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# Maxima & Minima

149.00

The module incepts with engineering relevance and a seamless transition from single variable situation to multi variable situation. A holistic discussion of the graphical interpretation of Hessian matrix with emphasis on principal curvatures and eigen values and vectors. 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 Elements of Differential Calculus
• 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

MAXIMA & MINIMA

• Maxima & Minima
• Introduction to Idea of Curvature
• Concept of Maxima & Minima in the context of 1-variable
• Concept of the Stationary Point (Slope/Gradient) in a multivariable Situation
• Introduction to Hessian Matrix (Curvature Information)
• Graphical Interpretation of the Hessian Matrix Part 1
• Graphical Interpretation of the Hessian Matrix Part 2
• Eigen Value for a Hessian Matrix
• Eigen Vector for a Hessian Matrix
• Intrepreting Maxima & Minima via Eigen values and Conclusion
• Maxima & Minima (2-variable) – Problems
• Procedure for Problem Solving
• Problem 1
• Problem 2
• Problem 3

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