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. Elevate your mathematical prowess with our online engineering mathematics course tailored for Mechanical Engineering students at Visvesvaraya Technological University (Course Code: 21MAT11). Uncover the essentials as you journey through Calculus, Series Expansion, Multivariable Calculus, Ordinary Differential Equations, Higher Order ODEs, and Linear Algebra in Modules 1 to 5 respectively. Seamlessly blending theory and application, this course empowers you with the mathematical tools crucial for excelling in Mechanical Engineering. M1 for mechanical and civil engineers incepts with polar coordinates for general situations in mechanics and physics. Derivative and successive derivatives are used for tailor series. Further there is a perfect transition from single variable to multivariable calculus, hence total derivative and jacobian which are powerfully used in mechanical engineering for simulation and optimization. The basic math modelling is via higher order ordinary discussion of differential equations. Finally Linear algebra with emphasis on rank, eigenvalues and eigen vectors makes it a perfect base curriculum be it stress or vibration analysis or fluid or thermal analysis.
Introduction to Polar Curves
Polar and Cartesian Equivalance
Converting Cartesian and Polar Curves - (Parabola - Cartesian to Polar)
Converting Cartesian and Polar Curves - (Circle - Polar to Cartesian)
Converting Cartesian and Polar Curves - (Offset Circle - Cartesian to Polar)
Converting Cartesian and Polar Curves - (Cardioid - Polar and Cartesian Equivalance)
Converting Cartesian and Polar Curves - (Rose Curve - Polar and Cartesian Equivalance)
Parametric Equation for Cycloid - (Visualizing the Cycloid formation)
Parametric Equation for Cycloid - (Parametric for a typical Cycloid)
Parametric Equation for Ellipse
Polar Curves - (Introduction to angle between curves)
Polar Curves - (Evolution of angle between geometric entities)
Polar Curves - (Angle between radius and tangent vector - Derivation 1 and Common Mistakes)
Polar Curves - (Angle between radius and tangent vector - Incidental Facts)
Polar Curves - (Angle between radius and tangent - Memory Structure)
Polar Curves - (Procedure for angle between two curves)
Solving angle between Curves - (Problem 1 (Circle))
Solving angle between Curves - (Problem 1 - Method 2 (Circle))
Solving angle between Curves - (Problem 2 (Cardioid))
Solving angle between Curves - (Problem 2 - Critical Observations)
Solving angle between Curves - (Problem 3)
Solving angle between Curves - (Problem 4)
Solving angle between Curves - (Problem 4 - Method 2)
Solving angle between Curves - (Problem 5 (Parabola))
Solving angle between Curves - (Problem 6 (Cardioid Slope))
Solving angle between Curves - (Problem 8)
Pedal Equation: (Derivation)
Pedal Equation - Derivation: (Memory Structure)
Pedal Equation - Problems: (Procedure)
Pedal Equation - Problems: (Problem 1)
Pedal Equation - Problems: (Problem 2)
Pedal Equation - Problems: (Problem 3)
Pedal Equation - Problems: (Problem 4)
Pedal Equation - Problems: (Problem 5)
Pedal Equation - Problems: (Problem 6)
Pedal Equation - (Unravelling the Examiner's Mind)
Concept of Curvature - (Introduction - Understanding Curvature)
Concept of Curvature: Applications - (Application 1)
Concept of Curvature: Applications - (Application 2)
Concept of Curvature: Applications - (Application 3)
Deriving Radius of Curvature - (Cartesian form)
Deriving Radius of Curvature - (Cartesian Form - Memory Structure)
Deriving Radius of Curvature - (Pedal and Polar form - Holistic Understanding)
