教學大綱與進度

課程基本資料：

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
113-1	338589	數值分析	1	3.0	3	★	楊侑倫	製科所 機電博所 機電外國學生專班	17	0	製科所、機電博班及外生班合開,限20人

教學大綱與進度：

教師姓名	楊侑倫　教師諮商時間(Office Hours)
Email	y.yang@ntut.edu.tw
最後更新時間	2024-09-19 12:30:52
課程大綱	先修課程：負責教授同意 本課程介紹如何應用數值分析理論求解工程問題。 1. 數值方法基本觀念及其領域 2. 數值方法之誤差及穩定性 3. 非線性代數方程式之數值解法 4. 聯立代數方程式之數值解法 5. 矩陣特徵值求法 6. 非線性聯立方程式之數值解法 7. 多項式插值法及曲線配湊 8. 數值微分與積分 9. 常微分方程式之數值解法 10. 偏微分方程式之數值解法 To introduce the numerical analysis techniques for solving engineering problems. 1. Introduction to the basic concepts of the numerical analysis 2. The errors and stability of the numerical methods 3. Numerical methods of solving nonlinear algebraic equations 4. Numerical methods of solving systems of linear equations. 5. Algebraic eigen-value problems 6. Numerical methods of solving systems of nonlinear equations 7. Numerical interpolation and curve fitting 8. Numerical differentiation and integration 9. Numerical solution of ordinary differential equations 10. Numerical solution of partial differential equation
課程進度	Week 1: Course Introduction and Overview Introduction to Numerical Methods Mathematical Modeling and Problem-Solving with Computers Week 2: Foundations of Numerical Computing Numerical Computing Languages Floating-Point Arithmetic and Representation Week 3: Mathematical Modeling Techniques Translating Real-World Problems into Mathematical Models Introduction to Numerical Algorithms Week 4: Error Analysis Numerical Accuracy, Stability, and Round-Off Errors Week 5: Linear Algebra - Basic Concepts Matrix Operations and Computational Aspects 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 Week 8: Numerical Integration and Differentiation Techniques for Numerical Integration Numerical Differentiation Week 9: Solving Ordinary Differential Equations (ODEs) Numerical Methods for ODEs Initial and Boundary Value Problems Week 10: Solving Partial Differential Equations (PDEs) Numerical Methods for PDEs Finite Difference and Finite Element Methods Week 11: Monte Carlo Methods Monte Carlo Simulations Applications in Science and Engineering Week 12: Numerical Optimization Concepts in Optimization Gradient-Based and Gradient-Free Methods Week 13: Advanced Topics in Numerical Linear Algebra Sparse Matrix Techniques Advanced Decomposition Methods Week 14: Numerical Methods in Data Science Data Fitting and Regression Techniques Introduction to Machine Learning Algorithms Week 15: High-Performance Numerical Computing Parallel Computing and Numerical Methods Introduction to GPUs and Distributed Computing Week 16: Review and Project Work Comprehensive Review of Course Material Guidance for Final Projects Week 17: Final Project Presentations Presentation of Final Projects Peer Review and Feedback Week 18: Course Wrap-up and Examination Final Examination Course Feedback and Closure
評量方式與標準	Homework/In class assignment/Group discussion 40% 課堂報告，分組，在家作業 In class writting and presentation 30% 課堂寫作，下課交 Midterm exam 30%
使用教材、參考書目或其他	【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 self-made materials
課程諮詢管道	teams private message
課程對應SDGs指標	SDG4：優質教育（Quality Education） SDG7：可負擔的潔淨能源（Affordable and Clean Energy） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure） SDG16：和平正義與有力的制度（Peace, Justice and Strong Institutions） SDG17：夥伴關係（Partnerships for the Goals）
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