📘 Course Title: Numerical Analysis

Code: 29023-AUX

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🏁 Introduction:

Numerical Analysis is a vital branch of applied mathematics focusing on developing and analyzing algorithms to obtain approximate solutions to mathematical problems that may not have exact solutions.

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✨ Course Description:

This course introduces fundamental and advanced techniques for solving nonlinear and linear equations, interpolation, numerical differentiation and integration, and solving differential equations numerically. Students will apply these techniques in practical computational problems across various fields such as engineering, physics, and finance.

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🎯 Target Audience:

• Mathematics, Physics, and Engineering students.

• Professionals in computational sciences and quantitative fields.

• Researchers and analysts working with mathematical modeling and simulations.

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📚 What You Will Learn:

• Solve nonlinear and linear systems using efficient numerical methods.

• Perform polynomial interpolation and approximation.

• Apply numerical differentiation and integration techniques.

• Solve ordinary differential equations (ODEs) using various numerical methods.

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🧑‍🏫 Instruction Methodology:

• 📖 Conceptual Lectures and Problem-Solving Workshops.

• 💻 Hands-on Coding Labs (Python/ MATLAB/ Octave).

• 🧪 Practical Application Projects.

• 📝 Weekly Quizzes and Assignments.

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🧩 Main Modules:

1️⃣ Solving Nonlinear Equations

• ➗ Bisection Method

• ➗ Newton-Raphson Method

2️⃣ Solving Linear Systems

• 🧮 Gaussian Elimination

• 🧮 LU Decomposition

3️⃣ Numerical Approximation

• 📈 Interpolation Techniques

• 📈 Polynomial Approximation

4️⃣ Numerical Differentiation and Integration

• 📐 Numerical Integration Rules (Trapezoidal Rule, Simpson’s Rule)

• 📐 Numerical Differentiation Methods

5️⃣ Solving Differential Equations

• 🧩 Single-Step Methods (e.g., Euler’s Method, Runge-Kutta Methods)

• 🧩 Multi-Step Methods (e.g., Adams-Bashforth Method)

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🎒 Materials Included:

• 📘 Detailed Lecture Notes and Problem Sets

• 🛠️ Access to Numerical Computation Tools and Libraries

• 🎥 Video Tutorials for Method Demonstrations

• 📑 Weekly Assignments with Solutions

• 📊 Mini-Projects Applying Numerical Methods

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🕒 Course Duration:

• 10 weeks — 2 sessions per week (Each session: 2 hours).

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📈 Level:

• Intermediate to Advanced (Requires prior knowledge of calculus, basic linear algebra, and introductory programming skills).