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課程名稱 |
或然率理論與模型
Probability Theory and Modeling |
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開課學期 |
102-1 |
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授課對象 |
工學院 水利工程組 |
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授課教師 |
蔡宛珊 |
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課號 |
CIE7165 |
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課程識別碼 |
521EM7540 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一5,6,7(12:20~15:10) |
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上課地點 |
土研406 |
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備註 |
本課程以英語授課。以英語授課
總人數上限：14人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1021CIE7165_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
PRELIMINARIES
FUNDAMENTALS OF REAL VARIABLES
MATHEMATICAL PRELIMINARIES
FUNDAMENTALS OF UNCERTAINTY ANALYSIS
FUNDAMENTALS OF RANDOM PROCESSES
MARTINGALES, STOPPING TIMES AND FILTRATIONS
STOCHASTIC PROCESSES AND SIGMA FIELDS
STOPPING TIMES
CONTINUOUS TIME MARTINGALES
REYNOLDS TRANSPORT THEOREM
CONSERVATION OF DISSOLVED CONSTITUENT MASS
BROWNIAN MOTION
BROWNIAN MOTION
MARKOV PROPERTY
THE BROWNIAN SAMPLE PATHS
STOCHASTIC INTEGRATION
CONSTRUCTION OF THE STOCHASTIC INTEGRAL
THE CHANGE-OF-VARIABLE FORMULA
GENERALIZED ITO RULE FOR BROWNIAN MOTION
STOCHASTIC DIFFERENTIAL EQUATIONS (IF TIME PERMITTED)
STRONG SOLUTIONS
WEAK SOLUTIONS
APPROXIMATION METHODS FOR UNCERTAINTY ANALYSIS
FIRS-ORDER VARIANCE ESTIMATION METHOD
ROSENBLUETH;S PROBABILISTIC POINT ESTIMATE METHOD
HARR’S PROBABILISTIC POINT ESTIMATE METHOD
LI’S PROBABILISTIC POINT ESTIMATE METHOD |
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課程目標 |
THE OVERALL OBJECTIVE OF THIS COURSE IS TO FAMILIARIZE STUDENTS WITH BASIC CONCEPTS OF MATHEMATICAL MODELING UNDER UNCERTAINTY. STUDENTS ARE EXPECTED TO GAIN A BASIC UNDERSTANDING OF STOCHASTIC PROCESSES, UNCERTAINTY ANALYSIS AND FUNDAMENTAL STOCHASTIC CALCULUS USEFUL FOR STOCHASTIC MODELING. THIS COURSE WILL PROVIDE STUDENTS WITH FUNDAMENTAL KNOWLEDGE AND QUANTITATIVE APPROACHES NECESSARY FOR MODELING NATURAL PROCESSES UNDER UNCERTAINTY. THIS COURSE WILL BE TAUGHT IN ENGLISH. |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
待補 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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第1週 |
9/09 |
Introduction |
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第2週 |
9/16 |
Research Hypothesis, Academic writing and introduction to probability modeling |
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第3週 |
9/23 |
Uncertainty Analysis and Risk Assessment |
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第4週 |
9/30 |
Stochastic Calculus (Gaussian process, stationarity, Standard Brownian motion) |
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第5週 |
10/07 |
Brownian motion |
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第6週 |
10/14 |
No class |
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第7週 |
10/21 |
Queuing theory and Markov chains (1) |
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第8週 |
10/28 |
Markov chains (2) |
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第9週 |
11/04 |
Markov chains (3) |
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第10週 |
11/11 |
Markov chains (4) |
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第11週 |
11/18 |
Markov chains (5) |
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