| | 微積分(一) Calculus (I) | (一)教材 書名：CALCULUS, one and several variables (第10版),2006
作者： Salas, Hille 和 Etgen (二)課程內容及大綱 1.無限的概念，函數概念。
2. 極限與連續性。
3. 微分
4. 微分均值定理及其應用。 5.積分
6. 積分的應用
|  | 微積分(二) Calculus (II) | 預備知識: 微積分(一) (一)教材 書名： CALCULUS, one and several variables (第10版),2006
作者： Salas, Hille 和 Etgen (二)課程介紹 微積分是所有數學課程的基礎，本課程從最基本談起由淺入深並探討 微積分的應用。 (三)課程內容及大綱 1. Integrals
2. Application of Integration
3. Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
4. Techniques of Integration
5. Further Applications of Integration - Arc Length
6. Infinite Sequence and Series
| | 微積分(三) Calculus (III) | 預備知識: 微積分(一)(二) (一)教材 書名： CALCULUS, one and several variables (第9版)
作者： Salas, Hille 和 Etgen (二)參考書 Any calculus text book is fine. (三)課程介紹 This semester will be treated as the Multivariable Calculus or we can call it vector analysis. We generally cover the remaining parts of the course which covers mostly in multivariable subjects. If time is available, we will go back to do some review about the content of Parametric equation. (四)課程內容及大綱 1. Vectors and the Geometry of Surface
2. Vector Functions
3. Partial Derivatives
4. Multiple Integrals
5. Vector Calculus |  | 普通物理(一) Physics (I) | (一)教材 Vector Mechanics for Engineers, Ferdinand P. Beer and E. Russell Johnston Jr., McGraw Hill (二)參考書 Engineering Mechanics, Statics, R. C. Hibbeler and S.C. Fan, Prentice Hall (三)課程介紹 The main purpose of this class is to provide the student with a clear and thorough presentation of the theory and applications of statics.
(四)課程內容及大綱 1. Introduction
2. Statics of Particles
3. Rigid Body: Equivalent Systems of Forces
4. Equilibrium of Rigid Bodies
5. Distributed Forces: Centroids and Centers og Gravity
6. Analysis of Structures
7. Forces in Beams and Cables
8. Friction
9. Distributed Forces: Moments of Inertia
10. Method of Virtual Work |  | 物理(二) Physics (II) | 預備知識: 物理(一) (一)教材 Vector Mechanics for Engineers, Dynamics, Ferdinand P. Beer, E. Russell Johnston Jr., McGraw-Hill (二)課程內容 The main objective of this course should be to develop in the student the ability to analyze any problem in a simple and logical manner and to its solution a few well-understood principles. (三)課程大綱 1. Kinematics of Particles
2. Kinetics of Particles: Newtons Second Law
3. Kinetics of Particles: Energy and Momentum Methods
4. System of Particles
5. Kinematics of Rigid Bodies
6. Plane Motion of Rigid Bodies: Forces and Accelerations
7. Plane Motion of Rigid Bodies: Energy and Momentum Methods
8. Mechanical Vibrations | | 線性代數(一) Linear Algebra (I) | (一)教材 LINEAR ALGEBRA, 3rd edittion
JOHN B. FRALEIGH
RAYMOND A. BEAUREGARD (二)課程介紹 認識向量空間，矩陣的運算及分類。 (三)課程內容及大綱 1. definition of vector spaces
2.linear combination, span, linearly independent, basis
3.definition of linear transformations
4.kernel, rank
5.rank equation |  | 線性代數(二) Linear Algebra (II) | 預備知識: 線性代數(一) (一)教材 LINEAR ALGEBRA, 3rd edittion
JOHN B. FRALEIGH
RAYMOND A. BEAUREGARD (二)參考書 Linear Algebra, Larson (三)課程介紹 認識向量空間，矩陣的運算及分類。 (四)課程內容及大綱 1. VECTOR，MATRICES，AND LINEAR SYSTEMS。 2. VECTOR SPACES。 3. EIGENVALUES AND EIGENVECTORS。 4. CHANGE OF BASIS。 5. JORDAN FORMS。 6. INFINITE DIMENSIONAL VECTOR SPACE。 | | 高等微積分(一) Advanced Calculus (I) | (一)教材 Introduction to Real Analysis, third Edition
Author: Robert G. Bartle & Donald R. Sherbert (二)參考書 A Friendly Introduction to Analysis:Single and Multivariable, second Edition
