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Practical Data Analysis in Chemistry, Volume 26 [Kõva köide]

(School of Environmental and Life Sciences, The University of Newcastle, Chemistry, Australia), (School of Environmental and Life Sciences, The University of Newcastle, Chemistry, Australia)
  • Formaat: Hardback, 340 pages, kõrgus x laius: 240x165 mm, kaal: 810 g, With 141 Matlab programs and 19 Excel spreadsheets provided; graphical output includes 185 figures.; Illustrations, unspecified
  • Sari: Data Handling in Science and Technology
  • Ilmumisaeg: 06-Jul-2007
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444530541
  • ISBN-13: 9780444530547
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  • Formaat: Hardback, 340 pages, kõrgus x laius: 240x165 mm, kaal: 810 g, With 141 Matlab programs and 19 Excel spreadsheets provided; graphical output includes 185 figures.; Illustrations, unspecified
  • Sari: Data Handling in Science and Technology
  • Ilmumisaeg: 06-Jul-2007
  • Kirjastus: Elsevier Science Ltd
  • ISBN-10: 0444530541
  • ISBN-13: 9780444530547
Teised raamatud teemal:
The majority of modern instruments are computerised and provide incredible amounts of data. Methods that take advantage of the flood of data are now available; importantly they do not emulate 'graph paper analyses' on the computer. Modern computational methods are able to give us insights into data, but analysis or data fitting in chemistry requires the quantitative understanding of chemical processes. The results of this analysis allows the modelling and prediction of processes under new conditions, therefore saving on extensive experimentation. Practical Data Analysis in Chemistry exemplifies every aspect of theory applicable to data analysis using a short program in a Matlab or Excel spreadsheet, enabling the reader to study the programs, play with them and observe what happens. Suitable data are generated for each example in short routines, this ensuring a clear understanding of the data structure. Chapter 2 includes a brief introduction to matrix algebra and its implementation in Matlab and Excel while Chapter 3 covers the theory required for the modelling of chemical processes. This is followed by an introduction to linear and non-linear least-squares fitting, each demonstrated with typical applications. Finally Chapter 5 comprises a collection of several methods for model-free data analyses.

* Includes a solid introduction to the simulation of equilibrium processes and the simulation of complex kinetic processes.
* Provides examples of routines that are easily adapted to the processes investigated by the reader
* 'Model-based' analysis (linear and non-linear regression) and 'model-free' analysis are covered
Preface ix
Symbols xiii
Introduction
1(6)
Matrix Algebra
7(22)
Matrices, Vectors, Scalars
8(18)
Elementary Matrix Operations
10(1)
Transposition
10(2)
Addition and Subtraction
12(4)
Multiplication
16(5)
Special Matrices
21(1)
Square Matrix
21(1)
Symmetric Matrix
22(1)
Diagonal Matrix
22(1)
Identity Matrix
23(1)
Inverse Matrix
24(1)
Orthogonal and Orthonormal Matrices
25(1)
Solving Systems of Linear Equations
26(3)
Physical/Chemical Models
29(72)
Beer-Lambert's Law
33(3)
Chromatography / Gaussian Curves
36(4)
Titrations, Equilibria, the Law of Mass Action
40(36)
A Simple Case: Fe3+ + SCN-
40(3)
The General Case, Definitions
43(2)
A Chemical Example, Cu2+, Ethylenediamine, Protons
45(3)
Solving Complex Equilibria
48(1)
The Newton-Raphson Algorithm
48(8)
Example: General 3-Component Titration
56(2)
Example: pH Titration of Acetic Acid
58(2)
Equilibria in Excel
60(2)
Complex Equilibria Including Activity Coefficients
62(2)
Special Case: Explicit Calculation for Polyprotic Acids
64(5)
Solving Non-Linear Equations
69(1)
One Equation, One Parameter
69(2)
Systems of Non-Linear Equations
71(5)
Kinetics, Mechanisms, Rate Laws
