工程數學(一)

臺北科技大學 115-1 學期課程，課號 362215。

課程大綱

先修課程：微積分或負責教授同意。常微分方程式、線性常微分方程式、拉普拉氏轉換、級數及傅立葉級數、線性代數及矩陣、積分定理。 Introduction of the deformation, Strain and stress of structure (Beam, Column, Pressure vessel) under different loading conditions such as Tension, Compression, Shear force, Torsion and Bending moment.

課程進度

週次 章節內容 備註 01 Course introduction & Basic Concepts and Ideas 02 Geometrical Meaning of y’=f(x,y) & Separable Differential Eq. 03 Exact ODES & Linear ODEs 04 Determinants (Second-/Third-order; Properties; Cramer’s Rule). 9/28教師節 05 Inverse of a Matrix & Gauss–Jordan Elimination. Quiz 06 Homogeous Linear ODEs. of Second Order & Euler-Cauchy Eq. 07 Existence and Uniqueness of Solutions & Nonhomogeous ODEs 08 Mid-term exam 9/26光復節補假 09 Solution by Variation of Parameters & Homogenous Linear ODEs of High Orders 10 Homogeous Linear Eq. of High Orders with Constant Coefficients & Nonhomogeous Linear ODEs of High Orders 11/09校慶慶祝大會暨園遊會補假 11 Power Series Method & Theory of the Power Series Method 12 Line Integrals; Path Independence; Double Integrals; Green’s Theorem. Quiz 13 Legendre’s Equation; Legendre Polynomials Pn(x) & Frobenius Method 14 Bessel’s Equation. Bessel Functions Jv(x) & Laplace Transform 15 Transforms of Derivatives and Integrals. ODEs & Unit Step Function 16 Final exam 17 透過提講義，協助學生進行自主學習 (Short Impulses; Convolution. Integral Equations) 自主學習 18 透過提講義，協助學生進行自主學習 (Differentiation and Integration of Transforms) 自主學習

評量方式

平時40%(內含小考30%，平時出缺席考核與課堂行為觀察10%，點名缺席一次扣1%，最多扣至10%)，期中考25%，期末考25%，自主學習作業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 1. 自編教材 2. Erwin Kreyszig, Advanced Engineering Mathematics, 10th edition,