What you will learn
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Important Formulae and Procedures
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Derivations
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Engineering relevance of critical concepts
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Model Question Paper Problems
Get ready to power up your mathematical prowess with 21MAT41! Designed for 4th-semester Electrical & Electronics Engineering students at VTU, this course is your gateway to mastering complex analysis, special functions, and statistical methods. From unravelling the mysteries of probability distributions to exploring joint probability and sampling theory, each module is a thrilling adventure into the world of numbers and equations. Join us on this electrifying journey as we spark your curiosity and ignite your passion for engineering mathematics!
Representing a Circle using Complex Numbers
Problems on Complex Numbers: (Problem 1)
Problems on Complex Numbers: (Problem 2)
Introduction to Engineering Complex Analysis - (Phase 1 - Caclulus of Complex Functions)
Introduction to Engineering Complex Analysis - (Phase 2 - Conformal Mapping)
Deriving Cauchy-Riemann Equation in Cartesian From
Cauchy-Riemann Criteria - Example (Cartesian Form)
Deriving Cauchy-Riemann Equation in Polar From
Cauchy-Riemann Criteria - Example (Polar Form)
Understanding the Harmonic Property (Cartesian Form)
Understanding the Harmonic Property (Polar Form)
Analytic Functions - Problems - (Problem 1)
Analytic Functions - Problems - (Problem 2)
Analytic Functions - Problems - (Problem 3)
Analytic Functions - (Problem 3 (Optional) - Using Regular Differentiation)
Understanding Milne-Thompson Method of Constructing Analytic Functions
Milne-Thomson Method - Problems: (Problem 1)
Milne-Thomson Method - Problems: (Problem 2)
Milne-Thomson Method - Problems: (Problem 3)
Milne-Thomson Method - Problems: (Problem 4)
Deriving the Cauchy's Integral Formula
Cauchy's Theorem - Problems: (Problem 1)
Cauchy's Theorem - Problems: (Problem 2)
Cauchy's Theorem - Problems: (Problem 3)
Cauchy's Theorem - Problems: (Problem 4)
Cauchy's Theorem - Problems: (Problem 5)
Cauchy's Theorem - Problems: (Problem 6)
Introducing the Learning Components/Metrix
Introducing Bessel's Differential Equation and Series Solution
Introducing Recurrence Properties for Bessel's Function
Introducing Orthogonality of Bessel's Functions
Set 1 - Numericals: (Problem 1)
Set 1 - Numericals: (Problem 2)
Set 1 - Numericals: (Problem 3)
Set 1 - Numericals: (Problem 4)
Set 1 - Numericals: (Problem 5)
Set 1 - Numericals: (Problem 6 - Optional (Physics Based))
Set 1 - Numericals: (Problem 7)
Introducing the Legendre Differential Equation and Polynomial - Rodrigue's Formula
Legendre's Polynomial for various values of "n" and Orthogonality & Properties
Set 2 - Numericals: (Problem 1)
Set 2 - Numericals: (Problem 2)
Set 2 - Numericals: (Problem 3)
Set 2 - Numericals: (Problem 4)
Set 2 - Numericals: (Problem 5)
Introducing the Need for Regression
Understanding Simple Linear Regression
Limitation of Linear Regression
Introducing Correlation Coefficient
Understanding Rank Correlation Coefficient
Set 1 - Numericals: (Problem 1)
Set 1 - Numericals: (Problem 2)
Set 1 - Numericals: (Problem 3)
Set 1 - Numericals: (Problem 4)
Set 1 - Numericals: (Problem 5)
Set 1 - Numericals: (Problem 6)
Set 1 - Numericals: (Problem 7)
Set 1 - Numericals: (Problem 8)
Set 1 - Summary
Fitting a curve of the form
Set 2 - Numericals: (Problem 1 - Linear Curve Fitting)
Set 2 - Numericals: (Problem 2 - Linear Curve Fitting)
Fitting curve of the form
Set 2 - Numericals: (Problem 1 - Exponential Curve Fitting)
Fitting a curve of the form
Set 2 - Numericals: (Problem 1 - Parabolic Curve Fitting)
Set 2 - Numericals: (Problem 2 - Parabolic Curve Fitting)
Set 2 - Summary
Introduction to Discrete Random Variables
Expectation of Discrete Random Variables: E(X)
Variance of Discrete Random Variables: Var(X)
Variance - Example
Expectation - Example
Discrete Probability Distribution - Problem 1
Discrete Probability Distribution - Problem 2
Introduction to Continuous Random Variables
Introduction to Normal Distribution
Pre-requisites for deriving Mean and Variance for Normal Distribution
Deriving mean for normal distribution
Deriving Variance for normal distribution
Deriving Mean of Binomial Distribution
Deriving Variance of Binomial Distribution
Introductin to Poisson Distribution
Deriving Mean for Poisson Distribution
Deriving Variance for Poisson Distribution
Introduction to Exponential Distribution
Deriving Mean of Exponential Distribution
Deriving Variance of Exponential Distribution - Using Laplace Transforms
Deriving Variance of Exponential Distribution - By Integration
Problems on Probability Distributions: (Problem 1 - Binomial Distribution)
Problems on Probability Distributions: (Problem 2 - Binomial Distribution)
Problems on Probability Distributions: (Problem 3 - Binomial Distribution)
Problems on Probability Distributions: (Problem 4 - Binomial Distribution)
Problems on Probability Distributions: (Problem 5 - Poisson Distribution)
Problems on Probability Distributions: (Problem 6 - Poisson Distribution)
Problems on Probability Distributions: (Problem 7 - Poisson Distribution)
Problems on Probability Distributions: (Problem 8 - Continuous Distribution)
Problems on Probability Distributions: (Problem 9 - Normal Distribution)
Problems on Probability Distributions: (Problem 10 - Exponential Distribution)
Problems on Probability Distributions: (Problem 11 - Exponential Distribution)
Problems on Probability Distributions: (Problem 12 - Continuous Distribution)
Problems on Probability Distributions: (Problem 13 - Continuous Distribution)
Numericals: (Problem 1)
Numericals: (Problem 2)
Numericals: (Problem 3)
Numericals: (Problem 4)
Numericals: (Problem 5)
Summary
Understanding Random Sampling & Simple Sampling Attributes
Understanding Sampling Distribution & Standard Error
Example: Sampling Distribution & Standard Error
Hypothesis Testing, Level of Significance, Confidence Limits and Errors
Set 1 - Numericals: (Problem 1)
Set 1 - Numericals: (Problem 2)
Set 1 - Numericals: (Problem 3)
Set 1 - Numericals: (Problem 4)
Set 1 - Numericals: (Problem 5)
Summary
Understanding Central Limit Theorem
Central limit Theorem - Example
Understanding Students t-Distribution & Formulae
Set 1 - Numericals: (Problem 1)
Set 1 - Numericals: (Problem 2)
Set 1 - Numericals: (Problem 3)
Set 1 - Numericals: (Problem 4)
Set 1 - Numericals: (Problem 5)
Set 1 - Numericals: (Problem 6)
Summary
Introduction to Chi-square
Set 2 - Numericals: (Problem 1 - Chi-square)
Set 2 - Numericals: (Problem 2 - Chi-square)
Set 2 - Numericals: (Problem 3 - Chi-square)
Set 2 - Numericals: (Problem 4 - Chi-square)
Set 2 - Numericals: (Problem 5 - Chi-square)
Summary
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Course Duration0
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Course LevelIntermediate
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LanguageEnglish
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