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
BMATE201: Mathematics-II for Electrical & Electronics engineering stream of Visvesvaraya Technological University (VTU). The curriculum incepts with vector calculus which is highly useful for applications in antenna design. This is followed by vector space and linear transformation which is a power tool especially for communication, signal processing and circuit analysis. Third topic happens to be Laplace transforms which is fundamental to applications based on frequency domain representation and control engineering. Finally, we have numerical methods which are highly necessitated in the era of digitization be it solving polynomial or differential equations.
Understanding the Concept of Divergence
Understanding the concept of Curl
Gradient, Divergence & Curl - Formula and Procedure
Gradient, Divergence & Curl - Problems: (Problem 2 - Gradient)
Gradient, Divergence & Curl - Problems: (Problem 3 - Divergence)
Gradient, Divergence & Curl - Problems: (Problem 4 - Divergence)
Gradient, Divergence & Curl - Problems: (Problem 5 - Divergence & Curl)
Gradient, Divergence & Curl - Problems: (Problem 6 - Curl)
Gradient, Divergence & Curl - Problems: (Problem 7 - Curl)
Gradient, Divergence & Curl - Problems: (Problem 8 - Directional Derivative)
Gradient, Divergence & Curl - Problems: (Problem 9 - Directional Derivative)
Gradient, Divergence & Curl - Problems: (Problem 10 - Gradient)
Gradient, Divergence & Curl - Problems: (Problem 11 - Gradient)
Gradient, Divergence & Curl - Problems: (Problem 11 - Curl of a Gradient)
Gradient, Divergence & Curl - Problems: (Problem 11 - Divergence of a Curl)
Line Integral - Problems: (Problem 1)
Line Integral - Problems: (Problem 2)
Line Integral - Problems: (Problem 3)
Important Observations for Problems 2 & 3
Line Integral - Problems: (Problem 4)
Line Integral - Problems: (Problem 5)
Introduction to Stoke's Theorem
Introduction to Green's Theorem
Green & Stoke's Theorem - Problems: (Problem 1 - Stoke's Theorem)
Green & Stoke's Theorem - Problems: (Problem 1 (verification) - Stoke's Theorem)
Green & Stoke's Theorem - Problems: (Problem 2 - Stoke's Theorem - Using Line Integral)
Green & Stoke's Theorem - Problems: (Problem 3 - Stoke's Theorem - Using Double Integral)
Green & Stoke's Theorem - Problems: (Problem 4 - Stoke's Theorem)
Green & Stoke's Theorem - Problems: (Problem 5 - Green's Theorem)
Green & Stoke's Theorem - Problems: (Problem 6 - Green's Theorem)
Green & Stoke's Theorem - Problems: (Problem 7 (Area Bounded by ellipse) - Green's Theorem)
Green & Stoke's Theorem - Problems: (Problem 8 (Area Bounded by 2 parabolas) - Green's Theorem)
Linear Independence and Dependence for a 3D vector set/Matrix
Understanding the Idea of Vector Space and Subspace
Understanding Basis, Linear span and Dimension
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Visualizing Linear Transformation
Understanding Rank & Nullity
Numerical Understanding of Nullity - Square Matrix
Numerical Understanding of Nullity - Rectangular Matrix
Inner Product and Orthogonality
Rotation as a linear Transformation - Self Study Topic
Reflection as a linear Transformation - Self Study Topic
Problem 1
Problem 2
Problem 3
Problem 5 - Understanding left Null Space
Understanding Laplace Transform - Symbolism
Difference between Laplace & Fourier Transforms
Understanding the Role of the exponential function in the laplace integral - Part 1
Understanding the Role of the exponential function in the laplace integral - Part 2
Understanding Transfer Function
Engineering Applications of Laplace Transform: (Practical Example - Second Order System)
Important formula and standard results to remember
Important Properties of Laplace Transforms
Laplace Transforms - Problems: (Problem 1 - sin(at) and cos(at): Physical Interpretation)
Laplace Transforms - Problems: (Problem 2 - sinh(at) and cosh(at))
Laplace Transforms - Problems: (Problem 3)
Laplace Transforms - Problems: (Problem 4)
Laplace Transforms - Problems: (Problem 5)
Laplace Transforms - Problems: (Problem 6)
Laplace Transforms - Problems: (Problem 7)
Laplace Transforms - Problems: (Problem 8)
Introduction to Gamma functions
Finding the Laplace Transform
Relevance of Gaussian Function
Gamma Function - Problem
Laplace Transforms - Problems: (Problem 9)
Laplace Transforms - Problems: (Problem 10)
Laplace Transforms - Problems: (Problem 11)
Laplace Transforms - Problems: (Problem 12)
Laplace Transforms - Problems: (Problem 13)
Laplace Transforms - Problems: (Problem 14)
Laplace Transforms - Problems: (Problem 15)
Laplace Transforms - Problems: (Problem 16)
Understanding Region of Convergence (ROC)
Example - ROC
Properties of Laplace Transforms: (Linearity)
Properties of Laplace Transforms: (Scaling)
Properties of Laplace Transforms: (Time Shifting)
Properties of Laplace Transforms: (Differentiation in Frequency Domain)
Properties of Laplace Transforms: (Differentiation in Time Domain)
Properties of Laplace Transforms: (Integration in Frequency Domain)
Properties of Laplace Transforms: (Integration in Time Domain)
