一、課程說明(Course Description)



This is a mandatory mathematics course for students in the second year of

ESS department. The topics of this course include:



1) Ordinary Differential Equations: 1st order ODEs, 2nd order ODEs, higher

order ODEs, systems of ODEs

2) Special functions and power series method

3) Laplace Transform



* 課程預備知識: 需已修習過微積分





二、指定用書(Text Books)



Zill, Wright, and Ding, "Engineering Mathematics", Jones & Bartlett, metric

version



三、參考書籍(References)







四、教學方式(Teaching Method)



3.5 hours lecture per week。





五、教學進度(Syllabus)



Week 1: Introduction to Differential Equation, definition of basic

terminology



Week 2,3: Qualitative solution and numerical methods (Chapter 2 and 6)



Week 4-6: Linear ODE (homogeneous, non-homogeneous): Euler's integrating

factor method, Lagrange's variations of parameter method, Separable

equation, exact equation and integrating factors. (Chapter 2)



Week 7-8: Linear ODE of 2nd order or higher, linear independent/dependent,

Wronskian, basis set of solution of DE, existence and uniqueness for

Initial-Value Problem, homogeneous equation with

constant coefficients (characteristic equation, distinct roots, repeated

roots ), harmonic oscillator (free oscillation) (Chapter 3)



Week 9-10: Linear nonhomogeneous equation with constant coefficients (method

of undetermined coefficients, method of inverse operators), Forced harmonic

oscillator, system of linear ODE with constant coefficients, Linear ODE with

variable coefficients (Cauch-Euler equation, Method of reduction of order,

Method of variation of parameters)(Chapter 3)



Week 11-13: Laplace transform, inverse Laplace transform, special functions,

application to the solution of ODE. (Chapter 4)



Week 14-15: power series method, Method of Frobenius, Legendre equation,

Gamma function, Bessel equation, modified Bessel equation (Chapter 5)







六、成績考核(Evaluation)



Midterm exam I(30~33%)

Midterm exam I(30~34%)

Final exam (30~33%)

小考&點名 (0~10%)



*課堂上仍會給回家作業讓同學練習但不計分



七、可連結之網頁位址 (Web site)

請登入eeclass