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Advanced Engineering Mathematics

Advanced Engineering Mathematics (Prof. P. N. Agrawal, IIT Roorkee). Instructor: Prof. P. N. Agrawal, Department of Mathematics, IIT Roorkee. This course is a basic course offered to UG/PG students of Engineering/Science background. It contains Analytic Functions, applications to the problems of potential flow, Harmonic functions, Harmonic conjugates, Milne's method, Complex integration, sequences and series, uniform convergence, power series, Hadamard's formula for the radius of convergence, Taylor and Laurent series, zeros and poles of a function, meromorphic function, the residue at a singularity, Residue theorem, the argument principle and Rouche's theorem, contour integration and its applications to evaluation of a real integral. (from nptel.ac.in)

Lecture 17 - Zeros and Singularities of an Analytic Function


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Lecture 01 - Analytic Function
Lecture 02 - Cauchy-Riemann Equations
Lecture 03 - Harmonic Functions, Harmonic Conjugates and Milne's Method
Lecture 04 - Applications to the Problems of Potential Flow I
Lecture 05 - Applications to the Problems of Potential Flow II
Lecture 06 - Complex Integration
Lecture 07 - Cauchy's Theorem I
Lecture 08 - Cauchy's Theorem II
Lecture 09 - Cauchy's Integral Formula for the Derivatives of an Analytic Function
Lecture 10 - Morera's Theorem, Liouville's Theorem and Fundamental Theorem of Algebra
Lecture 11 - Winding Number and Maximum Modulus Principle
Lecture 12 - Sequences and Series
Lecture 13 - Uniform Convergence of Series
Lecture 14 - Power Series
Lecture 15 - Taylor Series
Lecture 16 - Laurent Series
Lecture 17 - Zeros and Singularities of an Analytic Function
Lecture 18 - Residue of a Singularity
Lecture 19 - Residue Theorem
Lecture 20 - Meromorphic Functions
Lecture 21 - Evaluation of Real Integrals using Residues I
Lecture 22 - Evaluation of Real Integrals using Residues II
Lecture 23 - Evaluation of Real Integrals using Residues III
Lecture 24 - Evaluation of Real Integrals using Residues IV
Lecture 25 - Evaluation of Real Integrals using Residues V
Lecture 26 - Bilinear Transformations
Lecture 27 - Cross Ratio
Lecture 28 - Conformal Mapping I
Lecture 29 - Conformal Mapping II
Lecture 30 - Conformal Mapping from Half Plane to Disk and Half Plane to Half Plane
Lecture 31 - Conformal Mapping from Disk to Disk and Angular Region to Disk
Lecture 32 - Application of Conformal Mapping to Potential Theory
Lecture 33 - Review of z-Transforms I
Lecture 34 - Review of z-Transforms II
Lecture 35 - Review of z-Transforms III
Lecture 36 - Review of Bilateral z-Transforms
Lecture 37 - Finite Fourier Transforms
Lecture 38 - Fourier Integral and Fourier Transforms
Lecture 39 - Fourier Series
Lecture 40 - Discrete Fourier Transforms I
Lecture 41 - Discrete Fourier Transforms II
Lecture 42 - Basic Concepts of Probability
Lecture 43 - Conditional Probability
Lecture 44 - Bayes Theorem and Probability Networks
Lecture 45 - Discrete Probability Distribution
Lecture 46 - Binomial Distribution
Lecture 47 - Negative Binomial Distribution and Poisson Distribution
Lecture 48 - Continuous Probability Distribution
Lecture 49 - Poisson Process
Lecture 50 - Exponential Distribution
Lecture 51 - Normal Distribution
Lecture 52 - Joint Probability Distribution I
Lecture 53 - Joint Probability Distribution II
Lecture 54 - Joint Probability Distribution III
Lecture 55 - Correlation and Regression I
Lecture 56 - Correlation and Regression II
Lecture 57 - Testing of Hypotheses I
Lecture 58 - Testing of Hypotheses II
Lecture 59 - Testing of Hypotheses III
Lecture 60 - Application to Queueing Theory and Reliability Theory