課程名稱 |
工程數學下 Engineering Mathematics (2) |
開課學期 |
110-2 |
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 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
課程大綱
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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 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 |
課程要求 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
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評量方式 (僅供參考) |
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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 |
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