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# Curvature

149.00

This module incepts with a detailed account on the engineering significance of curvature. The 4 important derivations for curvature in cartesian, parametric, pedal and polar forms have been given detailed discussions. Significant number of model questions paper problems have been solved to give a comprehensive understanding of the examiner’s perspective.

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
• 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

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