{"product_id":"mathematical-methods-for-physical-and-analytical-chemistry-isbn-9780470473542","title":"Mathematical Methods for Physical and Analytical Chemistry","description":"\u003ci\u003eMathematical Methods for Physical and Analytical Chemistry\u003c\/i\u003e presents mathematical and statistical methods to students of chemistry at the intermediate, post-calculus level. The content includes a review of general calculus; a review of numerical techniques often omitted from calculus courses, such as cubic splines and Newton’s method; a detailed treatment of statistical methods for experimental data analysis; complex numbers; extrapolation; linear algebra; and differential equations. With numerous example problems and helpful anecdotes, this text gives chemistry students the mathematical knowledge they need to understand the analytical and physical chemistry professional literature. Preface xiii \u003cp\u003eList of Examples xv\u003c\/p\u003e \u003cp\u003eGreek Alphabet xix\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart I. Calculus\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Functions: General Properties 3\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Mappings 3\u003c\/p\u003e \u003cp\u003e1.2 Differentials and Derivatives 4\u003c\/p\u003e \u003cp\u003e1.3 Partial Derivatives 7\u003c\/p\u003e \u003cp\u003e1.4 Integrals 9\u003c\/p\u003e \u003cp\u003e1.5 Critical Points 14\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Functions: Examples 19\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Algebraic Functions 19\u003c\/p\u003e \u003cp\u003e2.2 Transcendental Functions 21\u003c\/p\u003e \u003cp\u003e2.3 Functional 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Coordinate Systems 33\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Points in Space 33\u003c\/p\u003e \u003cp\u003e3.2 Coordinate Systems for Molecules 35\u003c\/p\u003e \u003cp\u003e3.3 Abstract Coordinates 37\u003c\/p\u003e \u003cp\u003e3.4 Constraints 39\u003c\/p\u003e \u003cp\u003e3.5 Differential Operators in Polar Coordinates 43\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Integration 47\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Change of Variables in Integrands 47\u003c\/p\u003e \u003cp\u003e4.2 Gaussian Integrals 51\u003c\/p\u003e \u003cp\u003e4.3 Improper Integrals 53\u003c\/p\u003e \u003cp\u003e4.4 Dirac Delta Function 56\u003c\/p\u003e \u003cp\u003e4.5 Line Integrals 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Numerical Methods 61\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Interpolation 61\u003c\/p\u003e \u003cp\u003e5.2 Numerical Differentiation 63\u003c\/p\u003e \u003cp\u003e5.3 Numerical Integration 65\u003c\/p\u003e \u003cp\u003e5.4 Random Numbers 70\u003c\/p\u003e \u003cp\u003e5.5 Root Finding 71\u003c\/p\u003e \u003cp\u003e5.6 Minimization* 74\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Complex Numbers 79\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Complex Arithmetic 79\u003c\/p\u003e \u003cp\u003e6.2 Fundamental Theorem of Algebra 81\u003c\/p\u003e \u003cp\u003e6.3 The Argand Diagram 83\u003c\/p\u003e \u003cp\u003e6.4 Functions of a Complex Variable* 87\u003c\/p\u003e \u003cp\u003e6.5 Branch Cuts* 89\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Extrapolation 93\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Taylor Series 93\u003c\/p\u003e \u003cp\u003e7.2 Partial Sums 97\u003c\/p\u003e \u003cp\u003e7.3 Applications of Taylor Series 99\u003c\/p\u003e \u003cp\u003e7.4 Convergence 102\u003c\/p\u003e \u003cp\u003e7.5 Summation Approximants* 104\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart II. Statistics\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Estimation 111\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Error and Estimation Ill\u003c\/p\u003e \u003cp\u003e8.2 Probability Distributions 113\u003c\/p\u003e \u003cp\u003e8.3 Outliers 124\u003c\/p\u003e \u003cp\u003e8.4 Robust Estimation 126\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Analysis of Significance 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Confidence Intervals 131\u003c\/p\u003e \u003cp\u003e9.2 Propagation of Error 136\u003c\/p\u003e \u003cp\u003e9.3 Monte Carlo Simulation of Error 139\u003c\/p\u003e \u003cp\u003e9.4 Significance of Difference 140\u003c\/p\u003e \u003cp\u003e9.5 Distribution Testing* 144\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Fitting 