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
21MATME41: Mathematics-IV for Mechanical Engineering & Allied branches of Visvesvaraya Technological University (VTU). The course incepts with detailed ideas on complex analysis including analytic functions, conformal mapping and complex integration, which will be useful to mechanical engineers predominantly in fluid mechanics and heat transfer. Further the concept of probability distribution is introduced which is very crucial in stochastic analysis and design in mechanical engineering. Finally, LPP is introduced for optimization of linear objective with linear constraints, transportation and assignment.
Representing a Circle using Complex Numbers
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)
Applications for Flow Functions - (Introduction to Potential Flow)
Applications for Flow Functions - (Defining Complex Potential)
Applications for Flow Functions - (Verifying the CR Criteria)
Applications for Flow Functions - (Deriving Complex Velocity - Cartesian Form)
Applications for Flow Functions - (Deriving Complex Velocity - Polar Form)
Application to Flow Functions - Problems: (Problem 1)
Application to Flow Functions - Problems: (Problem 2)
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)
Linear mapping - Example 2
Understanding Conformal Mapping: Equation 1
Understanding Conformal Mapping: Equation 2
Understanding Conformal Mapping: Equation 3
Bilinear Transformation - (Important Observations)
Bilinear Transformation - (Understanding why Determinant cannot go to zero)
Bilinear Transformation - Problems: (Problem 1)
Bilinear Transformation - Problems: (Problem 2)
Bilinear Transformation - Problems: (Problem 3)
Bilinear Transformation - Problems: (Problem 4)
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)
Example (Addition Theorem) - Reliability of and Electric vehicle
Introduction to Discrete Random Variables
Variance of Discrete Random Variables: Var(X)
Variance - Example
Expectation - Example
Discrete Probability Distribution - Problem 2
Discrete Probability Distribution - Problem 3
Introduction to Continuous Random Variables
Introduction to Normal Distribution
Deriving mean for normal distribution
Deriving Variance for normal distribution
Introduction and Problems for Binomial Distribution
Deriving Mean of Binomial Distribution
Deriving Variance of Binomial Distribution
Introduction 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 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)
Basic Solution, Basic Feasible Solution and Optimal Solution
Simplex Method - (Problem 2)
Big-M Method - (Problem 3)
Big-M Method - (Problem 4)
2-Phase Simplex Method - (Problem 5)
2-Phase Simplex Method - (Problem 6)
2-Phase Simplex Method - (Problem 7)
North-West Corner Method - Problems - (Problem 1)
Least Cost Method - Problems - (Problem 2)
Vogel Approximation Method - Problems - (Problem 3)
Vogel Approximation Method with Optimality Check - Problems - (Problem 4)
Least Cost Method with Optimization - Problems - (Problem 5)
Introducing the Idea and Model for Assignment Problems
Assignment Problems (Hungarian Method) - (Problem 1)
Assignment Problems (Hungarian Method) - (Problem 2)
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₹ 1999.00
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Course Duration0
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Course LevelIntermediate
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Student Enrolled0
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LanguageEnglish
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