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:

• 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.