M1 with Pre-requisites

Jacobian – Understanding the concept
3 Topics
Figure description
Strategy
Deriving the Jacobian
Jacobian – (Formulating the Jacobian Matrix for Transformation)
1 Topic
Formulating the Jacobian Matrix for Transformation
Jacobian – Problems
5 Topics
Problem 1
Problem 2
Problem 3
Problem 4
Unravelling the Examiner’s Mind
Introduction to Maxima and Minima
2 Topics
Introduction to Idea of Curvature
Concept of Maxima and Minima in the context of 1-variable
Maxima & Minima – Part 1
1 Topic
Concept of Stationary point (Slope/Gradient) in a multivariable situation
Maxima & Minima – Part 2
6 Topics
Introduction to Hessian Matrix (Curvature information)
Graphical interpretation of the Hessian Matrix – Part 1
Graphical interpretation of the Hessian Matrix – Part 2
Eigen values for a Hessian Matrix
Eigen vectors for a Hessian Matrix
Interpreting Maxima and Minima via Eigen values and conclusion
Maxima & Minima (2-variable) – Problems
5 Topics
Procedure for Problem solving
Problem 1
Problem 2
Problem 3
Unravelling the Examiner’s Mind
Holistic Summary
13 Topics
Taylor series (Maclaurin’s series): (Formula & Procedure)
Taylor series (Maclaurin’s series): (Obvious & Unobvious Facts)
Taylor series (Maclaurin’s series): (Engineering Facts/Mapping)
Indeterminate Form: (Formula & Procedure)
Indeterminate Form: (Obvious & Unobvious Facts)
Total Derivative: (Formula & Procedure)
Total Derivative: (Obvious & Unobvious Facts)
Jacobian: (Formula & Procedure)
Jacobian: (Obvious & Unobvious Facts)
Jacobian: (Applications)
Maxima & Minima: (Formula & Procedure)
Maxima & Minima: (Obvious & Unobvious Facts)
Maxima & Minima: (Engineering Applications)
Concept Check
1 Quiz
Module-2: Differential Calculus – 2 | Quiz Questions
Module-3: Ordinary Differential Equations (ODEs) of First Order
Engineering Relevance – Part 1
5 Topics
Understanding Formation of DE’s
Predicting the System Behavior
Testing System Behavior
Complexities in Solving DE’s
Need for PDE’s for Solving DE’s
Engineering Relevance – Part 2
2 Topics
Understanding Non-linearity in DE’s
A Brief Histor of DE’s
Differential Equations (1st Order)
4 Topics
Understanding the Representations of DE’s
Mathematical Observations of DE’s
Deriving the Integrating Factor (IF)
Integrating factor (IF) – Memory Structure
Linear and Bernoulli’s DE’s – Problems
9 Topics
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Unravelling the Examiner’s Mind
Exact Differential Equations
1 Topic
Introduction
Exact & Reducible Exact DE’s – Problems
8 Topics
Problem 1 – Exact DE
Problem 2 – Exact DE
Problem 3 – Reducible Exact DE
Problem 4 – Reducible Exact DE
Problem 5 – Reducible Exact DE
Problem 6 – Reducible Exact DE
Problem 7 – Reducible Exact DE
Unravelling the Examiner’s Mind
Application of ODE’s
10 Topics
Newton’s Law of Cooling – Conceptual Understanding
Newton’s Law of Cooling – Problem 1 – Cooling
Newton’s Law of Cooling – Problem 2 – Heating
Unravelling the Examiner’s Mind
Orthogonal Tragectories – Conceptual Understanding
Orthogonal Tragectories – Problem 1
Orthogonal Tragectories – Problem 2
Orthogonal Tragectories – Problem 3
Orthogonal Tragectories – Problem 4
Unravelling the Examiner’s Mind
Non-Linear Differential Equations
2 Topics
Engineernig Relevance
Introduction
Non-linear Differential Equations – Problems
7 Topics
Problem 1 – ‘p’ type
Problem 2 – ‘p’ type
Problem 3 – ‘Clairaut’ type
Problem 4 – ‘Clairaut’ type
Problem 5 – ‘Reducible Clairaut’ type
Problem 6 – ‘Reducible Clairaut’ type
Unravelling the Examiner’s Mind
Summary – Part 1
1 Topic
Linear Differential Equations: (Formula & Procedure)
Summary – Part 2
1 Topic
Linear Differential Equations: (Memory Structure)
3 of 6
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Concept of Stationary point (Slope/Gradient) in a multivariable situation

M1 with Pre-requisites Maxima & Minima – Part 1 Concept of Stationary point (Slope/Gradient) in a multivariable situation
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