Deriving Radius of Curvature - (Pedal form - Derivation)
Deriving Radius of Curvature - (Pedal form - Memory Structure)
Deriving Radius of Curvature - (Polar form - Derivation)
Deriving Radius of Curvature - (Polar form - Memory Structure)
Deriving Radius of Curvature - (Parametric form - Holistic Understanding)
Deriving Radius of Curvature - (Parametric form - Derivation)
Deriving Radius of Curvature - (Parametric form - Physical Basis)
Deriving Radius of Curvature - (Parametric form - Memory Structure)
Radius of Curvature - Problems - (Problem 1 - Cartesian Approach)
Radius of Curvature - Problems - (Problem 1 - Parametric Approach)
Radius of Curvature - Problems - (Problem 1 - Summary)
Radius of Curvature - Problems - (Problem 2)
Radius of Curvature - Problems - (Problem 3)
Radius of Curvature - Problems - (Problem 4)
Radius of Curvature - Problems - (Problem 5)
Radius of Curvature - Problems - (Problem 6)
Radius of Curvature - Problems - (Problem 7)
Radius of Curvature - Problems - (Problem 8)
Radius of Curvature - Problems - (Problem 9)
Radius of Curvature - Problems - (Formulae Summary)
Radius of Curvature - (Unravelling the Examiner's Mind)
Taylor Series - (Introduction)
Taylor Series - (Graphical Understanding - sin(x))
Taylor Series - (Graphical Understanding - cos(x))
Taylor Series - (Idea of Taylor Series)
Expanding functions using Maclaurin Serie - (Function 1 - sin x)
Expanding functions using Maclaurin Serie - (Function 2 - cos x)
Expanding functions using Maclaurin Serie - (Function 3 - tan x)
Expanding functions using Maclaurin Series - (Function 3 - tan x - Alternate method)
Expanding functions using Maclaurin Series - (Function 4 - e^x)
Expanding functions using Maclaurin Series - (Function 5 - Log(1 + x))
Taylor & Maclaurin Series - Problems: (Problem 2 - Taylor Series)
Taylor & Maclaurin Series - Problems: (Problem 2 - Maclauren Series)
Taylor & Maclaurin Series - Problems: (Problem 3)
Taylor & Maclaurin Series - Problems: (Problem 4)
Taylor & Maclaurin Series - Problems: (Problem 4 - Alternate Method)
Taylor & Maclaurin Series - Problems: (Problem 5)
Taylor & Maclaurin Series - Problems: (Problem 6)
Taylor & Maclaurin Series - Problems: (Problem 6 - Observations)
Taylor & Maclaurin Series - Problems: (Problem 7)
Taylor & Maclaurin Series - Problems: (Problem 8)
Taylor & Maclaurin Series - Problems: (Problem 9)
Introduction to Partial Differentiation
Concept of Total Differential
Physical meaning of product of Derivatives
Concept of Total Derivative: Engineering Relevance
Partial Differentiation - Problems: (Problem 2)
Partial Differentiation - Problems: (Problem 3)
Partial Differentiation - Problems: (Problem 4)
Partial Differentiation - Problems: (Problem 5)
Partial Differentiation - Problems: (Problem 6)
Total Derivatives - Problems: (Problem 1)
Total Derivatives - Problems: (Problem 2)
Total Derivatives - Problems: (Problem 3)
Total Derivatives - Problems: (Problem 4)
Total Derivative: (Unravelling the Examiners Mind)
Indetermediate Forms - (Understanding L-Hospital Rule)
Indeterminate form - Problems: (Problem 1)
Indeterminate form - Problems: (Problem 2)
Indeterminate form - Problems: (Problem 3)
Indeterminate form - Problems: (Problem 4)
Indeterminamt form - Problems: (Problem 5)
Indeterminate form - Problems: (Problem 5 - Alternate Method)
Indeterminate form - Problems: (Problem 6)
Indeterminate form - Problems: (Problem 8)
Indeterminate Form: (Unravelling the Examiners Mind)
Jacobian - (Understanding the concept of Jacobian - Purpose Defintion)
