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
This course is an inaugural offer with 30 days validity, ensuring you can grasp these foundational concepts within a focused timeframe. Discover our comprehensive online engineering mathematics course designed specifically for Mechanical Engineering students at Visvesvaraya Technological University. With course code 21MAT21, "Mathematics-II for Mechanical & Civil Engineering," you'll delve into essential topics including Integral Calculus, Vector Calculus, Partial Differential Equations (PDEs), and Numerical Methods - both in Module-4 and Module-5. Elevate your understanding and skills in these fundamental areas through our accessible and interactive online platform. The curriculum incepts with multiple integrals which is highly useful for applications in solid and fluid mechanics for mechanical engineers. This is followed by vector calculus which is a power tool especially for fluid mechanics. Third topic happens to be partial differential equations (PDE’s) , the topic is of great importance as many engineering situations are governed by (PDE’s). Finally, we have numerical methods which are highly necessitated in the era of digitization be it solving a polynomial or differential equations.
Understanding the Examiner's Expectations
Why learn Multiple Integrals
Understanding the Idea of Double Integral to compute Area
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 3)
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 1)
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
Important results for Gamma Functions
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 Gradient
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 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)
Introduction to Line Integral (For Work done)
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)
PDE's by eliminating Constants and Functions - Problems: (Problem 1)
PDE's by eliminating Constants and Functions - Problems: (Problem 2)
PDE's by eliminating Constants and Functions - Problems: (Problem 3)
PDE's by eliminating Constants and Functions - Problems: (Problem 4)
PDE's by eliminating Constants and Functions - Problems: (Problem 5)
PDE's by eliminating Constants and Functions - Problems: (Problem 6)
Solution of Non-Homogenous PDE by Direct Integration - Problems: (Problem 1)
Solution of Non-Homogenous PDE by Direct Integration - Problems: (Problem 2)
Solution of Non-Homogenous PDE by Direct Integration - Problems: (Problem 3)
Solution of Non-Homogenous PDE by Direct Integration - Problems: (Problem 4)
Solution of Non-Homogenous PDE by Direct Integration - Problems: (Problem 5)
Solution of Homogenous PDE's for 1-variable - Problems: (Problem 1)
Solution of Homogenous PDE's for 1-variable - Problems: (Problem 2)
Solution of Homogenous PDE's for 1-variable - Problems: (Problem 3)
Solution of Homogenous PDE's for 1-variable - Problems: (Problem 4)
Solution of Lagrange's Linear PDE - Problems: (Problem 1)
Solution of Lagrange's Linear PDE - Problems: (Problem 2)
Solution of Lagrange's Linear PDE - Problems: (Problem 3)
One-Dimensional Wave Equation - Derivation
One-Dimensional Heat Equation - Derivation
Understanding the Newton-Raphson Method
Newton-Raphson Method - Problems: (Problem 1)
Newton-Raphson Method - Problems: (Problem 2)
Newton-Raphson Method - Problems: (Problem 3)
Newton-Raphson Method - Problems: (Problem 4)
Newton-Raphson Method - Problems: (Problem 5)
Newton-Raphson - Problems (Using Calculator): Problem 1
Newton-Raphson - Problems (Using Calculator): Problem 2
Newton-Raphson - Problems (Using Calculator): Problem 3
Newton-Raphson - Problems (Using Calculator): Problem 4
Newton-Raphson - Problems (Using Calculator): Problem 5
Understanding the Regula-Falsi Method
Regula-Falsi - Problems: (Problem 1)
Regula-Falsi - Problems: (Problem 2)
Regula-Falsi - Problems: (Problem 3)
Regula-Falsi - Problems (Using Calculator): Problem 1
Regula-Falsi - Problems (Using Calculator): Problem 2
Regula-Falsi - Problems (Using Calculator): Problem 3
Introduction to Finite Differences
Application of 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 2)
Numerical Integration - Problems: (Problem 3)
Numerical Integration - Problems: (Problem 4)
Numerical Integration - Problems: (Problem 5)
Numerical Integration - Problems: (Problem 6)
Introduction to Numerical Solution of Differential Equations of First Order and First Degree
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 4)
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 1)
Milne's Predictor-Corrector Method - Problems: (Problem 2)
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Course Duration0
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Course LevelIntermediate
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LanguageEnglish
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