Elsevier S & T

Practical Data Analysis in Chemistry

Maeder, Marcel; Neuhold, Yorck-Michael

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Table of contents
  • Cover
  • Table of Contentsv
  • PREFACEix
  • SYMBOLSxiii
  • Chapter 1 INTRODUCTION1
  • Chapter 2 MATRIX ALGEBRA7
  • 2.1 Matrices, Vectors, Scalars8
  • 2.1.1 Elementary Matrix Operations10
  • Transposition10
  • Addition and Subtraction12
  • Multiplication16
  • 2.1.2 Special Matrices21
  • Square Matrix21
  • Symmetric Matrix22
  • Diagonal Matrix22
  • Identity Matrix23
  • Inverse Matrix24
  • Orthogonal and Orthonormal Matrices25
  • 2.2 Solving Systems of Linear Equations26
  • Chapter 3 PHYSICAL/CHEMICAL MODELS29
  • 3.1 Beer-Lambert's Law33
  • 3.2 Chromatography / Gaussian Curves36
  • 3.3 Titrations, Equilibria, the Law of Mass Action40
  • 3.3.1 A Simple Case: Fe3+ + SCN-40
  • 3.3.2 The General Case, Definitions43
  • A Chemical Example, Cu2+, Ethylenediamine, Protons45
  • 3.3.3 Solving Complex Equilibria48
  • The Newton-Raphson Algorithm48
  • Example: General 3-Component Titration56
  • Example: pH Titration of Acetic Acid58
  • Equilibria in Excel60
  • Complex Equilibria Including Activity Coefficients62
  • Special Case: Explicit Calculation for Polyprotic Acids64
  • 3.3.4 Solving Non-Linear Equations69
  • One Equation, One Parameter69
  • Systems of Non-Linear Equations71
  • 3.4 Kinetics, Mechanisms, Rate Laws76
  • 3.4.1 The Rate Law77
  • 3.4.2 Rate Laws with Explicit Solutions77
  • 3.4.3 Complex Mechanisms that Require Numerical Integration80
  • The Euler Method80
  • Fourth Order Runge-Kutta Method in Excel82
  • 3.4.4 Interesting Kinetic Examples86
  • Autocatalysis87
  • 0th Order Reaction89
  • The Steady-State Approximation91
  • Lotka-Volterra / Predator-Prey Systems92
  • The Belousov-Zhabotinsky (BZ) Reaction95
  • Chaos, the Lorenz Attractor97
  • Chapter 4 MODEL-BASED ANALYSES101
  • 4.1 Background to Least-Squares Methods102
  • 4.1.1 The Residuals and the Sum of Squares103
  • Linear Example: Straight Line103
  • Non-Linear Example: Exponential Decay105
  • 4.2 Linear Regression109
  • 4.2.1 Straight Line Fit - Classical Derivation109
  • 4.2.2 Matrix Notation113
  • 4.2.3 Generalised Matrix Notation114
  • 4.2.4 The Normal Equations115
  • The Pseudo-Inverse117
  • Linear Dependence, Rank of a Matrix119
  • Numerical Difficulties120
  • 4.2.5 Errors in the Fitted Parameters121
  • 4.2.6 Excel Linest125
  • 4.2.7 Applications of Linear Least-Squares Fitting127
  • Linearisation of Non-Linear Problems127
  • Polynomials, the Savitzky-Golay Digital Filter130
  • Smoothing of Noisy Data131
  • Calculation of the Derivative of a Curve135
  • Polynomial Interpolation138
  • 4.2.8 Linear Regression with Multivariate Data139
  • Applications143
  • Computation of Component Spectra, Known Concentrations144
  • Computation of Component Concentrations, Known Spectra145
  • The Pseudo-Inverse in Excel146
  • 4.3 Non-Linear Regression148
  • 4.3.1 The Newton-Gauss-Levenberg/Marquardt Algorithm148
  • A First, Minimal Algorithm149
  • Termination Criterion, Numerical Derivatives153
  • The Levenberg/Marquardt Extension155
  • Standard Errors of the Parameters161
  • Multivariate Data, Separation of the Linear and Non-Linear Parameters162
  • Constraint: Positive Component Spectra168
  • Structures, Fixing Parameters169
  • Known Spectra, Uncoloured Species175
  • Reduced Eigenvector Space180
  • Global Analysis183
  • 4.3.2 Non-White Noise, Chi 2-Fitting189
  • Linear Chi 2-Fitting190
  • Non-Linear Chi 2-Fitting195
  • 4.3.3 Finding the Correct Model197
  • 4.4 General Optimisation198
  • 4.4.1 The Newton-Gauss Algorithm198
  • 4.4.2 The Simplex Algorithm204
  • 4.4.3 Optimisation in Excel, the Solver207
  • Chi 2-Fitting in Excel211
  • Chapter 5 MODEL-FREE ANALYSES213
  • 5.1 Factor Analysis, FA213
  • 5.1.1 The Singular Value Decomposition, SVD214
  • 5.1.2 The Rank of a Matrix217
  • Magnitude of the Singular Values219
  • The Structure of the Eigenvectors221
  • The Structure of the Residuals222
  • The Standard Deviation of the Residuals223
  • 5.1.3 Geometrical Interpretations224
  • Two Components224
  • Reduction in the Number of Dimensions228
  • Lawton-Sylvestre231
  • Three and More Components235
  • Mean Centring, Closure239
  • HELP Plots241
  • Noise Reduction243
  • 5.2 Target Factor Analyses, TFA246
  • 5.2.1 Projection Matrices250
  • 5.2.2 Iterative Target Transform Factor Analysis, ITTFA251
  • 5.2.3 Target Transform Search/Fit253
  • Parameter Fitting via Target Testing257
  • 5.3 Evolving Factor Analyses, EFA259
  • 5.3.1 Evolving Factor Analysis, Classical EFA260
  • 5.3.2 Fixed-Size Window EFA, FSW-EFA268
  • 5.3.3 Secondary Analyses Based on Window Information271
  • Iterative Refinement of the Concentration Profiles271
  • Explicit Computation of the Concentration Profiles276
  • 5.4 Alternating Least-Squares, ALS280
  • 5.4.1 Initial Guesses for Concentrations or Spectra281
  • 5.4.2 Alternating Least-Squares and Constraints282
  • 5.4.3 Rotational Ambiguity288
  • 5.5 Resolving Factor Analysis, RFA290
  • 5.6 Principle Component Regression and Partial Least Squares, PCR and PLS295
  • 5.6.1 Principal Component Regression, PCR296
  • Mean-Centring, Normalisation297
  • PCR Calibration298
  • PCR Prediction300
  • Cross Validation303
  • 5.6.2 Partial Least Squares, PLS306
  • PLS calibration308
  • PLS Prediction / Cross Validation309
  • 5.6.3 Comparing PCR and PLS310
  • FURTHER READING313
  • LIST OF MATLAB FILES317
  • LIST OF EXCEL SHEETS321
  • INDEX322
Book details
  • Vendor Elsevier S & T
  • SKU 9780444530547
  • ISBN-13 9780080548838
  • Author Maeder, Marcel; Neuhold, Yorck-Michael
  • Category Science
  • Subject Analytic

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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