L 3 C 3
Teachers Continuous Evaluation: 40 marks. Term-End Semester Examination: 60 marks.
Course outcomes
- Apply elementary probability and statistical methods to analyze engineering data, quantify uncertainty, and support engineering decision-making.
- Apply the principles of complex analysis to solve engineering problems involving analytic functions and contour integration.
- Employ Laplace and Fourier analytical techniques for solving ordinary differential equations and engineering models.
- Formulate and solve classical partial differential equations arising in heat transfer, wave propagation, and related engineering applications.
Unit I
Probability concepts, Conditional probability, Bayes' theorem, Random variables, Discrete and continuous probability distributions, Binomial, Poisson and Normal distributions, Mathematical expectation and variance, Correlation and regression, Sampling distributions, Confidence intervals, Tests of hypotheses for means and proportions, Engineering applications.
Unit II
Complex functions, Analytic functions, Cauchy–Riemann equations, Harmonic functions and Laplace equation, Exponential, trigonometric, hyperbolic and logarithmic functions, Euler's formula, De Moivre's theorem (without proof), General power and principal value, Singularities and zeros, Line integrals in the complex plane, Cauchy's integral theorem, Cauchy's integral formula, Taylor and Laurent series, Residue theorem, Evaluation of definite real integrals using residues.
Unit III
Laplace transforms: Definition, properties, transforms of derivatives and integrals, Shifting theorems, Unit step function, Dirac delta function, Inverse Laplace transforms, Convolution theorem, Solution of ordinary differential equations. Fourier analysis: Fourier series, Functions of arbitrary period, Half-range expansions, Sturm–Liouville problems, Introduction to Fourier transforms and engineering applications.
Unit IV
Basic concepts of partial differential equations, Wave equation, Heat equation, Method of separation of variables, D'Alembert's solution, Laplace equation in two dimensions, Boundary value problems, Fourier series solutions, Engineering applications.
References
- K. F. Riley, M. P. Hobson, and S. J. Bence, Mathematical Methods for Physics and Engineering, 3rd ed. Cambridge, U.K.: Cambridge University Press, 2013.
- K. A. Stroud and D. J. Booth, Engineering Mathematics, 8th ed. London, U.K.: Macmillan International Higher Education, 2020.
- L. C. Andrews, Special Functions of Mathematics for Engineers, 2nd ed. New York, NY, USA: Oxford University Press,
- L. Turyn, Advanced Engineering Mathematics. Boca Raton, FL, USA: CRC Press (Taylor & Francis Group), 2014.
- D. G. Zill, Advanced Engineering Mathematics, 5th ed. Burlington, MA, USA: Jones & Bartlett Learning, 2018.
- D. G. Duffy, Advanced Engineering Mathematics with MATLAB, 4th ed. Boca Raton, FL, USA: CRC Press (Taylor & Francis Group), 2017.
- M. C. Potter, J. L. Lessing, and E. F. Aboufadel, Advanced Engineering Mathematics, 4th ed. Cham, Switzerland: Springer, 2019