Angle between Polar curves

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

Angle between polar curves

• Introduction to Polar curves
  • Introduction
• Polar and Cartesian Equivalence 
  • Polar and Cartesian Equivalence
• Converting Cartesian and Polar curves
  • Parabola – Cartesian to Polar
  • Circle – Polar to Cartesian
  • Offset Circle – Cartesian to Polar
  • Cardioid – Polar and Cartesian Equivalence
  • Rose Curve – Polar and Cartesian Equivalence
• Parametric Equation for Cycloid
  • Visualizing the Cycloid formation
• Parametric Equation for Ellipse
  • Parametric Equation for Ellipse
• Polar Curves
  • Introduction to angle between curves
  • 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 vector – Memory Structure
  • Procedure for angle between two curves
• Solving angle between curves 
  • 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 Examiners Mind