課程資訊

Engineering Mathematics (1)

109-1

ME2001

502E20001

02

3.0

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1091ME2001_02

NOTE: This class may be conducted in-person or on-line. Which form of teaching depends on the development of the COVID-19 pandemic.

In this course, we shall introduce series of mathematical methods and techniques that are applied in solving mathematical governing equations frequently encountered in modern science and engineering analyses. The lectures and classes will mostly be devoted to solving problems. However, emphasis will also be placed on the connections between mathematics and engineering applications, the modeling of the physical problems using mathematical equations, and finally the physical significances of the mathematical solutions obtained through problem solving.

Topics discussed this semester generally include:
1. First Order Ordinary Differential Equations
Introduction to engineering mathematics and mathematical modeling;
Definitions and concepts of differential equations;
Separable, linear, and exact differential equations;
Integrating factors;
Some special equations;
Applications of 1st order ODE

2. Second Order Linear Ordinary Differential Equations
2nd order linear ODE and the reduction of order;
The constant coefficient homogeneous linear equation and Euler’s equation;
Nonhomogeneous 2nd order linear ODEs and higher order equations;
Applications of 2nd order linear ODEs

3. The Laplace Transform
Fundamentals of Laplace transform;
Solving IVPs with Laplace transform;
1st and 2nd shifting theorems;
Convolution and integral/integro-differential equations;
Heaviside, unit impulse, and the Dirac delta functions;
More solution techniques using Laplace transform

4. Series Solutions
Power series solutions: IVPs and recurrence relations;
The method of Frobenius: singular points, second solutions

5. Orthogonal expansions and BVPs
The Sturm-Liouville problem and orthogonal expansions;
Special functions: Bessel and Legendre functions

6. Fundamentals of Linear Algebra
Vector algebra and vector products;
The vector space: linear independence, spanning sets, and dimension;
Matrices and operations of matrices;
Row and column spaces of a matrix;
Homogeneous systems of linear equations and its solution space;
Nonhomogeneous systems of linear equations;
Inverse and determinant of matrices;
Cramer’s rule;
Eigenvalues, eigenvectors, and diagonalization of matrices;
Orthogonal and symmetric matrices
Solving 1st and 2nd order systems differential equations using diagonalization

To learn advanced mathematical tools as well as how to apply these mathematical tools in solving real life science and engineering problems. Our study will focus on differential equations and linear algebra for this semester.

Calculus

Office Hours

1. Zill and Cullen, Differential Equations with Boundary-value Problems, 5th edn., Brooks Cole
2. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press
3. Peter V. O’Neil, Advanced Engineering Mathematics

D.G. Zill, Advanced Engineering Mathematics, 6th edn., Jones & Bartlett

(僅供參考)

 No. 項目 百分比 說明 1. Problem sets 0% Problem sets will be assigned, but NOT graded. They are for your own practice purposes. 2. Mid-term #1 30% The form of, time when, and venue where the mid-term takes place depend on the development of the COVID-19 pandemic. 3. Mid-term #2 35% The form of, time when, and venue where the mid-term takes place depend on the development of the COVID-19 pandemic. 4. Final exam 35% If the conditions of the pandemic permit, the final exam will be held in finals week, and follows finals schedule.

 課程進度
 週次 日期 單元主題 第1週 9/14,9/16 Introduction, 1st order ODE (Ch 1, 2) 第2週 9/21,9/23 1st order ODE (Ch 2) 第3週 9/28,9/30 2nd and higher order ODE (Ch 3) 第4週 10/05,10/07 2nd and higher order ODE (Ch 3) 第5週 10/12,10/14 Laplace transform (Ch 4) 第6週 10/19,10/21 Laplace transform (Ch 4) 第7週 10/26,10/28 Laplace transform (Ch 4) 第8週 11/02,11/04 Series solutions (Ch 5) 第9週 11/09,11/11 Series solutions (Ch 5) 第10週 11/16,11/18 Special functions (Ch 5) 第11週 11/23,11/25 Sturm-Liouville boundary value problems (Ch 3.9, 12) 第12週 11/30,12/02 Sturm-Liouville boundary value problems (Ch 3.9, 12) 第13週 12/07,12/09 Vectors and vector space (Ch 7) 第14週 12/14,12/16 Matrices and linear algebra (Ch 8) 第15週 12/21,12/23 Matrices and linear algebra (Ch 8) 第16週 12/28,12/30 Matrices and linear algebra (Ch 8) 第17週 1/04,1/06 Systems equations (Ch 10) 第18週 1/11 Final exam