Introduction to Numerical Analysis and Error Analysis

Fundamental concepts of numerical analysis including sources of errors, floating-point arithmetic, machine epsilon, and error propagation. Introduction to Taylor series and its role in numerical methods.

• Understand the fundamental concepts and scope of numerical analysis
• Analyze different types of errors: round-off, truncation, and discretization errors
• Master IEEE 754 floating-point representation and machine epsilon calculations
• Apply Taylor series expansion for error analysis and algorithm development
• Compute absolute and relative errors, and understand error propagation
• Evaluate condition numbers and numerical stability concepts