INTRODUCTION TO NUMERICAL METHODS Presentation by: Karthik Balaji Keshavamurthi

Types of Equations . Linear Equations: y=kx Y directly proportional to Xtype equations Eg: Y-kx Non-Linear Equations: No proportionality. One variable is function of the other. Eg: Quadratic Equations YEX 2x-3 -2 -3

Algebraic Equations: Which consist of a perfect polynomial. Only Contains Arithmetic Functions. (y x+ 2) 2 Transcendental Equations: Consist of Trigonometric, logarithmic, exponential functions. (y= sin x)

Analytical Method - Use of basic equations and 2x-8 0 Add 8 to each side of the equation. formulae to find roots 2x 8 Divide each side of the equation by 2 - Easier for simple equations Take the square root of each side of the equation. x=2,-2 : Very Tedious for complex equations

Numerical Method . Uses a hit and trial Method to solve problems. . Iterative substitution of values is done to find root. . Can be used to find approximate solutions for very complex problems at a very rapid speed.

CHARACTERISTICS . Uses simple Arithmetic Functions to find solutions for complex problems. First Model is Constructed - Selection of Numerical method Applying Method to form Solution. . Verification of Solution

Common Numerical Methods Iteration Method . Bisection Method - Regula Falsi Method - Newton- Raphson Method - Secant Method

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Karthik Balaji Keshavamurthi

Final year B. E Mechanical Engineering student about to pursue MS in the USA, vocalist, chess player

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Sushant Sharma

7 months ago

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