## Numerical Analysis Course

**Welcome to this course**Ā on Numerical Methods and Series solutions of Differential Equations. This course is primarily intended for you if you are studying Math in College and if you are learning Engineering Math. Tips to help you understand Math better.

You will start with a brief introduction to **Taylor Series method and how to use Taylor Series method **to solve an equation upto 4 decimal places. As a modification of Taylor series method, you will learn modified Euler's theorem and how to use it to solve equations. As a side note, these formulas involve a lot of calculations at the problem solving stage.

Next, you will be introduced to **Runge Kutta method of 4th order **and how to use it in solving problems. 2 predictor and corrector methods are taught here, namely Milne' s Predictor method and Adam Bashforth methods. The numericals here involve several iterations and have been explained step by step.

In lesson 3, you will be introduced to **Bessel's Differential equation **and how to solve it. The solution is rather lengthy and has been explained keeping all steps in mind. This will lead you to the Bessel's function at the end . Note the use of Gamma functions in Bessel's function is shown.

Lesson 4 is on **Bessel's function **and it's properties. The orthogonality property of the Bessel's function is also proved leading to two cases, one of which leads to Lommel's Integral formula.

In Lesson 5, you will learn about **Legendre Differential equation a**nd how to solve it using the power series method. As a conclusion to this , you will learn about Legendre functions and how they are derived from Legendre Differential Equations. How Legendre Polynomials lead toĀ Rodrigue's formula is also shown.

Lesson 6 is a problem solving session where you will learn to use **Rodrigue's formula **to solve problems.

The course concludes with an assignment which discusses possible questions that can be asked. Note that each of these questions have been discussed during the course.

You'll also learn what is **nth order derivative of a function**Ā and how to evaluate it. An interesting and important topic.

Learn the method of **finite differences**Ā and the forward and backward difference table and how to use it in problem solving.

Ā Ā An important point to keep in mind is that this course is highly theoretical and involves you to **write these proofs**Ā to gain mastery.

Learn how to solve equations using the Regula Falsi Method in Numerical Analysis.

Motivating you to learn Mathematics!

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