M1 with Pre-requisites

Prerequisites for Module - 1 : 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 Trignometric 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 – Straight line
Concept of derivative – slope – Curve
Differentiation of Basic 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 sec x
Graphical understanding of trigonometric derivatives
Applications of Derivatives – Part 1
1 Topic
Finding nature of the curve
Applications of Derivatives – Part 2
1 Topic
Interpreting curvature of a curve
Applications of Derivatives – Part 3
5 Topics
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
Concept check
1 Quiz
Prerequisites for Module – 1 : Elements of Differential Calculus (Quiz Questions)
Module-1: Differential Calculus - 1
Introduction to Polar Curves
1 Topic
Introduction
Converting Cartesian and Polar Curves – Part 1
1 Topic
Parabola – Cartesian to Polar
Converting Cartesian and Polar Curves – Part 2
1 Topic
Circle – Polar to Cartesian
Converting Cartesian and Polar Curves – Part 3
3 Topics
Offset Circle – Cartesian to Polar
Cardioid – Polar and Cartesian Equivalance
Rose Curve – Polar and Cartesian Equivalance
Parametric Equation for Cycloid
1 Topic
Visualizing the Cycloid formation
Parametric Equation for Ellipse
1 Topic
Parametric Equation for Ellipse
Polar Curves
10 Topics
Angle between two curves -(Introduction)
Evolution of angle between geometric entities
Angle between radius and tangent vector – Purpose Definition
Angle between radius and tangent vector – Understanding the Figure
Angle between radius and tangent vector – Strategy
Angle between radius and tangent vector – Derivation
Angle between radius and tangent vector – Derivation 1 and Common Mistakes
Angle between radius and tangent vector – Incidental Facts
Angle between radius and tangent – Memory Structure
Deriving angle between two curves
Angle between curves – Problems
12 Topics
Problem 1 (Circle)
Problem 1 – Method 2 (Circle)
Problem 2 (Cardioid)
Problem 2 – Critical Observations
Problem 3
Problem 4
Problem 4 (Method 2)
Problem 5 (Parabola)
Problem 6 (Cardioid Slope)
Problem 7
Problem 8
Unravelling the Examiner’s Mind
Pedal Equation
3 Topics
Understanding the pedal equation
Derivation of pedal equation
Derivation – Memory Structure
Pedal Equation – Solved Problems
8 Topics
General – Procedure
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Unravelling the Examiner’s Mind
Concept of Curvature
4 Topics
Introduction – Understanding Curvature
Application – 1
Application – 2
Application – 3
1 of 6
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Interpreting curvature of a curve

M1 with Pre-requisites Applications of Derivatives – Part 2 Interpreting curvature of a curve
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