Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Fall Semester
Year 2025 351894 Numerical Analysis 1 3.0 3 ★ Fu-Shin Lee 4ERACE3 49 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Fall Semester Year 2025	351894	Numerical Analysis	1	3.0	3	★	Fu-Shin Lee	4ERACE3	49	0

Course Plan：

Instructor Fu-Shin Lee

Email fslee@huafan.hfu.edu.tw

Last Updated 2025-05-25 22:00:36

Course Objective Course Title: Numerical Analysis with MATLAB Course Objectives: This course introduces students to the fundamentals and applications of numerical methods to solve various engineering and scientific problems. By the end of the course, students will understand how to formulate mathematical models, analyze errors, solve nonlinear equations, perform matrix-based solutions of linear systems, apply curve fitting and interpolation techniques, and solve differential equations numerically. The course emphasizes practical MATLAB implementation, encouraging students to develop, test, and interpret numerical algorithms and simulations. Emphasis will also be placed on the methods' efficiency, stability, and accuracy. The course prepares students to be competent problem-solvers in real-world situations where analytical solutions are infeasible. Teaching Methods: The course employs a combination of lectures, hands-on MATLAB tutorials, problem-solving sessions, and project-based learning. Weekly lectures introduce theoretical foundations and derivations of algorithms, reinforced with illustrative engineering applications. Students will engage in weekly computer labs to implement and test methods in MATLAB, using provided templates or writing their scripts. Regular homework and in-class problem sets enhance analytical thinking and programming proficiency. Open discussions, collaborative projects, and quizzes provide formative feedback, while a final project allows for creative exploration of numerical methods in student-selected topics. Using graphical visualizations and case studies ensures connection to real-world phenomena, fostering theoretical understanding and practical competency.

Course Schedule 18-Week Course Outline Week Topic MATLAB Practice/Demonstration ========================================= 1 Introduction to Numerical Methods and Mathematical Modeling Euler’s method on motion models 2 MATLAB Fundamentals Vectors, matrices, scripts, and plotting 3 Programming in MATLAB M-files, loops, conditionals, input/output 4 Round-off and Truncation Errors Taylor series, error plots 5 Root Finding I: Bracketing Methods Bisection & false position with error estimation 6 Root Finding II: Open Methods Newton-Raphson, secant, fzero 7 Optimization Methods Golden-section search, fminbnd, fminsearch 8 Linear Systems I: Direct Methods Gauss elimination, LU decomposition 9 Midterm Exam — — 10 Linear Systems II: Iterative Methods Jacobi, Gauss-Seidel, fsolve 11 Matrix Properties and Conditioning Matrix inverse, norms, condition number 12 Polynomial Interpolation Newton, Lagrange, polyfit/polyval 13 Spline and Piecewise Interpolation Natural, clamped, and not-a-knot cubic splines 14 Regression: Linear and Nonlinear Linear regression, multiple regression, lsqcurvefit 15 Eigenvalues and Eigenvectors Polynomial method, power method, eig function 16 Fourier Analysis FFT, power spectrum analysis, Nyquist frequency 17 Numerical Integration Trapezoidal, Simpson’s, Gauss quadrature, integral 18 Final Exam — —

Evaluation and grading policy 1. Attendance and lesson plan practice (30%) 2. Homework and quizzes (30%) 3. Midterm exam (20%) 4. Final exam (20%)

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
• Title: Applied Numerical Methods with MATLAB for Engineers and Scientists (4th Edition) • Author: Steven C. Chapra • Publisher: McGraw-Hill Education

The access to curricular consultation Students with questions about the course are welcome to contact the instructor via email at fslee747@gmail.com. The teacher will respond by email and address common questions during the next class.

