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
BMATS201: Mathematics-II for Computer Science and engineering stream of Visvesvaraya Technological University (VTU). The curriculum incepts with integral calculus which is needed for many geometric evaluations. This is followed by vector differentiation and curvilinear coordinates, which is highly useful for applications in image recognition, transformation etc. This is followed by vector space and linear transformation which is a power tool computer graphics and data analytics. Finally, we have numerical methods which are highly necessitated in the era of digitization be it solving polynomial or differential equations.
Why learn Multiple Integrals
Understanding the Idea of Double Integral to compute Volume
Understanding the Idea of Triple Integral
Understanding the concept of Limits - Situation 1
Understanding the concept of Limits - Situation 2
Learning Matrix/Order
Evaluation of Double & Triple Integrals - (Problem 1)
Evaluation of Double & Triple Integrals - (Problem 2)
Evaluation of Double & Triple Integrals - (Problem 4)
Understanding changing the order of Integration
Double integrals by changing the order of Integration - (Problem 1)
Double integrals by changing the order of Integration - (Problem 2)
Double integrals by changing the order of Integration - (Problem 3)
Double integrals by changing the order of Integration - (Problem 4)
Double integrals by changing the order of Integration - (Problem 5)
Switching to Polar Coordinates
Switching to Polar Coordinates - Problems: (Problem 1)
Switching to Polar Coordinates - Problems: (Problem 2)
Switching to Polar Coordinates - Problems: (Problem 3)
Switching to Polar Coordinates - Problems: (Problem 4)
Applications of Double and Triple Integrals - (Problems 2)
Applications of Double and Triple Integrals - (Problems 3)
Applications of Double and Triple Integrals - (Problems 3 - High School Method)
Applications of Double and Triple Integrals - (Problems 4 - Introduction to generating volume by revolution)
Applications of Double and Triple Integrals - (Problems 4 - Solution)
Applications of Double and Triple Integrals - (Problems 5)
Introduction to Beta & Gamma Function
Relation between Beta & Gamma Functions
Beta & Gamma Functions - Problems: (Problem 1)
Beta & Gamma Functions - Problems: (Problem 2)
Beta & Gamma Functions - Problems: (Problem 3)
Beta & Gamma Functions - Problems: (Problem 4)
Beta & Gamma Functions - Problems: (Problem 5)
Understanding the Concept of Divergence
Understanding the concept of Curl
Gradient, Divergence & Curl - Formula and Procedure
Gradient, Divergence & Curl - Problems: (Problem 1 - 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 12 - Curl of a Gradient)
Gradient, Divergence & Curl - Problems: (Problem 13 - Divergence of a Curl)
Introduction to the Learning Metrics
Understanding Scaling Factor & Basis Vector
Deriving Basis Vectors for Cylindrical Polar Coordinates
Deriving Basis Vectors for Spherical Polar Coordinates
Understanding Transformation between Cartesian and Curvilinear Systems
Understanding Orthogonality
Curvilinear Coordinates - Problems: (Problem 1 - Scale Factor for Cylindrical Polar Coordinate System)
Curvilinear Coordinates - Problems: (Problem 2 - Scale Factor for Spherical Polar Coordinate System)
Curvilinear Coordinates - Problems: (Problem 3 - Arc length in Spherical Polar Coordinate System)
Curvilinear Coordinates - Problems: (Problem 4 - Volume of Enclosed Region)
Curvilinear Coordinates - Problems: (Problem 5 - Vector in Spherical Polar Coordinate System)
Curvilinear Coordinates - Problems: (Problem 6 - Expressing Gradient in Spherical Coordinate System)
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
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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