Auhtor: Witold A. J. Kosmala (三)課程 介紹 本課程是繼微積分之後將強調公式及計算的數學放進證明的演譯，強調定義、定理邏輯性的推理，希望將數學分析的各種性質以更嚴謹的方式告訴學生，對於學生未來在持續學習數學或是在應用科學都會有助益。 (四)課程大綱 Chapter 1: Preliminaries
Chapter 2: The REal Numbers
Chapter 3: Sequences and Series
Chapter 4: Limits
Chapter 5: Continuous Functions |  | 高等微積分(二) Advanced Calculus (II) | (一)教材 Introduction to Real Analysis, third Edition
Author: Robert G. Bartle & Donald R. Sherbert (二)參考書 A Friendly Introduction to Analysis:Single and Multivariable, second Edition
Auhtor: Witold A. J. Kosmala (三)課程 介紹 It is one of the most important course among mathematics courses in department of Applied Mathematics. The training to write and think in analysis way is the key for success learning in mathematics. Several majors can also benefit for this course, including engineering and management. (四)課程大綱 1. Continuous Functions
2. Differentiation
3. The Riemann Integral
4. Sequence of Functions
5. Infinite Series | | 數值分析(一) Numerical Analysis (I) | (一)教材 Title: Numerical Analysis---8th edition, 2004
Authors: Richard L. Burden and J. Douglas Faires (二)參考書 Introduction To MATLAB 7 For Engineers, William J. Palm III (三)課程 介紹 1.Error Analysis
2. Solutions of Equations in One Variable
3. Interpolation and Polynomial Approximation
4.Numerical Differentiation and Integration
5. Initial-Value Problems for Ordinary Differential Equations (四)課程大綱 1. Round-Off Errors
2. Algorithms and Convergence
3. The Bisection Method
4. Fixed-Point Iteration
5. Newton's Method
6. Divided Differences
7. Cubic Spline Interpolation
8. Richardson's Extrapolation
9. Romberg Integration
10. Runge-Kutta Methods |  | 數值分析(二) Numerical Analysis (II) | (一)教材 Title: Numerical Analysis---8th edition, 2004
Authors: Richard L. Burden and J. Douglas Faires (二)參考書 Introduction To MATLAB 7 For Engineers, William J. Palm III (三)課程 介紹 1. Initial-value problems for Ordinary Differential Equations
2. Approximation Theory
3. Direct Methods for solving Linear Systems
4. Iterative Techniques in Matrix Algebra
5. Approximating Eigenvalues (四)課程大綱 1. Runge-Kutta Methods
2. Error Control and the Runge-Kutta-Fehlberg Method
3. Multistep Method
4. Stiff Differential Equations
5. Discrete Least Squares Approximation
6. Orthogonal Polynomials and Economination of Power series
7. Fast Fourier Transformation
8. Pivoting Strategies
9. Iterative Techniques for Solving Linear Systems
10. The Conjugate Gradient Method | | 計算機概論(一) Introduction to Computer Science (I) | (一)教材 C 語言詳論, 第五版 作者:Jeri R. Hanly and Elliot B. Koffman 譯者:潘育群 、蔡明志 (二)課程介紹 瞭解電腦的硬體及軟體
深入研究 C語言結構
邏輯訓練
(三)課程內容及大綱 1. Overview Of Computers and Programming 電腦及程式語言概論 2. Windows and Unix Operating Systems 作業系統介紹 3. Overview Of C 縱觀C語言 4. Functions 函數
5. Selection Structures 選取結構
6. Repetition 迴圈
7. Modular Programming 模組化程式設計 |  | 計算機概論(二) Introduction to Computer Science (II) | (一)教材 C 語言詳論, 第五版 作者:Jeri R. Hanly and Elliot B. Koffman 譯者:潘育群 、蔡明志 (二)課程介紹 深入研究 C語言結構
(三)課程內容及大綱 1. C 語言基礎語法
2. 高階模組化程式設計
3. 資料型態
4. 陣列
5. 字串與指標
6. 遞迴
7. 結構
8. C++ 語法 | | 計算機概論實習(一) Computer Labs (I) | (一)教材 C 語言詳論, 第五版 作者:Jeri R. Hanly and Elliot B. koffman 譯者:潘育群 、蔡明志 (二)課程介紹 配合計算機概論課程之內容，執行程式實作。 (三)課程內容及大綱 1. Overview 2. Operating Systems
3. WWW
4. C programs | | 計算機概論實習(二) Computer Labs (II) | (一)教材 C 語言詳論, 第五版 作者:Jeri R. Hanly and Elliot B. Koffman 譯者:潘育群 、蔡明志 (二)課程介紹 配合計算機概論課程之內容，執行程式實作。
(三)課程內容及大綱 1. C 語言基礎語法
2. 高階模組化程式設計
3. 資料型態
4. 陣列
5. 字串與指標
6. 遞迴
7. 結構
