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課程名稱 |
高等化工應用數學一
Advanced Applied Mathematics for Chemical Engineering (Ⅰ) |
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開課學期 |
103-1 |
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授課對象 |
工學院 化學工程學研究所 |
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授課教師 |
藍崇文 |
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課號 |
ChemE7016 |
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課程識別碼 |
524 M1520 |
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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 |
必修 |
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上課時間 |
星期二2(9:10~10:00)星期五3,4(10:20~12:10) |
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上課地點 |
工綜213工綜207 |
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備註 |
本課程中文授課,使用英文教科書。高等應數(一)、(二)，只能擇一列為核心課程。如有外籍生選課則以英文授課。
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1031ChemE7016_ |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
高等化工應用數學一 |
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課程目標 |
大部分的化學工程問題都是非線
性的, 因此, 本這程著重在非線
性工程問題的解析工作.
偏重在數值線性代數與非線性解
析等方法. 特別重視動手寫程
式, 解決實際研究上遇到的
問題. |
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課程要求 |
作業約五次, 佔成績40%. 期中考
一次, 佔成績30%,期末報告一
份, 需寫程式解決實際研究
問題, 佔成績30%. |
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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 |
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參考書目 |
主要教科書
1. R. Seydel, Practical Bifurcation and Stability Analysis - from Equilibrium
to Chaos, 2nd, Springer-Verlag, 1994. An excellent book for computational
methods for nonlinear analysis.
2. M.E. Davis, Numerical Methods and Modeling for Chemical Engineers, John
Wiley & Sons, 1984. Easy to read. Some introduction of numerical softwares is
very nice.
3. B.A. Finlayson, Nonlinear Analysis in Chemical Engineering, McGraw-Hill,
1980. Emphasis on methods for solving nonlinear differential equations. Good
chapters on ODE and BVP (orthogonal collocation methods and finite element
methods), written from an engineering point of view.
Other references:
Numerical linear algebra
N.R. Amundson, Mathematical Methods in Chemical Engineering, Prentice-Hall,
1966. Linear Algebra with C.E. applications. Well worth reading.
G.W. Steward, Introduction of Matrix Computations, Academic Press, 1973.
Excellent discussion of numerical linear algebra.
A.R. Gourlay and G.A. Watson, Computation Methods for Matrix Eigenproblems,
Jone Wiley & Sons, 1970. A good text for eigenvalue calculation.
G.H. Golub and C.F. Van Loan, Matrix Computation, 2nd ed., John Hopkins Univ.
Press, 1989. Detailed text on numerical linear algebra.
W. W. Hager, Applied Numerical Linear Algebra, Prentice-Hall, 1988. Good
introductory text. The package Napack can be found in Netlib.
I.S. Duff, A.M. Erisman, and J.K. Reid, Direct Methods for Sparse Matrices,
Oxford Science, 1986. A well cited book on direct matrix methods for
sparsematrices. (Famous MA28 and MA48) can be obtained in Harwell subroutine
libraries)
Y.Saad, Iterative Methods for sparse Linear Systems, PWS, 1996. A good book on
Krylov Subspace based iterative matrix solvers. Some subroutines can be found
in Sparskid.
Ordinary differential equations
C.W. Gear, Numerical Initial-Value Problems in Ordinary Differential
Equations, Prentice-Hall, 1971. Overview of most solution techniques.
K.E. Brenan, S.L. Campbell, and L.R. Petzold, Numerical Solution of Initial-
Value Problems in Differential- Algebraic Equations, NorthHolland, 1989. A
good reference book for DASSL.
Partial differential equations
G.Strang and G.J. Fix, An Analysis of the Finite Element Method, Prentice-
Hall, 1973. Uncommonly readable treatment of FEM and its mathematical
underpinnings. The starting point for serious user.
G.F. Carey and J.T. Oden, Finite Elements, Vols. 1-6, Prentice-Hall, 1984.
Excellent books from fundamentals to applications.
J.C. strikwerda, Finite Difference Schemes and Partial Differential Equations,
Wadsworth & Brooks, 1989. Detailed analysis on finite difference schemes.
General numerical methods
G. Golub and J.M. Ortega, Scientific Computing-An introduction with Parallel
Computing, Academic Press, 1993. An excellent book for numerical methods (very
useful).
W.H. Press, S.A. Teukolsky, W.T. Vetterling, and B.P. Flannery, Numerical
Recipes - The Art of Scientific Computing, Cambridge, 1992. An excellent
source in the Numerical subroutines.
A. Iserles, A First Course in the Numerical Analysis of Differential
Equations, Cambridge, 1996. Very worth reading.
Nonlinear Analysis
G. Iooss and D.D. Joseph, Elementary Stability and Bifurcation Theory, 2nd
ED., Springer, 1990. A classic book on bifurcation theory.
S.h. Strogatz, Nonlinear dynamics and Chaos, Addison Wesley, 1994. An
exceptionally well written introduction to the modern theory of dynamics
system and differential equations, with many interesting applications.
P. Glendinning, Stability, Instability, and Chaos: An Introduction to the
theory of nonlinear differential equations, Cambridge, 1994. Many good
qualitative methods (e.g., perturbation methods) for nonlinear differential
equations, bifurcations, and chaos.
P.G. Drazi, Nonlinear Systems, Cambridge, 1992. A wide range of mathematical
tools and ideas for the solutions of nonlinear equations.
S.K. Scott, Chemical Chaos, Oxford, 1991. Excellent books on nonlinear
analysis of chemical reactions and reactors.
Where to find more information?
Find it WWW, e.g., http://www.netlib.org. Also use internet search in
Netscape.
(Netlib can be found at http://www.cdrom.com/pub/netlib/).
GAMS is also a good site to find all related numerical methods and tools. |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Midterm |
30% |
A three-hour written examination will be given. |
2. |
Homework |
40% |
All the homeworks require computer programming; programming languages are opened, Fortran, C++, etc.. |
3. |
Term project and presentation |
30% |
The term project requires computer programming and compare your own results with the reported ones. Students are asked for a 10-min presentation for their results. |
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週次 |
日期 |
單元主題 |
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第1週 |
09/16, 19 |
Introduction: what is nonlinear analysis? |
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第2週 |
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Basics of Linear Algebra, Algebraic Eigenvalue Problems |
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第3週 |
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Numerical Linear Algebra (LU Factorization, Norms and Solution Accuracy) |
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第4週 |
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Numerical Linear Algebra (LU Factorization, Norms and Solution Accuracy); homework Two; Maybe no classes (out of town) |
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第5週 |
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Nonlinear Algebraic Equations (Eigenvalue Computation) |
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第7週 |
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Nonlinear Algebraic Equations; homework three |
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第8週 |
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Basics of Bifurcation Theory (I) |
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第9週 |
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Basics of Bifurcation Theory (II) |
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第10週 |
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Continuation |
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第11週 |
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Midterm Exam. |
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第12週 |
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Initial Value Problems (I) |
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第13週 |
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Initial Value Problems (II) |
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第14週 |
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Boundary Value Problems |
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第15週 |
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Finite Element Methods |
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第16週 |
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Partial Differentiation Equations |
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第17週 |
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Term paper presentation |
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