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## Duration:

**FREE**

## This course includes:

Unlimited Duration

## Badge on Completion

## Certificate of completion

Unlimited Duration

### Description

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**)

### Course Curriculum

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

### About the instructor

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