課程資訊

Engineering Mathematics (2)

110-2

ME2002

502E20002

04

3.0

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.

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 Cauchy-Riemann 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

Office Hours

(僅供參考)

 No. 項目 百分比 說明 1. Quiz 20% There are four twenty-minute 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, closed-note. 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 mid-term exams in this course. The mid terms are scheduled on – Mid-term I: March 07 in class. – Mid-term II: April 11 in class. – Mid-term III: May 02 in class. Mid-terms are closed-book, closed-note. No electronics, including calculators, cell phones, and smart watches are allowed. Mid-terms will be used to access demonstration of the learning objectives and may include the combinations of true & false and work-out 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 closed-book, closed-note. No electronics, including calculators, cell phones, and smart watches are allowed. The final is cumulative and may include the combinations of true & false and work-out 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.

 課程進度
 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