Introduction to Laplace Transform of Periodic Functions
Deriving Formula for Laplace Transform for Periodic Functions
Laplace Transfroms of Special Functions: (Square Wave)
Laplace Transfroms of Special Functions: (Saw-Tooth Wave)
Laplace Transforms of Special Functions: (Triangular wave - Part 1)
Laplace Transfroms of Special Functions: (Triangular Wave - Part 2)
Laplace Transfroms of Special Functions: (Full-Rectified Wave)
Laplace Transforms of Special Functions: (Half Rectified Wave)
Laplace Transforms of Special Functions - Problems: (Problem 1 (By Euler Definition) - [sinωt]
Laplace Transforms of Special Functions - Problems: (Problem 1 (By Integration by parts) - [sinωt]
Laplace Transforms of Special Functions - Problems: (Problem 1 (By time shift) - [sinωt ]
Introduction to Heavy Side Function
Computing Standard Results - Laplace Transforms of Heavy Side Function
Computing the Laplace Transform of a function multiplied by a Heavy Side Function
Construction of a Pulse using Heavy Side Function
Heavy Side Function - Problems: (Problem 1)
Heavy Side Function - Problems: (Problem 2)
Heavy Side Function - Problems: (Problem 3)
Introduction to Laplace Transform of Unit Impulse Function
Introduction to Inverse Laplace Transforms
Inverse Laplace Transforms - Understanding Method by Inspection
Inverse laplace Transforms - Problems: (Problem 1 - By completing the Square)
Rule for finding Inverse Laplace Transform for "Log and Inverse trignometric functions"
Inverse laplace Transforms - Problems: (Problem 2 - By Differentiation)
Inverse laplace Transforms - Problems: (Problem 3 - By Differentiation & Completing the squares)
Inverse laplace Transforms - Problems: (Problem 4 - By Partial Fraction)
Inverse laplace Transforms - Problems: (Problem 5 - By Partial Fraction)
Introduction to Convolution Theorem
Convolution Theorem - Problems: (Problem 1)
Convolution Theorem - Problems: (Problem 2)
Convolution Theorem - Problems: (Problem 3)
Introduction of solution of Ordinary Differential Equations using Laplace Transforms
Differential Equations - Laplace Transforms Problems: (Problem 1)
Differential Equations - Laplace Transforms Problems: (Problem 2)
Differential Equations - Laplace Transforms Problems: (Problem 3)
Newton-Raphson Method - Problems: (Problem 1)
Newton-Raphson Method - Problems: (Problem 2)
Newton-Raphson Method - Problems: (Problem 3)
Newton-Raphson Method - Problems: (Problem 5)
Newton-Raphson Method - Problems: (Problem 1) Using Scientific Calculator
Newton-Raphson Method - Problems: (Problem 2) Using Scientific Calculator
Newton-Raphson Method - Problems: (Problem 3) Using Scientific Calculator
Newton-Raphson Method - Problems: (Problem 4) Using Scientific Calculator
Newton-Raphson Method - Problems: (Problem 5) Using Scientific Calculator
Understanding the Regula-Falsi Method
Regula-Falsi - Problems: (Problem 1)
Regula-Falsi - Problems: (Problem 3)
Regula-Falsi - Problems: (Problem 1) Using Scientific Calculator
Regula-Falsi - Problems: (Problem 2) Using Scientific Calculator
Regula-Falsi - Problems: (Problem 3) Using Scientific Calculator
Introduction to Finite Differences
Formulae for Backward, Forward and Divided Differences
Newton's Forward and Backward Difference - Problems: (Problem 1)
Newton's Forward and Backward Difference - Problems: (Problem 2)
Newton's Forward and Backward Difference - Problems: (Problem 3)
Newton's Forward and Backward Difference - Problems: (Problem 4)
Newton's Forward and Backward Difference - Problems: (Problem 5)
Newton's Divided Difference - Problems: (Problem 1)
Newton's Divided Difference - Problems: (Problem 2)
Understanding Lagrange's Interpolation
Lagrange's Interpolation - Problems: (Problem 1)
Lagrange's Interpolation - Problems: (Problem 2)
Introduction to Numerical Integration
Numerical Integration - Problems: (Problem 1)
Numerical Integration - Problems: (Problem 3)
Numerical Integration - Problems: (Problem 4)
Numerical Integration - Problems: (Problem 5)
Numerical Integration - Problems: (Problem 6)
Intution of Taylor's Formulae
Taylor's Series Method - Problems: (Problem 1)
Taylor's Series Method - Problems: (Problem 2)
Taylor's Series Method - Problems: (Problem 3)
Taylor's Series Method - Problems: (Problem 5)
Taylor's Series Method - Problems: (Problem 6 - Practical Example)
Intution of Formulae for Numerical Solution of First order DE's
Runge-Kutta Method - Problems: (Problem 1)
Runge-Kutta Method - Problems: (Problem 2)
Runge-Kutta Method - Problems: (Problem 3)
Modified Euler Method - Problems: (Problem 1)
Modified Euler Method - Problems: (Problem 2)
Modified Euler Method - Problems: (Problem 3)
Milne's Predictor-Corrector Method - Problems: (Problem 2)
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₹ 1999.00
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Course Duration0
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Course LevelIntermediate
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LanguageEnglish
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