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# Newton’s Law of Cooling and Orthogonal Trajectories

149.00

Validity: 45 days

This module incepts with a practical introduction to the topics with emphasis on the physics involved. The discussion considers heating and cooling and also polar and cartesian orthogonal family of curves. 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
• Model question paper

Course Contents:

Pre-requisites to Maxima & Minima

• 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

PRE-REQUISITES – ELEMENTS OF INTEGRAL CALCULUS

• Pre-requisites – Elements of Integral Calculus
• 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 function
• 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)

NEWTON’S LAW OF COOLING & ORTHOGONAL TRAJECTORIES

• Application od ODE’s
• Newton’s Law of Cooling – Conceptual Understanding
• Newton’s Law of Cooling – Problem 1 – Cooling
• Newton’s Law of Cooling – Problem 2 – Heating
• Orthogonal Tragectories – Conceptual Understanding
• Orthogonal Tragectories – Problem 1
• Orthogonal Tragectories – Problem 2
• Orthogonal Tragectories – Problem 3
• Orthogonal Tragectories – Problem 4

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