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