PME 2002-2

Brief

數學為探討各種自然與工程問題的重要分析工具，工程數學在微積分的基礎之 上，更深入探討各種微分方程式的應用及求解方法與技巧，並了解求出其解之 特性。透過課堂講授、習題演練及測驗，希望同學能認識並熟悉各類方程式所 描述物理現象與解的性質，為未來修習動機系各項專業課程 (材料力學、流體 力學、控制理論等) 打下基礎。本課程分為上、下兩學期，下學期講授 vector calculus 、Fourier analysis、partial differential equations、complex analysis。

Description

Course keywords: vector calculus, Fourier analysis, partial differential equations, complex analysis 一、課程說明 (Course Description) 數學為探討各種自然與工程問題的重要分析工具，工程數學在微積分的基礎之上，更深入探討各種微分方程式 的應用及求解方法與技巧，並了解求出其解之特性。透過課堂講授、習題演練及測驗，希望同學能認識並熟悉 各類方程式所描述物理現象與解的性質，為未來修習動機系各項專業課程 (材料力學、流體力學、控制理論等) 打下基礎。本課程分為上、下兩學期，下學期講授 vector calculus、Fourier analysis、partial differential equations、complex analysis。 Mathematical tools are essential in analysis and prediction for a wide range of engineering problems. Engineering Mathematics is a post-calculus course for undergraduate students. It extends the discussion to various types of differential equations and advanced mathematical topics. Through class lectures, homework assignments and exams, you will acquire the skill to solve some but not all the equations with engineering interest, and be ready for using it in engineering specializations such as fluid mechanics, solid mechanics, control theory etc. Furthermore, you should have a good grasp of the physical meaning behind the \math, and also be able to interpret the solution. This is a two-semester series. In the second semester we will cover vector calculus, Fourier analysis, partial differential equations, complex analysis. 二、指定用書 (Text Book) Kreyszig, E., "Advanced Engineering Mathematics", abridged version 10th ed., John Wiley (2018) 三、參考書籍 (References) Zill, D.S., "Advanced Engineering Mathematics", 7th ed., Jones & Bartlett (2022) O'Neil, P.V., "Advanced Engineering Mathematics", 8th ed., Cengage Learning (2018) Arfken, G.B., "Mathematical Methods for Physicists", 7th ed., Academic Press (2012) Riley, K.F., "Mathematical Methods for Physics and Engineering", 3rd ed., Cambridge University Press (2006) 四、教學方式 (Teaching Method) 課堂講授，包括方程式與解的推導演算，搭配其物理意義與實際應用例子的展示及解說。 Lecture. Demonstrate the derivation and solution steps for equations, explain the physics and their engineering applications. 五、教學進度 (Syllabus) 1. Vector calculus 2. Fourier series and integral 3. Fourier transform 4. Partial differential equations 5. Complex analysis 六、成績考核 (Grading) Homework 20% Quizzes 20% Midterm 30% Final 30% 課程網頁：

Timetable

Scores

Average Percentage 73

Std. Deviation 13.02

Remarks

Restrictions

限動機系大學部2年級3年級4年級華班

Compulsory

Elective

Cross Discipline

First Specialization

Second Specialization