151\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Method of Least Squares 151\u003c\/p\u003e \u003cp\u003e10.2 Fitting with Error in Both Variables 157\u003c\/p\u003e \u003cp\u003e10.3 Nonlinear Fitting 162\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Quality of Fit 165\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Confidence Intervals for Parameters 165\u003c\/p\u003e \u003cp\u003e11.2 Confidence Band for a Calibration Line 168\u003c\/p\u003e \u003cp\u003e11.3 Outliers and Leverage Points ' 171\u003c\/p\u003e \u003cp\u003e11.4 Robust Fitting* 173\u003c\/p\u003e \u003cp\u003e11.5 Model Testing 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12\u003c\/b\u003e Experiment \u003cb\u003eDesign 181\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Risk Assessment 181\u003c\/p\u003e \u003cp\u003e12.2 Randomization 185\u003c\/p\u003e \u003cp\u003e12.3 Multiple Comparisons 188\u003c\/p\u003e \u003cp\u003e12.4 Optimization* 195\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart III. Differential Equations\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Examples of Differential Equations 203\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Chemical Reaction Rates 203\u003c\/p\u003e \u003cp\u003e13.2 Classical Mechanics 205\u003c\/p\u003e \u003cp\u003e13.3 Differentials in Thermodynamics 212\u003c\/p\u003e \u003cp\u003e13.4 Transport Equations 213\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 Solving Differential Equations, I 217\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 Basic Concepts 217\u003c\/p\u003e \u003cp\u003e14.2 The Superposition Principle 220\u003c\/p\u003e \u003cp\u003e14.3 First-Order ODE's 222\u003c\/p\u003e \u003cp\u003e14.4 Higher-Order ODE's 225\u003c\/p\u003e \u003cp\u003e14.5 Partial Differential Equations 228\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Solving Differential Equations, II 231\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Numerical Solution 231\u003c\/p\u003e \u003cp\u003e15.2 Chemical Reaction Mechanisms 236\u003c\/p\u003e \u003cp\u003e15.3 Approximation Methods 239\u003c\/p\u003e \u003cp\u003e\u003cb\u003ePart IV. Linear Algebra\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Vector Spaces 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Cartesian Coordinate Vectors 247\u003c\/p\u003e \u003cp\u003e16.2 Sets 248\u003c\/p\u003e \u003cp\u003e16.3 Groups 249\u003c\/p\u003e \u003cp\u003e16.4 Vector Spaces 251\u003c\/p\u003e \u003cp\u003e16.5 Functions as Vectors 252\u003c\/p\u003e \u003cp\u003e16.6 Hilbert Spaces 253\u003c\/p\u003e \u003cp\u003e16.7 Basis Sets 256\u003c\/p\u003e \u003cp\u003e\u003cb\u003e17 Spaces of Functions 261\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e17.1 Orthogonal Polynomials 261\u003c\/p\u003e \u003cp\u003e17.2 Function Resolution 267\u003c\/p\u003e \u003cp\u003e17.3 Fourier Series 270\u003c\/p\u003e \u003cp\u003e17.4 Spherical Harmonics 275\u003c\/p\u003e \u003cp\u003e\u003cb\u003e18 Matrices 279\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e18.1 Matrix Representation of Operators 279\u003c\/p\u003e \u003cp\u003e18.2 Matrix Algebra 282\u003c\/p\u003e \u003cp\u003e18.3 Matrix Operations 284\u003c\/p\u003e \u003cp\u003e18.4 Pseudoinverse* 286\u003c\/p\u003e \u003cp\u003e18.5 Determinants 288\u003c\/p\u003e \u003cp\u003e18.6 Orthogonal and Unitary Matrices 290\u003c\/p\u003e \u003cp\u003e18.7 Simultaneous Linear Equations 292\u003c\/p\u003e \u003cp\u003e\u003cb\u003e19 Eigenvalue Equations 297\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e19.1 Matrix Eigenvalue Equations 297\u003c\/p\u003e \u003cp\u003e19.2 Matrix Diagonalization 301\u003c\/p\u003e \u003cp\u003e19.3 Differential Eigenvalue Equations 305\u003c\/p\u003e \u003cp\u003e19.4 Hermitian Operators 306\u003c\/p\u003e \u003cp\u003e19.5 The Variational Principle* 309\u003c\/p\u003e \u003cp\u003e\u003cb\u003e20 Schrödinger's Equation 313\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e20.1 Quantum Mechanics 313\u003c\/p\u003e \u003cp\u003e20.2 Atoms and Molecules 319\u003c\/p\u003e \u003cp\u003e20.3 The One-Electron Atom 321\u003c\/p\u003e \u003cp\u003e20.4 Hybrid Orbitals 325\u003c\/p\u003e \u003cp\u003e20.5 Antisymmetry* 327\u003c\/p\u003e \u003cp\u003e20.6 Molecular Orbitals* 329\u003c\/p\u003e \u003cp\u003e\u003cb\u003e21 Fourier Analysis 333\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e21.1 The Fourier Transform 333\u003c\/p\u003e \u003cp\u003e21.2 Spectral Line Shapes* 336\u003c\/p\u003e \u003cp\u003e21.3 Discrete Fourier Transform* 339\u003c\/p\u003e \u003cp\u003e21.4 Signal Processing 342\u003c\/p\u003e \u003cp\u003e\u003cb\u003eA Computer Programs 351\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.l Robust Estimators 351\u003c\/p\u003e \u003cp\u003eA.2 FREML 352\u003c\/p\u003e \u003cp\u003eA.3 Neider-Mead Simplex Optimization 352\u003c\/p\u003e \u003cp\u003e\u003cb\u003eB Answers to Selected Exercises 355\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003cb\u003eC Bibliography 367\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eIndex 373\u003c\/p\u003e  \u003cp\u003e“Finally it can be said that this book helps to refresh and extend the knowledge about mathematical and statistical methods to be used for physico-chemical or analytical applications.”  (\u003ci\u003eMaterials and Corrosion\u003c\/i\u003e, 1 November 2012)\u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cp\u003e \u003c\/p\u003e \u003cb\u003eDavid Z. Goodson\u003c\/b\u003e, Associate Professor of Chemistry at the University of Massachusetts Dartmouth, has a BA in chemistry from Pomona College and a PhD in chemical physics from Harvard University. An interdisciplinary scientist, he is author of numerous articles on a wide range of topics including quantum chemistry, molecular spectroscopy, reaction rate theory, atomic physics, and applied mathematics.  \u003cb\u003eBridging the gap between undergraduate calculus and the mathematics of chemistry\u003c\/b\u003e  \u003cp\u003eA focused presentation of statistical and advanced mathematical methods likely to be encountered by chemists, \u003ci\u003eMathematical Methods for Physical and Analytical Chemistry\u003c\/i\u003e can serve as a text for a one-semester course at the undergraduate or graduate level, or as a resource for independent study by students and professionals in all areas of chemistry and in related fields such as environmental science, geochemistry, and chemical engineering.\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematical Methods for Physical and Analytical Chemistry\u003c\/i\u003e covers:\u003c\/p\u003e \u003cp\u003e\u003cb\u003eCALCULUS\u003c\/b\u003e—review of the basics, coordinate systems, degrees of freedom, special functions, numerical methods, complex numbers, singular points, improper integrals, Taylor series\u003c\/p\u003e \u003cp\u003e\u003cb\u003eSTATISTICS\u003c\/b\u003e—probability theory, distribution functions, confidence intervals, propagation of error, significance of difference, ANOVA, method of least squares, calibration, model testing, fits with error in both variables, experiment design, randomization, optimization\u003c\/p\u003e \u003cp\u003e\u003cb\u003eDIFFERENTIAL EQUATIONS\u003c\/b\u003e—chemical reaction rate equations, Lagrangian and Hamiltonian mechanics, transport equations, the superposition principle, separation of variables, methods for exact, approximate, and numerical solutions\u003c\/p\u003e \u003cp\u003e\u003cb\u003eLINEAR ALGEBRA\u003c\/b\u003e—groups, Hilbert spaces, basis sets, matrices, determinants, orthogonal polynomials, spherical harmonics, Fourier series, eigenvalue equations, diagonalization, Fourier transform, spectral lineshapes, convolution, principles of quantum mechanics, Schrödinger's equation, hydrogen orbitals, hybrid orbitals, molecular orbitals\u003c\/p\u003e \u003cp\u003e\u003ci\u003eMathematical Methods for Physical and Analytical Chemistry\u003c\/i\u003e features:\u003c\/p\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eModern topics such as Monte Carlo simulation, robust estimation, and discrete Fourier transform, which are otherwise available only in more specialized texts\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eNumerous figures and worked out examples and more than 200 exercises, many of which take advantage of computer algebra\u003c\/p\u003e \u003c\/li\u003e \u003cli\u003e \u003cp\u003eAn annotated bibliography of references for further study\u003c\/p\u003e \u003c\/li\u003e \u003c\/ul\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989586493669,"sku":"NP9780470473542","price":129.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780470473542.jpg?v=1761784705","url":"https:\/\/k12savings.com\/products\/mathematical-methods-for-physical-and-analytical-chemistry-isbn-9780470473542","provider":"K12savings","version":"1.0","type":"link"}