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Engineering Mathematics - Numerical Analysis & more
Rating: 4.3 out of 5(2 ratings)
65 students
Created byJ Aatish Rao
Last updated 7/2024
English

What you'll learn

  • Understand the fundamental principles of numerical methods and their applications in engineering.
  • Develop proficiency in utilizing the Newton-Raphson method to find roots of equations and solve nonlinear systems.
  • Master the Secant method for approximating roots and its advantages over other methods.
  • Learn the Bisection method and its applications in finding roots of equations.
  • Gain proficiency in numerical integration techniques, including the Trapezoidal rule and Simpson's rule, for accurate estimation of definite integrals.

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Course content

2 sections • 8 lectures • 1h 8m total length

  • Newton Raphson Method11:11

    In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.

  • Secant Method6:54

    In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method. 

  • Bisection Method10:25

    The bisection method in mathematics is a root-finding methodthat repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. .... The method is also called the interval halving method, the binary searchmethod, or the dichotomy method. 

  • Trapezoidal & SImson's 1/3 Rule17:27

    In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral. . The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area. 

    Use multiple-segment Simpson's 1/3 rule of integration to solve integrals, and derive the true error formula for multiple-segment Simpson's 1/3 rule. The trapezoidal rule was based on approximating the integrand by a first order polynomial, and then integrating the polynomial over interval of integration. 

Requirements

  • A solid foundation in calculus, linear algebra, and basic programming concepts is essential for success in this course.
  • Students should have a working knowledge of differentiation, integration, matrix operations, and basic programming constructs.

Description

This course is focused on engineering mathematics. After completing the tutorial, you will be able to understand the basic advantageous knowledge of numerical analysis techniques. Certain bonus lectures are also included.

This course introduces students to a range of powerful numerical methods and approximation techniques that are essential for solving complex engineering problems. Through a combination of theoretical understanding and practical application, students will gain the necessary skills to analyze, model, and solve mathematical problems encountered in various engineering disciplines. The course focuses on four key numerical methods: Newton-Raphson method, Secant method, Bisection method, and numerical integration techniques such as Trapezoidal rule and Simpson's rule.

Course Topics:


  1. Introduction to Numerical Methods: Importance and applications in engineering.

  2. Newton-Raphson Method: Derivation, convergence analysis, and implementation.

  3. Secant Method: Advantages, convergence, and application in solving nonlinear equations.

  4. Bisection Method: Algorithm, convergence, and root-finding applications.

  5. Numerical Integration Techniques: Trapezoidal rule and Simpson's rule, error analysis, and practical implementation.

  6. Applications in Engineering: Solving engineering problems involving nonlinear equations and definite integrals.

By the end of this course, students will have developed a strong understanding of numerical methods and approximation techniques, enabling them to confidently apply these tools to solve complex engineering problems. They will also have gained valuable experience in implementing these methods using computational tools, enhancing their problem-solving and critical thinking skills.


Note: The audio and video quality of this course may not meet the standards of modern production due to its age. However, we kindly request students to bear with any limitations in these aspects and focus on the valuable content and knowledge that this course has to offer.

Who this course is for:

  • Engineering graduates & undergraduates.
  • Higher education students.
  • Mathematics students and professionals.
  • Aspirants of GATE/IES/PSU's

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