Engineering Mathematics - Numerical Analysis
Why Do You Enroll?
Elevate your academic journey with our semester-long Numerical Methods in Engineering Mathematics course! This program is tailored for students seeking to deepen their understanding of mathematical techniques essential for solving engineering problems. You'll explore key concepts such as Newton Raphson, secant method, Bisection method, cayley, and Laplace transformation, all while applying these methods to real-world scenarios. With a blend of theory and practical applications, this course prepares you for advanced studies and equips you with valuable skills for your engineering career. Join us and enhance your academic portfolio with critical problem-solving tools!
Key Topics Covered
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Course Details
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: the Newton-Raphson method, the Secant method, the bisection method, and numerical integration techniques such as the trapezoidal rule and Simpson's rule.
Course Topics:
Introduction to Numerical Methods: Importance and Applications in Engineering.
Newton-Raphson Method: Derivation, convergence analysis, and implementation.
Secant Method: Advantages, convergence, and application in solving nonlinear equations.
Bisection Method: Algorithm, convergence, and root-finding applications.
Numerical Integration Techniques: Trapezoidal rule and Simpson's rule, error analysis, and practical implementation.
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.
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Course Content
1. Newton Raphson Method
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.
2. Secant Method
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.
3. Bisection Method
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.