Advanced Engineering Mathematics

Por: Swayam . en: ,

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-IIWeek 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 AlgebraWeek 3 : Winding Number and Maximum Modulus Principle, Sequences and Series, Uniform Convergence of Series, Power Series, Taylor seriesWeek 4:Laurent Series,Zeros and Singularities of an Analytic Function,Residue at a Singularity,Residue Theorem,Meromorphic FunctionsWeek 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-VWeek 6 : Bilinear Transformations, Cross ratio, Conformal Mapping-I, Conformal Mapping-II, Conformal mappings from half plane to disk and half plane to half plane-IWeek 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-IIIWeek 8: Review of bilateral Z-transforms, Finite Fourier transforms, Fourier integrals and Fourier transforms, Fourier Series, Discrete Fourier transforms-IWeek 9: Discrete Fourier transforms-II, Basic concepts of probability, Conditional probability, Bayes theorem and Probability networks, Discrete probability distributionWeek 10: Binomial distribution, Negative binomial distribution and Poisson distribution, Continuous probability distribution, Poisson Process, Exponential distributionWeek 11: Normal distribution , Joint distribution-I, Joint probability distribution-III, Joint probability distribution-III, Correlation and regression-IWeek 12: Correlation and regression-II, Testing of hypotheses-I, Testing of hypotheses-II, Testing of hypotheses-III, Application to Queueing Theory and Reliablility Theory