Advanced Engineering Mathematics

Dr. P. N. Agrawal is a Professor in the Department of Mathematics, IIT Roorkee. His area of research includes approximation Theory and Complex Analysis. He delivered 13 video lectures on Engineering Mathematics in NPTEL Phase I and recently completed Pedagogy project on Engineering Mathematics jointly with Dr. Uaday Singh in the same Department. Further he has completed online certification course “Mathematical methods and its applications” jointly with Dr. S.K. Gupta and two more courses namely “Integral equations and calculus of variations and its applications” and “Numerical Linear Algebra” with Dr. D. N. Pandey of the same department. He has taught engineering mathematics to B.Tech and M.Tech students at IIT Roorkee for many years. He has supervised twelve Ph.D. theses and has published more than 200 research papers in reputed international journals of the world. Currently, he is supervising eight research students.

COURSE LAYOUT:

Week 1  :  Analytic Functions, Cauchy-Riemann Equations, Harmonic Functions, Harmonic Conjugates and Milne’s Method, Applications to the problems of potential flow-I, Applications to the problems of potential flow-II
Week 2  :  Complex integration, Cauchy’s theorem-I, Cauchy’s theorem-II , Cauchy’s Integral Formula for the Derivatives of an Analytic Function , Morera’s theorem, Liouville’s theorem and Fundamental Theorem of Algebra
Week 3  :   Winding Number and Maximum Modulus Principle, Sequences and Series, Uniform Convergence of Series, Power Series, Taylor series
Week 4  : 
Week 5  :  Evaluation of real integrals using residues-I, Evaluation of real integrals using residues-II , Evaluation of real integrals using residues-III, Evaluation of real integrals using residues-IV, Evaluation of real integrals using residues-V
Week 6  :   Bilinear Transformations, Cross ratio, Conformal Mapping-I, Conformal Mapping-II, Conformal mappings from half plane to disk and half plane to half plane-I
Week 7 :  Conformal mappings from disk to disk and angular region to disk, Application of Conformal mapping to potential theory, Review of Z-transforms-I, Review of Z-transforms-II, Review of Z-transforms-III
Week 8  :  Review of bilateral Z-transforms, Finite Fourier transforms, Fourier integrals and Fourier transforms, Fourier Series, Discrete Fourier transforms-I
Week 9  :  Discrete Fourier transforms-II, Basic concepts of probability, Conditional probability, Bayes theorem and Probability networks, Discrete probability distribution
Week 10  :  Binomial distribution, Negative binomial distribution and Poisson distribution, Continuous probability distribution, Poisson Process, Exponential distribution
Week 11  :  Normal distribution , Joint distribution-I, Joint probability distribution-III, Joint probability distribution-III, Correlation and regression-I
Week 12  :  Correlation and regression-II, Testing of hypotheses-I, Testing of hypotheses-II, Testing of hypotheses-III, Application to Queueing Theory and Reliablility Theory

SUGGESTED READING MATERIALS:

Kreyszig, E., “Advanced Engineering Mathematics”, Wiley, New York.2. Jain, R.K. and Iyenger, S.R.K., Advanced Engineering Mathematics, 2nd Edition, Narosa Publishing House.3. Churchill, J. W. and Brown, R. V., “Complex Analysis”, McGraw Hill.4. Ahlfors, L. V., "Complex Analysis", McGraw Hill.5. Conway, J. B., "Functions of One Complex Variable", Narosa Publishing House.6. Debnath, L., Bhatta, D., “Integral Transforms and Their Tpplications”, Chapman & Hall/CRC (2nd edition)7. Miller, I. and Miller, M: “John E. Freund’s Mathematical Statistics with Applications”, 7th Edition, Prentice Hall.8. Mayer, P. L., “Introductory Probability and Statistical Applications”, Oxford & IBH Publishing Co. Pvt. Ltd.