課程大綱

課程資訊

課程名稱

工程數學下
Engineering Mathematics (2)

開課學期

113-2

授課對象

工學院院學士學位

授課教師

林以凡

課號

ME2002

課程識別碼

502E20002

班次

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。院學士核心必修-甲組、乙組
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 com- plex 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

預期每週課前或/與課後學習時數

Office Hours

指定閱讀

參考書目

P. V. O’Neil, Advanced Engineering Mathematics, CENGAGE Learning, 8th Ed, 2018.

評量方式
(僅供參考)

No.	項目	百分比	說明
1.	Quiz	20%	There will be twenty-minute quiz from 9 am to 9:20 am on every Wednesday. On each quiz, you will solve one to two questions chosen from our exercises and sample problems in the textbook. Quizzes are closed-book, closed-note. No electronics, including calculators, cell phones, or smart watches are allowed. Some formulas and tables may be provided.
2.	Team Collaboration	10%
3.	Homework	10%
4.	Midterms	45%	(15% each). There are three mid-term exams in this course. The mid terms are scheduled on – Mid-term I: March 17 in class. – Mid-term II: April 21 in class. – Mid-term III: May 12 in class. Mid-terms are closed-book, closed-notes. No electronics, including calculators, cell phones, or 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.
5.	Final Exam	15%	The date of the final exam will be on June 02. The final is closed-book, closed-notes. No electronics, including calculators, cell phones, or 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.

課程進度

週次	日期	單元主題
第1週	2/17, 2/19	Vector Differential Calculus
第2週	2/24, 2/26	The Gradient Field, Divergence, and Curl
第3週	3/03, 3/05	Vector Integral Calculus
第4週	3/10, 3/12	Divergence Theorem and Stoles' Theorem
第5週	3/17, 3/19	Midterm I, Functions of a Complex Variable
第6週	3/24, 3/26	Functions of a Complex Variable
第7週	3/31, 4/02	Integration in the Complex Plane
第8週	4/07, 4/09	Series and Residues
第9週	4/14, 4/16	Series and Residues Fourier Series
第10週	4/21, 4/23	Midterm II Fourier Series
第11週	4/28, 4/30	Fourier Integral
第12週	5/05, 5/07	Fourier Transform
第13週	5/12, 5/14	Midterm III Partial Differential Equation
第14週	5/19, 5/21	PDE - Heat Equations PDE - Laplace Equations
第15週	5/26, 5/28	PDE - Laplace Equations PDE - Wave Equations
第16週	6/02, 6/04	Final Exam