Jacobian - (Understanding the Concept of Jacobian - Figure description, Strategy, Deriving the Jacobian)
Jacobian - (Formulating the Jacobian Matrix for Transformation)
Jacobian - Problems: (Problem 1)
Jacobian - Problems: (Problem 2)
Jacobian - Problems: (Problem 3)
Jacobian - Problems: (Problem 4)
Jacobian: (Unravelling the Examiners Mind)
Maxima & Minima: (Introduction to Idea of Curvature)
Maxima & Minima: (Concept of Maxima and Minima in the context of 1-variable)
Maxima & Minima: (Concept of Stationary point (Slope/Gradient) in a multivariable situation)
Maxima & Minima: (Introduction to Hessian Matrix (Curvature information))
Maxima & Minima: (Graphical interpretation of the Hessian Matrix - Part 1)
Maxima & Minima: (Graphical interpretation of the Hessian Matrix - Part 2)
Maxima & Minima: (Eigen values for a Hessian Matrix)
Maxima & Minima: (Eigen vectors for a Hessian Matrix)
Maxima & Minima: (Interpreting Maxima and Minima via Eigen values and conclusion)
Maxima & Minima for 2-variables: (Procedure for Problem solving)
Maxima & Minima (2-variable) - Problems: (Problem 1)
Maxima & Minima (2-variable) - Problems: (Problem 2)
Maxima & Minima (2-variable) - Problems: (Problem 3)
Maxima & Minima: (Unravelling the Examiners Mind)
Engineering Relevance: (Testing System Behavior)
Engineering Relevance: (Complexities in Solving DE's)
Engineering Relevance: (Need for PDE's for Solving DE's)
Engineering Relevance: (Understanding Non-linearity in DE's)
Engineering Relevance: (A Brief Histor of DE's)
Differential Equations (1st Order): (Understanding the Representations of DE's)
Differential Equations (1st Order): (Mathematical Observations of DE's)
Differential Equations (1st Order): (Deriving the Integrating Factor (IF))
Linear and Bernoulli's DE's - Problems: (Problem 1)
Linear and Bernoulli's DE's - Problems: (Problem 2)
Linear and Bernoulli's DE's - Problems: (Problem 3)
Linear and Bernoulli's DE's - Problems: (Problem 4)
Linear and Bernoulli's DE's - Problems: (Problem 5)
Linear and Bernoulli's DE's - Problems: (Problem 6)
Linear and Bernoulli's DE's - Problems: (Problem 7)
Linear and Bernoulli's DE's - Problems: (Problem 8)
Linear 1st Order Differential Equations: (Unravelling the Examiner's Mind)
Exact Differential Equations: (Introduction)
Exact Differential Equations - Problems: (Problem 1)
Exact Differential Equations - Problems: (Problem 2)
Reducible Exact Differential Equations - Problems: (Problem 1)
Reducible Exact Differential Equations - Problems: (Problem 2)
Reducible Exact Differential Equations - Problems: (Problem 3)
Reducible Exact Differential Equations - Problems: (Problem 4)
Reducible Exact Differential Equations - Problems: (Problem 5)
Exact Differential Equations: (Unravelling the Examiner's Mind)
Application of ODE's - (Newton's Law of Cooling - Conceptual Understanding)
Application of ODE's - Problems: (Newton's Law of Cooling - Problem 1 (Cooling))
Application of ODE's - Problems: (Newton's Law of Cooling - Problem 2 - Heating)
Newton's Law of Cooling: (Unravelling the Examiner's Mind)
Application of ODE's - (Orthogonal Tragectories - Conceptual Understanding)
Application of ODE's - Problems: (Orthogonal Tragectories - Problem 1)
Application of ODE's - Problems: (Orthogonal Tragectories - Problem 2)
Application of ODE's - Problems: (Orthogonal Tragectories - Problem 3)
Application of ODE's - Problems: (Orthogonal Tragectories - Problem 4)
Orthogonal Tragectories: (Unravelling the Examiner's Mind)
Non-Linear Differential Equations - (Engineernig Relevance)
Non-Linear Differential Equations - (Introduction)
Non-Linear Differential Equations - Problems: (Problem 1 - 'p' type)