The course corresponds to the SDGs SDG4：優質教育（Quality Education）
SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）

Does the course incorporate AI AI1：使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process）
AI2：鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
AI3：使用生成式AI進行課堂即時互動（Use generative AI for real-time classroom interaction）
AI4：簡單介紹AI的基本概念（Briefly introduce the basic concept of AI）

Note
　

Instructor	Fu-Shin Lee
Email	fslee@huafan.hfu.edu.tw
Last Updated	2025-05-25 22:00:36
Course Objective	Course Title: Numerical Analysis with MATLAB Course Objectives: This course introduces students to the fundamentals and applications of numerical methods to solve various engineering and scientific problems. By the end of the course, students will understand how to formulate mathematical models, analyze errors, solve nonlinear equations, perform matrix-based solutions of linear systems, apply curve fitting and interpolation techniques, and solve differential equations numerically. The course emphasizes practical MATLAB implementation, encouraging students to develop, test, and interpret numerical algorithms and simulations. Emphasis will also be placed on the methods' efficiency, stability, and accuracy. The course prepares students to be competent problem-solvers in real-world situations where analytical solutions are infeasible. Teaching Methods: The course employs a combination of lectures, hands-on MATLAB tutorials, problem-solving sessions, and project-based learning. Weekly lectures introduce theoretical foundations and derivations of algorithms, reinforced with illustrative engineering applications. Students will engage in weekly computer labs to implement and test methods in MATLAB, using provided templates or writing their scripts. Regular homework and in-class problem sets enhance analytical thinking and programming proficiency. Open discussions, collaborative projects, and quizzes provide formative feedback, while a final project allows for creative exploration of numerical methods in student-selected topics. Using graphical visualizations and case studies ensures connection to real-world phenomena, fostering theoretical understanding and practical competency.
Course Schedule	18-Week Course Outline Week Topic MATLAB Practice/Demonstration ========================================= 1 Introduction to Numerical Methods and Mathematical Modeling Euler’s method on motion models 2 MATLAB Fundamentals Vectors, matrices, scripts, and plotting 3 Programming in MATLAB M-files, loops, conditionals, input/output 4 Round-off and Truncation Errors Taylor series, error plots 5 Root Finding I: Bracketing Methods Bisection & false position with error estimation 6 Root Finding II: Open Methods Newton-Raphson, secant, fzero 7 Optimization Methods Golden-section search, fminbnd, fminsearch 8 Linear Systems I: Direct Methods Gauss elimination, LU decomposition 9 Midterm Exam — — 10 Linear Systems II: Iterative Methods Jacobi, Gauss-Seidel, fsolve 11 Matrix Properties and Conditioning Matrix inverse, norms, condition number 12 Polynomial Interpolation Newton, Lagrange, polyfit/polyval 13 Spline and Piecewise Interpolation Natural, clamped, and not-a-knot cubic splines 14 Regression: Linear and Nonlinear Linear regression, multiple regression, lsqcurvefit 15 Eigenvalues and Eigenvectors Polynomial method, power method, eig function 16 Fourier Analysis FFT, power spectrum analysis, Nyquist frequency 17 Numerical Integration Trapezoidal, Simpson’s, Gauss quadrature, integral 18 Final Exam — —
Evaluation and grading policy	1. Attendance and lesson plan practice (30%) 2. Homework and quizzes (30%) 3. Midterm exam (20%) 4. Final exam (20%)
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes • Title: Applied Numerical Methods with MATLAB for Engineers and Scientists (4th Edition) • Author: Steven C. Chapra • Publisher: McGraw-Hill Education
The access to curricular consultation	Students with questions about the course are welcome to contact the instructor via email at fslee747@gmail.com. The teacher will respond by email and address common questions during the next class.
The course corresponds to the SDGs	SDG4：優質教育（Quality Education） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）
Does the course incorporate AI	AI1：使用生成式AI作為教學過程的輔助工具（Use generative AI tools as an aid to the teaching process） AI2：鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools） AI3：使用生成式AI進行課堂即時互動（Use generative AI for real-time classroom interaction） AI4：簡單介紹AI的基本概念（Briefly introduce the basic concept of AI）
Note