Curvature

Salient features of this module are: 

• Pre-requisites to polar curves 
• Graphical visualization 
• Concept testing 
• Unravelling examiners mind 
• Memory structure (for derivations) 
• Model question paper 

Course Contents: 

Pre-requisites to Elements of Differential Calculus

• Sign of Trigonometric Identities
  • 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
  • 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 derivate – Slope
  • Concept of Derivative – Slope – Straight line
  • Concept of Derivative – Slope – Curve
• Differentiation of Basic functions
  • 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
• Application of Derivative
  • 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
  • Essential trigonometric identities 1
  • Essential trigonometric identities 2
  • Essential trigonometric identities 3
  • Essential trigonometric identities 4
  • Essential trigonometric identities 5

Curvature

• Concept of Curvature
  • Introduction – Understanding Curvature
  • Application 1
  • Application 2
  • Application 3

• Deriving Radius of Curvature
  • Cartesian form
  • Cartesian form – Memory Structure
  • Pedal and polar form – Holistic Understanding
  • Pedal form – Derivation
  • Pedal form – Memory Structure
  • Polar form – Derivation
  • Polar form – Memory Structure
  • Parametric form – Holistic Understanding
  • Parametric – Derivation
  • Parametric – Physical Basis
  • Parametric – Memory Structure

• Radius of Curvature – Solved Problem
  • Problem 1 – Cartesian Approach
  • Problem 1 – Parametric Approach
  • Problem 1 – Summary
  • Problem – 2
  • Problem – 3
  • Problem – 4
  • Problem – 5
  • Problem – 6
  • Problem – 7
  • Problem – 8
  • Problem – 9