Non-Linear Differential Equations - Problems: (Problem 2 - 'p' type)
Non-Linear Differential Equations - Problems: (Problem 3 - 'Clairaut' type)
Non-Linear Differential Equations - Problems: (Problem 4 - 'Clairaut' type)
Non-Linear Differential Equations - Problems: (Problem 5 - 'Reducible Clairaut' type)
Non-Linear Differential Equations - Problems: (Problem 6 - 'Reducible Clairaut' type)
Non-Linear Differential Equations: (Unravelling the Examiner's Mind)
Linear Differential Equtions: (Formula & Procedure)
Linear Differential Equtions: (Memory Structure)
Linear Differential Equations: (Obvious & Unobvious Facts)
Exact Differential Equations: (Formula & Procedure)
Exact Differential Equations: (Obvious & Unobvious Facts)
Applications of 1st Order ODE: (Formula & Procedure)
Applications of 1st Order ODE: (Obvious & Unobvious Facts)
Non-linear Differential Equations: (Formula & Procedure)
Non-linear Differential Equations: (Obvious & Unobvious Facts)
Non-linear Differential Equations: (Engineering Applications)
Higher Order Differential Equations - (Understanding General solution for Complementary Functions (CF))
Higher Order DE's - Problems: (Problem 2 - CF)
Higher Order DE's - Problems: (Problem 3 - CF)
Higher Order DE's - Problems: (Problem 4 - CF)
Higher Order DE's - Problems: (Problem 5 - CF)
Higher Order DE's - Problems: (Problem 6 - CF)
Higher Order Differential Equations - (Understanding General solution for Particular Integral (PI))
Higher Order DE's - Problems: (Problem 1 - CF+PI)
Higher Order DE's - Problems: (Problem 2 - CF+PI)
Higher Order DE's - Problems: (Problem 3 - CF+PI)
Higher Order DE's - Problems: (Problem 4 - CF+PI)
Higher Order DE's - Problems: (Problem 5 - CF+PI)
Higher Order DE's - Problems: (Problem 6 - CF+PI)
Higher Order DE's - Problems: (Problem 7 - CF+PI)
Particular Integral: (Unravelling the Examiner's Mind)
Variation of Parameters: (Introduction to Variation of Parameters)
Higher Order DE's - Problems: (Problem 1 - Variation of Parameters)
Higher Order DE's - Problems: (Problem 2 - Variation of Parameters)
Higher Order DE's - Problems: (Problem 3 - Variation of Parameters)
Higher Order DE's - Problems: (Problem 4 - Variation of Parameters)
Variation of Parameters: (Unravelling the Examiner's Mind)
Cauchy and Legendre homogenous equations: (Introduction to Cauchy and Legendre homogenous equations )
Cauchy and Legendre homogenous equations - Problems: (Problem 2 - Cauchy DE)
Cauchy and Legendre homogenous equations - Problems: (Problem 3 - Cauchy DE)
Cauchy and Legendre homogenous equations - Problems: (Problem 4 - Cauchy DE)
Cauchy and Legendre homogenous equations - Problems: (Problem 5 - Legendre DE)
Cauchy and Legendre homogenous equations - Problems: (Problem 6 - Legendre DE)
Cauchy and Legendre homogenous equations - Problems: (Problem 7 - Legendre DE)
Cauchy and Legendre homogenous equations: (Unravelling the Examiner's Mind)
Higher Order Differential Equation: (Formula & Procedure)
Higher Order Differential Equation: (General Solutions for Complementary Functions (CF))
Higher Order Differential Equation: (General Solutions for Particular Integral (PI))
Higher Order Differential Equation: (Recollecting Method of Variation of Parameters)
Higher Order Differential Equation: (Obvious & Unobvious Facts)
Higher Order Differential Equation: (Engineering Applications)
Concept of Rank - (Basis definition of Rank)
Concept of Rank - (Linearly dependent and independent vectors)
Concept of Rank - (Graphical Understanding - 1)
Linear Algebra - (Rank - Linear Algebra/Transformation Perspective)
