課程資訊
課程名稱
 工程數學下
Engineering Mathematics (2) 
開課學期
 111-2 
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401綜401 
備註
 本課程以英語授課。
總人數上限：42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
 The objective of this course is that by the end of the semester, you will learn
• gradient, divergence and curl of a vector point function and related identities;
• evaluation of line, surface and volume integrals using Gauss, Stokes and Green’s theorems and their verification;
• analytic functions and complex integration;
• Fourier series, integral, and transform;
• PDE in heat, wave, and Laplace equations.
You will also
• 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;
• 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
  
指定閱讀
  
參考書目
  
評量方式
(僅供參考)
    
課程進度
週次
日期
單元主題
第1週
 2/20, 2/22  Vector Differential Calculus 
第2週
 2/27, 3/01  Vector Differential Calculus 
第3週
 3/06, 3/08  Vector Integral Calculus 
第4週
 3/13, 3/15  Green's Theorem, Divergence Theorem, and Stokes' Theorem 
第5週
 3/20, 3/22  Midterm I
Function of a Complex Variable 
第6週
 3/27, 3/29  Function of a Complex Variable 
第7週
 4/03, 4/05  Spring Break 
第8週
 4/10, 4/12  Integration in the Complex Plane 
第9週
 4/17, 4/19  Series and Residues 
第10週
 4/24, 4/26  Midterm II
Fourier Series 
第11週
 5/01, 5/03  Fourier Series
Fourier Integral 
第12週
 5/08, 5/10  Fourier Transform 
第13週
 5/15, 5/17  Midterm III
Partial Differential Equation 
第14週
 5/22, 5/24  PDE -- Heat Equations
PDE -- Laplace Equations 
第15週
 5/29, 5/31  PDE -- Laplace Equations
PDE -- Wave Equations 
第16週
 6/05, 6/07  Final Exam