function, Convolution theorem, Differentiation and integration of transforms, Application of Laplace transforms to ordinary differential equations.

12 1,4
3

Real Analysis Sequences: Convergence and divergence; Series : Convergence and divergence, Ratio test, Comparison test, Integral test, Cauchy’s root test, Raabe’s test; Absolute and conditional convergence. Mean value theorems (Rolle’s, Lagrange’s, Cauchy’s), (without proofs), Taylor’s theorem and MacLaren’s theorem.

12 1,4
4

Matrices Matrices, Rank of a matrix, Solutions of system of linear equations – Gauss-Jordan, Gauss Elemination, LU decomposition methods.Eigen values, Eigen vectors, Cayley-Hamilton theorem - Applications, Digitalization of a matrix.

12 2,5
5

Numerical Methods Solutions of Algebraic and Transcendental equations: Bisection method, Regula-Falsi method, Newton-Raphson method. Interpolation: Errors in polynomial interpolation, Finite differences, Forward, backward and central differences, Newton’s formulae for interpolation, Central difference interpolation formulae, Gauss and Bessel central difference formulae, interpolation with unevenly spaced points, Lagrange’s interpolation formula.

12 2,5

Text Books :
1. A Textbook of Engineering Mathematics, Vol. I, T.K.V. Iyengar et al, S. Chand & Co.
2. Mathematical Methods, T.K.V. Iyengar et al, S. Chand & Co.
3. Engineering Mathematics – I, B. V. Ramana, Tata McGraw-Hill Publishing Co., 2008
4. Mathematical Methods, B. V. Ramana, Tata McGraw-Hill Publishing Co., 2008

Reference Books :

1. Advanced Engineering Mathematics, R.K. Jain, S.R.K. Iyengar, Narosa Publishing House
2. Higher Engineering Mathematics, B.V Ramana, Tata Mc Graw Hill.
3. Textbook of Engineering Mathematics, Vol I and II, Debashis Dutta, New Age International Publishers.
4. Higher Engineering Mathematics, B.S. Grewal, Khanna Publishers, Delhi

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