Linear Algebra - (Final observations/conclusions)
Rank/Row and Column Reduction - Problems: (problem 1 - Row reduction)
Rank/Row and Column Reduction - Problems: (problem 2 - Column reduction)
Rank/Row and Column Reduction - (Understanding the Echelon and observations)
Rank/Row and Column Reduction - (Understanding the Echelon and Normal form of a matrix)
Rank/Echelon form - Problems: (Problem 1)
Rank/Echelon form - Problems: (Problem 2)
Rank/Echelon form - Problems: (Problem 3)
Rank/Echelon form - Problems: (Problem 4)
Rank/Echelon form - Problems: (Problem 5)
Rank/Echelon form - Problems: (Problem 6)
Rank/Echelon form - Problems: (Problem 7)
Rank/Echelon form - Problems: (Problem 8)
Rank/Echelon form: (Unravelling the Examiner's Mind)
Simultaneous Equations - (Introduction)
Simultaneous Equations - (Classifications)
Simultaneous Equations - (Introductory Example)
Solutions to Simultaneous Equations - (Possibility 1 - Unique Solution)
Solutions to Simultaneous Equations - (Possibility 2 - No Solution)
Solutions to Simultaneous Equations - (Possibility 3 - Infinite Solution)
Solutions to Simultaneous Equations - (Understanding - 3 Variable situation)
Solutions to Simultaneous Equations - (Checking for Consistency of solution - 3 Variable situation)
Solutions to Simultaneous Equations - (Graphical Understanding of Consistancy - 3 Variable)
Solutions to Simultaneous Equations - Problems: (Problem 1)
Solutions to Simultaneous Equations - Problems: (Problem 2)
Solutions to Simultaneous Equations - Problems: (Problem 3)
Gauss - Jordan Method - Problems: (Problem 2)
Gauss - Jordan Method - Problems: (Problem 3)
Gauss - Elimination Method - Problems: (Problem 1)
Gauss - Elimination Method - Problems: (Problem 2 (2 approches))
Gauss-Seidel method - (Conceptual Understanding)
Gauss-Seidel method - Problems: (Problem 1)
Gauss-Seidel method - Problems: (Problem 2)
Simultaneous Equations: (Unravelling the Examiner's Mind)
Eigen values and vectors - (Introduction)
Eigen values and vectors - (Graphical Understanding of Eigen values and vectors)
Eigen values and vectors - (Understanding Eigen values - 2x2 matrix)
Eigen values and vectors - (Eigen values - Observations)
Eigen values and vectors - (Eigen values - Example)
Eigen values and vectors - (Deriving Eigen vectors - 2x2 matrix)
Eigen values and vectors - (Eigen vectors - Observations)
Eigen values and vectors - (Deriving Eigen value and vectors - 3x3 matrix)
Rayleigh's Power Method - (Conceptual Understanding)
Rayleigh's Power Method - Problems: (Problem 1)
Rayleigh's Power Method - Problems: (Problem 2)
Rayleigh's Power Method - (Conceptual Understanding of Rate of Convergence)
Eigen values & vectors: (Unravelling the Examiner's Mind)
Concept of Rank: (Formula & Procedure)
Concept of Rank: (Important Observations)
Concept of Rank: (Obvious and Unobvious Facts)
Concept of Rank: (Engineering Facts/Mapping)
Simultaneous Equations: (Formula & Procedure)
Simultaneous Equation Methods: (Formula & Procedure)
Gauss-Seidel Method: (Formula & Procedure)
Simultaneous Equations: (Obvious and Unobvious Facts)
Simultaneous Equations: (Engineering Facts/Mapping)
Eigen values and vectors: (Formula & Procedure)
Rayleigh Power Method: (Formula & Procedure)
Eigen values and vectors: (Obvious and Unobvious Facts)
Eigen values and vectors: (Engineering Facts/Mapping)
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Course Duration0
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Course LevelIntermediate
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LanguageEnglish
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