Computational Numerical Analysis Used in AI and Data Science

🚀 Mastering Numerical Methods from Theory to Practice 🚀

🧮 Course Headline: Also learn Nth order derivatives: Unraveling the complexity!

Welcome to Mastering Numerical Methods and Series Solutions of Differential Equations! 🎓

Whether you're a college student diving into Math or an Engineering Math learner, this course is tailored to enhance your understanding of numerical methods. With a focus on practical applications and theoretical foundations, this course will guide you through the intricacies of Numerical Methods with ease.

Course Structure:

1. Taylor Series Mastery:

• Taylor Series Method Explained: Learn how to apply the Taylor Series method to solve equations with precision up to 4 decimal places. 📐
• Modified Euler's Theorem: Understand and use this modification of Taylor series for problem-solving, which involves detailed calculations. ⚫️

2. Deep Dive into Runge-Kutta Method:

• 4th Order Runge-Kutta Method: Gain proficiency in solving problems using the 4th order Runge-Kutta method, complemented by explanations of 2 predictor and corrector methods: Milne's Predictor method and Adam Bashforth methods. 🐍

3. Solving Bessel's Differential Equation:

• Bessel's Differential Equation Solutions: Explore the lengthy solution process to Bessel's differential equation, including the role of Gamma functions in Bessel's function. 🔄

4. Properties and Applications of Bessel's Function:

• Orthogonality Property & Lommel's Integral Formula: Discover the orthogonality property of Bessel's function, leading to two cases, one culminating in Lommel's Integral formula. 📈

5. Legendre Differential Equation Solutions:

• Power Series Method & Legendre Functions: Learn how to solve the Legendre differential equation using the power series method and understand the derivation of Legendre functions from Legendre differential equations. 🌍

6. Practical Problem Solving with Rodrigue's Formula:

• Rodrigue's Formula Application: Engage in a problem-solving session where you'll apply Rodrigue's formula to solve various problems. 🔧

Key Takeaways:

• Nth Order Derivative Evaluation: Understand the concept of nth order derivatives and learn how to evaluate them, an essential aspect of Numerical Methods. 📈
• Method of Finite Differences: Delve into the method of finite differences, including forward and backward difference tables, and their application in problem-solving. ✏️

This course emphasizes a hands-on approach to learning Numerical Methods. You will be required to write proofs to solidify your understanding and mastery of the subject matter. By the end of this course, you'll have a comprehensive grasp of numerical methods, from the fundamental concepts to the advanced applications.

Dive into the world of Numerical Methods and transform your mathematical skills with this engaging course! 🌟