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 
<br>the power of applying this beautiful theory to solve various problems in 
<br>mathematics, science, and engineering. This course requires knowledge in 
<br>multiple variables calculus and ordinary differential equations such as MATH1020 
<br>and EE2010 or their equivalents. 
<br>
<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.
<br>
<br>三、參考書籍 (References)
<br>References will be mentioned in the lectures when cited.
<br>
<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 follow the contents of the textbook from Fourier analysis, partial 
<br>differential equations to complex variables. Supplemental materials will be 
<br>given when necessary. 
<br>3. Doing exercise problems is an essential part of learning any mathematical 
<br>subject, including this course. Recommended exercises will be assigned every 
<br>week for you to practice the basic ideas learned in the classroom and to prepare 
<br>the quiz which will be held basically every week. Students do not need to turn 
<br>in any solutions of the recommended exercises. 
<br>4. Except 09/13, 11/01, and 12/13, there is a quiz held in every Tuesday class. 
<br>5. There is an optional recitation session every Monday (even on 10/10/2022 and 
<br>01/02/2023 holidays) from 19:00 – 20:30 for TA to demonstrate problem solving or 
<br>to review midterm problems. You are encouraged to attend the TA recitation 
<br>sessions.
<br>6. It is essential that students attend lecture class each day and if you have 
<br>to miss a class, you should make every attempt to make up the work by watching 
<br>the recording uploaded to "CCLu Online Learning" on Youtube.
<br>7. All exams are closed book exams. You are allowed to bring in one A4 sheet of 
<br>paper for each midterm exam and two A4 sheets of papers for the final exam, 
<br>filled with hand-written or typed notes. You may write whatever you wish on both 
<br>sides of the paper.
<br>8. The final exam is cumulative and will cover everything taught in the whole 
<br>semester.
<br>
<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.
<br>
<br>六、成績考核 (Evaluation) 
<br>There are weekly quizzes (30%), first midterm (20%), second midterm (20%) and 
<br>one final (30%).  Alphabetical grade will be given as your final grade. The time 
<br>schedule is as follows: 
<br>(1) Quiz will be held basically every Tuesday from 1:20 to 2:10 pm. (Recommended 
<br>exercises are assigned for you to prepare the quizzes. You do not need to turn 
<br>in any solutions of the recommended exercises. Quiz problems will be ba<x>sed on 
<br>the recommended exercises.) There will be 15 quizzes and only the highest-scored 
<br>10 quizzes will be counted into the final score. No makeup quiz can be 
<br>requested.
<br>(2) Midterm I – 12:40 pm – 3:10 pm, October 27, 2022, Thursday. 
<br>   Coverage: Sections 11.1 – 12.4 of the textbook.
<br>(3) Midterm II –12:40 pm – 3:10 pm, December 08, 2022, Thursday.
<br>   Coverage: Sections 12.5 – 14.4 of the textbook.
<br>(4) Final –12:40 pm – 3:10 pm, January 12, 2023, Thursday. 
<br>   Coverage: Chapters 11-17 of the textbook.
<br>
<br>
<br>