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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 57 - Testing of Hypotheses I

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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