DELTA台達216 T5T6R5R6
This is a basic course on Fourier analysis, partial differential equations, and complex variables and analysis. The aim of this course is for students to fully understand the theory of Fourier analysis, to learn various approaches and techniques, from basic to advanced, to solve partial differential equations, and to discover the beauty of the theory of functions in one complex variable and the power of applying this beautiful theory to solve various problems in mathematics, science, and engineering.
一、課程說明 (Course Description) This is a basic course on Fourier analysis, partial differential equations, and complex variables and analysis. The aim of this course is for students to fully understand the theory of Fourier analysis, to learn various approaches and techniques, from basic to advanced, to solve partial differential equations, and to discover the beauty of the theory of functions in one complex variable and the power of applying this beautiful theory to solve various problems in mathematics, science, and engineering. This course requires knowledge in multiple variables calculus and ordinary differential equations such as MATH1020 and EE2010 or their equivalents. It is required for students to read Chapter 6: Laplace Transforms and Sections 13.1-13.2: Complex Numbers of the textbook by E. Kreyszig before class begins. Quiz #1 on Laplace transforms and complex numbers will be held during the 1st recitation class in 19:00-21:00 on Monday September 11th, 2023 in Delta 216. This course adopts a 16-week semester so that it is an intense course. 二、指定用書 (Textbook) 1. E. Kreyszig, Advanced Engineering Mathematics, 10th edn. John Wiley and Sons, Inc., 2011. 2. Instructor’s Lecturenotes. 三、參考書籍 (References) References will be mentioned in the lectures when cited. 四、教學方式 (Teaching Method) 1. This is an English–teaching course. In class, you are welcome to raise your questions in any language. If you speak a language other than English, Taiwanese or Mandarin, please have someone to translate it to any of the above three languages. 2. We will basically follow the contents of the textbook from Fourier analysis in Chapter 11, partial differential equations in Chapter 12 to complex analysis in Chapters 13-17. Additional materials, including supplemental lemmas and theorems, will be provided to facilitate and/or enrich the development of the theory. 3. Doing exercise problems is an essential part of learning any mathematical subject, including this course. Recommended exercises will be assigned every week for you to practice the basic concepts and results learned in the classroom and to prepare the quiz which will be held during the recitation class every Monday 19:00 – 21:00 in Delta 216, except holidays and the week right after a midterm. The 1st set of recommended exercises will be announced on NTHU eeclass course website on September 6th, 2023. Students do not need to turn in any solutions of the recommended exercises. 4. There will be a total of 15 quizzes. Only the 10 highest scored quizzes will be counted to calculate the semester quiz average. You may be absent from at most 5 quizzes so that there will be no make-up quizzes. The 1st quiz will be held during the 1st recitation class in 19:00-21:00 on Monday September 11th, 2023 in Delta 216. The coverage of the 1st quiz is Chapter 6 on Laplace transforms and Sections 13.1-13.2 on complex numbers of the textbook, which is required for you to review and study before class begins. 5. It is essential that students attend lecture class each day and if you have to miss a class, you should make every attempt to make up the work by watching the recording uploaded to "CCLu Online Learning" on Youtube. 6. All exams (quizzes, midterms, and the final) are closed book exams. You are allowed to bring in one A4 sheet of paper for each midterm exam and two A4 sheets of papers for the final exam, filled with hand-written or typed notes. You may write whatever you wish on both sides of the paper. 7. The final exam is cumulative and will cover everything taught in the whole semester. 五、教學進度 (Syllabus) 1. The first half of the semester will cover Fourier analysis and partial differential equations (PDEs), including Fourier series and periodic functions, Sturm-Liouville problems and generalized Fourier series, Fourier integral and Fourier transform, Fourier cosine and sine transforms, separating variables for PDEs, wave equation, heat equation, Laplace’s equation in rectangular, polar, cylindrical, and spherical coordinates.. 2. The second half of the semester will cover complex variables and analysis, including complex differentiation and analytic functions, complex integration, power and Laurent series, residue integration, and conformal mapping. 六、成績考核 (Evaluation) There are weekly quizzes (30%), first midterm (20%), second midterm (20%) and one final (30%). Alphabetical grade will be given as your final grade. The time schedule is as follows: (1) Recommended exercises will be announced on NTHU eeclass course website, which are for students to prepare the quizzes to be held during the recitation class every Monday 19:00 – 21:00 in Delta 216, except. The 1st set of recommended exercises will be announced on September 6th, 2023 before class begins. Students do not need to turn in any solutions of the recommended exercises. Quiz problems will be based on the recommended exercises. There will be 15 quizzes and only the highest-scored 10 quizzes will be counted into the final score. No makeup quiz can be requested. (2) Midterm I – 12:40 pm – 3:10 pm, October 19, 2023, Thursday. Coverage: Sections 11.1 – 12.4 of the textbook. (3) Midterm II –12:40 pm – 3:10 pm, November 23, 2023, Thursday. Coverage: Sections 12.5 – 14.4 of the textbook. (4) Final –12:40 pm – 3:10 pm, December 28, 2023, Thursday. Coverage: Chapters 11-17 of the textbook. 七、使用生成式AI之倫理聲明(Ethics Statement on Generative Artificial Intelligence) After careful consideration, the instructor of this course deems it inappropriate to use generative artificial intelligence in this class. This is because the content within generative AI contains numerous errors and may adversely affect students' understanding of foundational knowledge. In accordance with the published Guidelines for Collaboration, Co-learning, and Cultivation of Artificial Intelligence Competencies in University Education, this course adopts the following policy : Prohibited use Students enrolled in this course should be aware that they may not submit assignments, reports, or personal reflections generated using artificial intelligence. If such usage is discovered, instructors, the institution, or relevant units have the right to reevaluate the assignment or report or withhold scores. Students enrolled in this course agree to the above ethics statement if registering for the class.
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16週課程。本課程每週上課150分鐘,其餘時間由教授彈性運用。週一19:00~21:00為演習課與小考。
電機系大學部2年級3年級4年級,電資院學士班大學部2年級3年級4年級優先,第3次選課起開放全校修習
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