2nd Order Differential Equations

Pre-requisites to Elements of Differential Calculus
Sign of Trigonometric Identities
8 Topics
Sign of Trigonometric Identities – Introduction
Sign of Trigonometric Identities – Quad I
Sign of Trigonometric Identities – Quad II
Sign of Trigonometric Identities – Quad III
Sign of Trigonometric Identities – Quad IV
Sign of Trigonometric Identities – Summary
Sign of Trigonometric Identities – 1
Sign of Trigonometric Identities – 2
General solution for Trigonometric ratios
4 Topics
General solution for Trigonometric ratios (Example 1)
General solution for Trigonometric ratios (Example 2)
General solution for Trigonometric ratios (Example 3)
General solution for Trigonometric ratios (Example 4)
Concept of Derivative – Slope
2 Topics
Concept of Derivative – Slope – St line
Concept of derivative – slope – curve
Differentiation of Basis functions
14 Topics
Introduction – Chain and Quotient Rules
Derivative of tan x
Derivative of sec x
Derivative of cosec x
Derivative of cot x
Derivative of [y = e^x * x^n]
Derivative of [y = tan^(-1) x
Derivative of [y = x/(ax+b)] – Quotient rule
Derivative of [y = x/(ax+b)] – Chain rule
Derivative of [x^2 + y^2 = k]
Derivative of [y = 1/sqrt(ax^2 +b)]
Derivative of [y = a^x (log (1+x^2))]
Derivative of [y = a^sinx (1+sin^2 (x)) sec x]
Graphical understanding of trigonometric derivatives
Applications of Derivatives
7 Topics
Finding nature of the curve
Interpreting curvature of a curve
Linearization of a curve
L-Hospital Rule
Use of second derivative (curvature)
Maxima & Minima – 1
Maxima & Minima – 2
Angle between Curves & Radius of curvature
5 Topics
Essential trigonometric identities 1
Essential trigonometric identities 2
Essential trigonometric identities 3
Essential trigonometric identities 4
Essential trigonometric identities 5
Pre-requisites - Elements of Integral Calculus
Pre-requisites – Elements of Integral Calculus
17 Topics
Understanding Integration
Concept of Integration – Elementary Example
Introducing the Learning matrix
Why is Integration an anti-differentiation process?
Useful Rules and Symbolisms of Integration – (Rule 1)
Useful Rules and Symbolisms of Integration – (Rule 2)
Introducing Standard Integrals
Deriving Integrals of Basic Functions
Deriving Specific Integrals – 1
Deriving Specific Integrals – 2
Deriving Specific Integrals – 3
Deriving Specific Integrals – 4
Deriving Specific Integrals – 5
Useful Rules of Definite Integrals – (Rule 1)
Useful Rules of Definite Integrals – (Rule 2)
Useful Rules of Definite Integrals – (Rule 3)
Useful Rules of Definite Integrals – (Rule 4)
2nd Order Differential Equations
Higher Order Differential Equations – (Practical Understanding of Complementary and Particular Solution)
1 Topic
Higher Order Differential Equations – (Practical Understanding of Complementary and Particular Solution)
Higher Order Differential Equations – (Understanding General solution for Complementary Functions (CF))
1 Topic
Higher Order Differential Equations – (Understanding General solution for Complementary Functions (CF))
Higher order Homogenous DE’s – Problems
7 Topics
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Unravelling the Examiner’s Mind
Higher Order Differential Equations – (Understanding General solution for Particular Integral (PI))
1 Topic
Higher Order Differential Equations – (Understanding General solution for Particular Integral (PI))
Higher order Non-homogenous DE’s – Problems
8 Topics
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Unravelling the Examiner’s Mind
Variation of Parameters: (Introduction to Variation of Parameters)
1 Topic
Variation of Parameters: (Introduction to Variation of Parameters)
Higher Order DE’s – Variation of Parameters – Problems
5 Topics
Problem 1
Problem 2
Problem 3
Problem 4
Unravelling the Examiner’s Mind
Cauchy and Legendre homogenous equations
1 Topic
Introduction
Cauchy and Legendre homogenous equations – Problems
8 Topics
Problem 1 (Cauchy DE)
Problem 2 (Cauchy DE)
Problem 3 (Cauchy DE)
Problem 4 (Cauchy DE)
Problem 5 – (Legendre DE)
Problem 6 – (Legendre DE)
Problem 7 – (Legendre DE)
Unravelling the Examiner’s Mind
Summary
6 Topics
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)
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Higher Order Differential Equations – (Practical Understanding of Complementary and Particular Solution)

2nd Order Differential Equations Higher Order Differential Equations – (Practical Understanding of Complementary and Particular Solution)
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