Mathematics - iii (Differential Calculus) - Vol 4 | 5. Solution of Algebraic and Transcendental Equations by Abraham | Learn Smarter
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5. Solution of Algebraic and Transcendental Equations

Numerical methods serve as essential tools for solving both algebraic and transcendental equations that are not easily solvable through traditional analytical approaches. The chapter introduces various methods such as Bisection, Regula Falsi, Newton-Raphson, Secant, and Fixed Point Iteration, detailing their principles, steps, pros, and cons. Selecting the appropriate method depends on factors like the nature of the equation, the required accuracy, and whether the derivative information is available.

Sections

  • 5

    Interpolation & Numerical Methods

    This section explores numerical methods used to solve algebraic and transcendental equations that cannot be solved analytically.

    Learning Practice

  • 5.1

    Solution Of Algebraic And Transcendental Equations

    This section introduces numerical methods essential for solving algebraic and transcendental equations.

    Learning Practice

  • 5.1.1

    Introduction

    This section introduces numerical methods for solving algebraic and transcendental equations that are often unsolvable by direct analytical techniques.

    Learning Practice

  • 5.1.2

    Key Concepts

    This section discusses algebraic and transcendental equations and introduces various numerical methods for approximating their roots.

    Learning Practice

  • 5.1.2.1

    Types Of Equations

    This section discusses algebraic and transcendental equations and the numerical methods used to approximate their roots.

    Learning Practice

  • 5.1.2.1.1

    Algebraic Equations

    This section explores algebraic and transcendental equations, emphasizing the necessity of numerical methods for finding their roots.

    Learning Practice

  • 5.1.2.1.2

    Transcendental Equations

    Transcendental equations extend beyond algebraic solutions, requiring numerical methods for root approximation.

    Learning Practice

  • 5.1.3

    Numerical Methods For Solving Equations

    This section addresses how numerical methods are used to approximate the roots of algebraic and transcendental equations when analytical solutions are not feasible.

    Learning Practice

  • 5.1.3.1

    Bisection Method

    The Bisection Method is a numerical technique used to find roots of continuous functions by repeatedly halving an interval where the function changes sign.

    Learning Practice

  • 5.1.3.2

    Regula Falsi Method (False Position Method)

    The Regula Falsi Method is a numerical approach for finding roots of equations using linear interpolation between points.

    Learning Practice

  • 5.1.3.3

    Newton-Raphson Method

    The Newton-Raphson method is a powerful technique for finding roots of equations by using tangents based on initial guesses.

    Learning Practice

  • 5.1.3.4

    Secant Method

    The Secant Method is an iterative numerical technique for finding roots of equations that approximates a solution without requiring the derivative of the function.

    Learning Practice

  • 5.1.3.5

    Fixed Point Iteration Method

    The Fixed Point Iteration Method is an iterative numerical approach for finding the roots of equations by rearranging them into the form x = g(x).

    Learning Practice

  • 5.1.4

    Comparison Of Methods

    This section compares five numerical methods used to approximate the roots of algebraic and transcendental equations.

    Learning Practice

  • 5.1.5

    Stopping Criteria

    Stopping criteria in numerical methods determine when to halt iterations based on specific conditions.

    Learning Practice

  • 5.1.6

    Applications

    Numerical methods are essential for solving algebraic and transcendental equations in engineering and scientific applications.

    Learning Practice

  • 5.1.7

    Summary

    This section discusses numerical methods used for solving algebraic and transcendental equations that cannot be addressed analytically.

    Learning Practice

References

unit 4 ch5.pdf

Class Notes

Memorization

What we have learnt

  • Algebraic equations are for...
  • Numerical techniques are cr...
  • Each numerical method has i...

Final Test

Revision Tests