工程數學(一)

臺北科技大學 115-1 學期課程，課號 362201。

課程大綱

This course will introduce the mathematical principles in engineering, including following topics: First-Order ODEs, Second-Order Linear ODEs, Higher Order Linear ODEs, Systems of ODEs, Series Solutions of ODEs, and Laplace Transforms.

課程進度

1 Course introduction & Basic Concepts of First-Order ODEs. 2 Separable ODEs & Exact ODEs. 3 Linear ODEs & Existence and Uniqueness of Solutions for Initial Value Problems. 4 No lecture on 28 Sep (Confucius’ Birthday) & In-class Quiz 1. 5 Homogeneous Linear ODEs of Second Order & Homogeneous Linear ODEs with Constant Coefficients & Euler–Cauchy Equations. 6 Existence and Uniqueness of Solutions & Nonhomogeneous ODEs. 7 Review of First and Second-Order ODEs & Mid-term Exam. 8 No lecture on 26 Oct (Compensatory holiday for Retrocession Day) & Higher Order Homogeneous Linear ODEs and Higher Order Homogeneous Linear ODEs with Constant Coefficients. 9 Nonhomogeneous Linear ODEs & Systems of ODEs as Models in Engineering Applications. 10 No lecture on 9 Nov (Compensatory holiday for Taipei Tech’s anniversary celebration and school fair) & Power Series Method. 11 Legendre’s Equation & Extended Power Series Method. 12 Bessel’s Equation & General Solution of Bessel Functions & In-class Quiz 2. 13 Laplace Transform & Transforms of Derivatives and Integrals & Unit Step Function. 14 Differentiation and Integration of Transforms & Systems of ODEs. 15-16 Laplace Transform: General Formulas & Final Exam & Review. 17-18 Flexible Learning.

評量方式

Subject Mark = Attendance 10% + In-class quizzes 1&2 25% + Mid-term exam 25% + Final exam 30% + Student group practice and discussion 10%

教材

【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 Kreyszig, Erwin. “Advanced engineering mathematics.” 10th ed.