課程名稱 
工程數學下 Engineering Mathematics (2) 
開課學期 
1102 
授課對象 
機械工程學系 
授課教師 
林以凡 
課號 
ME2002 
課程識別碼 
502E20002 
班次 
04 
學分 
3.0 
全/半年 
全年 
必/選修 
必修 
上課時間 
星期一3,4(10:20~12:10)星期三2(9:10~10:00) 
上課地點 
綜502綜502 
備註 
本課程以英語授課。本課程以英語授課。 總人數上限：55人 


課程簡介影片 

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課程概述 
In this course, we will review vector calculus and introduce the elementary theory of the functions of a complex variable covering operations with complex numbers, analytic functions, complex integration, Cauchy's theorem and its applications, poles and residues, and power series. In the second half oh this semester, we will discuss Fourier series and Fourier transforms. Then we will study different types of partial differential equation problems. 
課程目標 
At the end of this semester, you will
 Compute vector differential calculus (knowing the physical meaning of gradient, divergence, and curl operators)
 Compute vector integral calculus (knowing divergence theorem and Stoke's theorem)
 Represent complex numbers algebraically and geometrically
 Apply the concept and consequences of analyticity and the CauchyRiemann equations and of results on
harmonic and entire functions including the fundamental theorem of algebra
 Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral
theorem in its various versions, and the Cauchy integral formula
 Represent functions as Taylor, power and Laurent series, classify singularities and poles, find residues and
evaluate complex integrals using the residue theorem
 Calculate Fourier integral and Fourier transform
 Understand how partial differential equations arise in the mathematical description of heat flow and vibration
 Demonstrate the ability to solve initial boundary value problems
 Express and explain the physical interpretations of common forms of PDEs
 Be acquainted with applications of partial differential equations in various disciplines of study 
課程要求 

預期每週課後學習時數 

Office Hours 

參考書目 

指定閱讀 

評量方式 (僅供參考) 
No. 
項目 
百分比 
說明 
1. 
Quiz 
20% 
There are four twentyminute quizzes on Wednesday from 9:00am to 9:20am (the rest of the time being used to continue through the material). In each quiz, you will solve two to three questions chosen from our exercises and sample problems in the textbook. Quizzes are closed book, closednote. No electronics, including calculators, cell phones, and smart watches are allowed. Some formulas and tables may be provided. The quizzes are scheduled on
– Quiz I: February 23.
– Quiz II: March 23.
– Quiz III: April 20.
– Quiz IV: May 18. 
2. 
Midterm 
60% 
There are three midterm exams in this course. The mid terms are scheduled on
– Midterm I: March 07 in class. – Midterm II: April 11 in class.
– Midterm III: May 02 in class.
Midterms are closedbook, closednote. No electronics, including calculators, cell phones, and smart watches are allowed. Midterms will be used to access demonstration of the learning objectives and may include the combinations of true & false and workout problems. Some formulas and tables may be provided. 
3. 
Final 
20% 
The date of the final exam will be on May 30. The final is closedbook, closednote. No electronics, including calculators, cell phones, and smart watches are allowed. The final is cumulative and may include the combinations of true & false and workout problems. Some formulas and tables may be provided. 
4. 
• Class Attendance and Attentiveness: 
0% 
5%. The purpose of this is to encourage you to attend every class that you can. You should also be attentive during the lecture; there are many ways to show you are engaged, one being to answer questions as they are asked.


週次 
日期 
單元主題 
Week 1 
2/14, 2/16 
Vector Differential Calculus 
Week 2 
2/21, 2/23 
Vector Integral Calculus 
Week 3 
2/28, 3/2 
Vector Integral Calculus 
Week 4 
3/7, 3/9 
Midterm I 
Week 5 
3/14, 3/16 
Functions of a Complex Variable 
Week 6 
3/21, 3/23 
Integration in the Complex Plane 
Week 7 
3/28, 3/30 
Series and Residues 
Week 8 
4/4, 4/6 
Fourier Series 
Week 9 
4/11, 4/13 
MidTerm II 
Week 10 
4/18, 4/20 
Fourier Integral 
Week 11 
4/25, 4/27 
Fourier Transform 
Week 12 
5/2, 5/4 
Midterm III 
Week 13 
5/9, 5/11 
PDE  Heat Equation 
Week 14 
5/16, 5/18 
PDE  Wave Equations 
Week 15 
5/23, 5/25 
PDE  Laplace Equations 
Week 16 
5/30, 6/1 
Final Exam 