76(25)
The Rate Law
77(1)
Rate Laws with Explicit Solutions
77(3)
Complex Mechanisms that Require Numerical Integration
80(1)
The Euler Method
80(2)
Fourth Order Runge-Kutta Method in Excel
82(4)
Interesting Kinetic Examples
86(1)
Autocatalysis
87(2)
Oth Order Reaction
89(2)
The Steady-State Approximation
91(1)
Lotka-Volterra / Predator-Prey Systems
92(3)
The Belousov-Zhabotinsky (BZ) Reaction
95(2)
Chaos, the Lorenz Attractor
97(4)
Model-Based Analyses
101(112)
Background to Least-Squares Methods
102(7)
The Residuals and the Sum of Squares
103(1)
Linear Example: Straight Line
103(2)
Non-Linear Example: Exponential Decay
105(4)
Linear Regression
109(39)
Straight Line Fit - Classical Derivation
109(4)
Matrix Notation
113(1)
Generalised Matrix Notation
114(1)
The Normal Equations
115(2)
The Pseudo-Inverse
117(2)
Linear Dependence, Rank of a Matrix
119(1)
Numerical Difficulties
120(1)
Errors in the Fitted Parameters
121(4)
Excel Linest
125(2)
Applications of Linear Least-Squares Fitting
127(1)
Linearisation of Non-Linear Problems
127(3)
Polynomials, the Savitzky-Golay Digital Filter
130(1)
Smoothing of Noisy Data
131(4)
Calculation of the Derivative of a Curve
135(3)
Polynomial Interpolation
138(1)
Linear Regression with Multivariate Data
139(4)
Applications
143(1)
Computation of Component Spectra, Known Concentrations
144(1)
Computation of Component Concentrations, Known Spectra
145(1)
The Pseudo-Inverse in Excel
146(2)
Non-Linear Regression
148(50)
The Newton-Gauss-Levenberg/Marquardt Algorithm
148(1)
A First, Minimal Algorithm
149(4)
Termination Criterion, Numerical Derivatives
153(2)
The Levenberg/Marquardt Extension
155(6)
Standard Errors of the Parameters
161(1)
Multivariate Data, Separation of the Linear and Non-Linear Parameters
162(6)
Constraint: Positive Component Spectra
168(1)
Structures, Fixing Parameters
169(6)
Known Spectra, Uncoloured Species
175(5)
Reduced Eigenvector Space
180(3)
Global Analysis
183(6)
Non-White Noise, Χ2-Fitting
189(1)
Linear Χ2-Fitting
190(5)
Non-Linear Χ2-Fitting
195(2)
Finding the Correct Model
197(1)
General Optimisation
198(15)
The Newton-Gauss Algorithm
198(6)
The Simplex Algorithm
204(3)
Optimisation in Excel, the Solver
207(4)
Χ2-Fitting in Excel
211(2)
Model-Free Analyses
213(100)
Factor Analysis, FA
213(33)
The Singular Value Decomposition, SVD
214(3)
The Rank of a Matrix
217(2)
Magnitude of the Singular Values
219(2)
The Structure of the Eigenvectors
221(1)
The Structure of the Residuals
222(1)
The Standard Deviation of the Residuals
223(1)
Geometrical Interpretations
224(1)
Two Components
224(4)
Reduction in the Number of Dimensions
228(3)
Lawton-Sylvestre
231(4)
Three and More Components
235(4)
Mean Centring, Closure
239(2)
HELP Plots
241(2)
Noise Reduction
243(3)
Target Factor Analyses, TFA
246(13)
Projection Matrices
250(1)
Iterative Target Transform Factor Analysis, ITTFA
251(2)
Target Transform Search/Fit
253(4)
Parameter Fitting via Target Testing
257(2)
Evolving Factor Analyses, EFA
259(21)
Evolving Factor Analysis, Classical EFA
260(8)
Fixed-Size Window EFA, FSW-EFA
268(3)
Secondary Analyses Based on Window Information
271(1)
Iterative Refinement of the Concentration Profiles
271(5)
Explicit Computation of the Concentration Profiles
276(4)
Alternating Least-Squares, ALS
280(10)
Initial Guesses for Concentrations or Spectra
281(1)
Alternating Least-Squares and Constraints
282(6)
Rotational Ambiguity
288(2)
Resolving Factor Analysis, RFA
290(5)
Principle Component Regression and Partial Least Squares, PCR and PLS
295(18)
Principal Component Regression, PCR
296(1)
Mean-Centring, Normalisation
297(1)
PCR Calibration
298(2)
PCR Prediction
300(3)
Cross Validation
303(3)
Partial Least Squares, PLS
306(2)
PLS calibration
308(1)
PLS Prediction / Cross Validation
309(1)
Comparing PCR and PLS
310(3)
Further Reading 313(4)
List of Matlab Files 317(4)
List of Excel Sheets 321(1)
Index 322