Numerical Analysis

This course introduces students to the study of algorithms used for solving numerical problems in scientific computing. The course covers topics such as error analysis, numerical solutions of linear and nonlinear equations, interpolation, numerical differentiation and integration, and solving differential equations. Students will learn how to implement numerical methods using programming languages and how to assess the efficiency and accuracy of algorithms in practical applications. The course emphasizes the application of numerical techniques to solve real-world problems in engineering, physics, and other scientific fields.

Upon successful completion of this course, students will be able to:

• Understanding Numerical Methods and Algorithms: Students will gain a thorough understanding of numerical methods for solving mathematical problems, including techniques for finding roots, solving systems of linear equations, and approximating functions.
• Analyzing Errors and Stability in Computation: Learn how to perform error analysis, including round-off and truncation errors, and how to assess the stability and convergence of numerical algorithms.
• Implementing Numerical Algorithms in Programming: Gain proficiency in implementing numerical algorithms using programming languages, applying methods such as Newton’s method, Gaussian elimination, and Simpson’s rule to solve real-world problems.
• Applying Numerical Techniques to Real-World Problems: Develop problem-solving skills by applying numerical techniques to model and solve complex problems in fields such as engineering, physics, and applied mathematics, ensuring accurate and efficient computation.

These outcomes aim to equip students with the knowledge and skills necessary for solving complex numerical problems using computational methods, preparing them for careers or further study in scientific computing, engineering, and applied mathematics.