Course Syllabus

Course Information：

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2025	345394	Numerical Methods	1	3.0	3	★	Yo-Lun Yan	4ME4A 4ME4B	14	0	大四合開；限20人

Course Plan：

Instructor	Yo-Lun Yan　Office Hours
Email	y.yang@ntut.edu.tw
Last Updated	2024-12-23 09:49:54
Course Objective	先修課程：3002011或負責教授同意。基本觀念及其領域、非線性代數之數值解法、聯立方程式之數值解、多項式內外插、微分、積分、常微分方程、起始與邊界值問題之數值解法。 1. Introduction to the basic concepts of the numerical method 2. Numerical methods of solving nonlinear algebraic equations. 3. Numerical methods of solving systems of linear equations. 4. Numerical interpolation and extrapolation. 5. Numerical differentiation and integration.6. Numerical methods of ordinary differential equations with initial-value problems and boundary value problems.
Course Schedule	Week 1: Course Introduction and Overview Introduction to Numerical Methods Overview of the course, expectations, and resources Introduction to mathematical modeling and problem-solving with computers Week 2: Foundations of Numerical Computing Introduction to numerical computing languages Basics of floating-point arithmetic and representation on computers Week 3: Mathematical Modeling Techniques Translating real-world problems into mathematical models Introduction to simple numerical algorithms Week 4: Error Analysis Understanding numerical accuracy, stability, and round-off errors Significance and impact of errors in computational methods Week 5: Linear Algebra - Basic Concepts Overview of matrix operations and their computational aspects Introduction to systems of linear equations Week 6: Linear Algebra - Advanced Concepts Direct and iterative methods for solving linear systems Eigenvalue problems and decompositions Week 7: Interpolation and Approximation Polynomial and spline interpolation Approximation theory and practice Week 8: Numerical Integration and Differentiation Techniques and methods for numerical integration Numerical differentiation and its applications Week 9: Solving Ordinary Differential Equations (ODEs) Overview of ODEs and numerical methods for solving them Initial value problems and boundary value problems Week 10: Solving Partial Differential Equations (PDEs) Introduction to PDEs and numerical methods for solving them Finite difference and finite element methods Week 11: Monte Carlo Methods Introduction to Monte Carlo simulations Applications in physical sciences and engineering Week 12: Numerical Optimization Basic concepts in optimization Gradient-based and gradient-free optimization methods Week 13: Advanced Topics in Numerical Linear Algebra Sparse matrix techniques Advanced decomposition methods and their applications Week 14: Numerical Methods in Data Science Numerical techniques in data fitting and regression Introduction to machine learning algorithms Week 15: High-Performance Numerical Computing Understanding parallel computing and its use in numerical methods Introduction to GPUs and distributed computing Week 16: Review and Project Work Comprehensive review of course material Guidance and consultation for final projects Week 17: Final Project Presentations Presentation of final projects by students Peer review and feedback sessions Week 18: Course Wrap-up and Examination Final examination covering the entire course content Feedback and course closure Each week will include lectures, readings from the recommended texts, and practical assignments or problem sets to reinforce the concepts taught.
Evaluation and grading policy	Homework/In class assignment 40% Midterm exam 30% Final (oral) report 30%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:No self-made materials
The access to curricular consultation	teams
The course corresponds to the SDGs	SDG2：消除飢餓（Zero Hunger） SDG4：優質教育（Quality Education）
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