8. C++ 語法 | | 複變函數分析 Complex Analysis | (一)教材 Complex Variables and Applications (第七版), by James Ward Brown and Ruel V. Churchill (二)課程 內容 複變函數在數學、物理、工程及其他應用科學上應用非常廣泛。我們將著重基本觀念的建立，嚴密的証明，定理欣賞及運用及完整的習題演練。 (三)課程大綱 1. 基本複數系統 (Complex number)
2. 解析函數 (Analytic functions)
3. 複變函數的積分(Integrals)
4. 複數級數及複變函數級數(Series)
5. 複變函數的留數(Residues)
6. 留數之應用(Applications of Residues)
7. 保角映射(Conformal mappings)
8. 保角映射之應用(Applications of Conformal mappings) |  | 微分方程(一) Differential Equations (I) | (一)教材 Advanced Engineering Mathematics, Third Edition, by D. G. Zill and M. R. Cullen (二)課程大綱 1. Introduction to Differential Equations
2. First-Order Differential Equations 3. Higher-Order Differential Equations
4. The Laplace Transform |  | 微分方程(二) Differential Equations (II) | (一)教材 Advanced Engineering Mathematics, Third Edition, by D. G. Zill and M. R. Cullen (二)課程大綱 1. Series Solutions of Linear Equations
2. Orthogonal Functions and Fourier Series
3. Boundary-Value Problems in Rectangular Coordinates | | 幾何學 Geometry | (一)教材 GEOMETRY by David A. Brannan, Matthew F. Esplen and Jeremy J. Gray (二)課程介紹 幾何學已有兩千年的歷史，本課程將介紹古典幾何重要的理論及其應用 ，尤其著重在電腦上的應用。 (三)課程大綱 1. Conics 2. Affine Geometry 3. Projective Geometry 4. Inversive Geometry 5. Non-Euclidean Geometry |  | 機率 Probability | 需先修過之課程: 微積分 (一)教材 A first course in probability (7th Edition), 2005, by Sheldon Ross.
中譯本：機率導論(七版), 2006, 林光賢譯 (二)參考書 Fundamentals of probability, with stochastic processes (3rd Edition), 2004, by S. Saeed Ghahramani. (三)課程介紹 使學生了解機率論之基本知識，並能用隨機變數及隨機方法來描述科學 之隨機現象. (四)課程大綱 random variables (隨機變數), distributions (分配), conditioning (條件), independence (獨立), expectation (期望值), variance (變異數) and moment generating functions (動差生成函數), special distributions and their relations (特殊分配及他們的關係), transformations (變數變換), convergence concepts (收斂觀念), limiting theorems (極限定理), stochastic process (隨機過程) and random signal processing (隨機訊號處理) |  | 數理統計(一) Mathematical Statistics (I) | 需先修過之課程: 微積分, 機率 (一)教材 Introduction to Mathematical Statistics (Sixth Edition), 2005, by R. V. Hogg, J. W. McKean, and A. T. Craig. (二)參考書 Introduction to the Theory of Statistics (Third Edition), 1974, by A. M. Mood, F. A. Graybill and D. C. Boes. (三)課程大綱 The theory of estimation including: likelihood functions , sufficiency, methods of moments and maximum likelihood , unbiasedness, consistency, Rao-Blackwell theorem, Fisher information and Cramer-Rao inequality, large sample properties of MLE's. Other topics include: confidence intervals, decision theory and Bayesian estimation. |  | 數理統計(二) Mathematical Statistics (II) | 需先修過之課程: 微積分, 機率, 數理統計(一) (一)教材 Introduction to Mathematical Statistics (Sixth Edition), 2005, by R. V. Hogg, J. W. McKean, and A. T. Craig. (二)參考書 Probability and Statistical Inference (Fourth Edition), 1993, by R. V. Hogg and E. A. Tanis. (三)課程大綱 The theory of hypothesis testing including: tests, significance levels,power, the Neyman-Pearson Lemma, uniformly most powerful unbiased tests, likelihood ratio tests and the associated large sample theory, goodness of fit tests, and tests in contingency tables. Other topics include: analysis of variance, introduction to the general linear model, and non-parametric methods. | | 代數 Abstract Algebra | (一)教材 Elements of Modern Algebra---Sixth edition, 2005 Author : Jimmie Gilbert & Linda Gilbert (二)課程內容 An introductory course in algebraic structures. (三)課程大鋼 1. Fundamentals
2. The Integers
3. Groups
4. Rings
5. Integral Domains & Fields | |
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