Numerical Computing

This course covers the mathematical theory underlying numerical methods used in scientific computing. Topics include computer arithmetic and error analysis, root-finding methods, direct and iterative methods for linear systems, eigenvalue problems, interpolation and approximation, numerical integration, and numerical solutions of differential equations. The course emphasizes theoretical understanding, convergence analysis, and stability theory rather than computational implementation. Students learn to analyze algorithm performance, understand when methods succeed or fail, and select appropriate techniques for different problem types.

Students will master the mathematical foundations of numerical methods including error analysis, convergence theory, and stability analysis. They will analyze and compare numerical algorithms for linear systems, nonlinear equations, interpolation, integration, and differential equations. Students will develop skills in condition number analysis, method selection based on problem structure, and theoretical performance evaluation of numerical algorithms.

In presenza

The course combines theoretical lectures with problem-solving sessions. Lectures focus on mathematical derivations, convergence proofs, and stability analysis. Problem sessions involve analytical exercises, error analysis, and method comparison without programming. Students work on case studies examining real-world applications and method selection criteria. Assessment includes regular quizzes to reinforce concepts and comprehensive examinations testing theoretical understanding and problem-solving skills.

Assessment consists of three components: midterm examination (30%), ten continuous quizzes (30%), and final examination (40%). The midterm covers weeks 1-7 material including foundations, error analysis, root-finding, and linear algebra methods. Quizzes are administered approximately every 1.5 weeks to ensure continuous learning. The final examination covers all course material with emphasis on advanced topics from weeks 8-14. All assessments focus on mathematical theory, convergence analysis, and method selection rather than computational implementation.