2 Index#

2D diffusion in a plate 11-4.13

2D Fourier Transforms 9-, 9-12

2D Ising spin 12-6.10

Abcd matrix 7-9

Absolute value 1-4.3, 2-1.2, 2-1.4, 2-1.5, 2-4.2, 4-4, 4-5.1, 5-9.1, 6-1.1, 6-2.1, 6-3, 6-11, 6-15, 6-15.1 to 6-15.4, 6-16, 7-6.12, 9-5.4, 9-6, 9-6.1, 9-6.3 to 9-6.7, 9-8.3, 9-9.2, 9-9.6, 9-10.5, 9-12, 9-13.1, 9-13.2, 9-13.7, 9-14.4, 10-17, 11-2.1, 11-3.2, 13-3.6, 13-10.2

Activation energy 10-2.4, 10-5.5, 12-2.1, 13-6.1

Adiabatic change 3-11.1

Adjoint 7-4.7, 8-4.1

Adjoint matrix 7-4.7

AFM 1-9.25, 10-12.1, 10-13.2

Airy 9-12, 10-18.1, 10-18.2

Algae/ Algal bloom 10-15.7

Aliasing 9-9.5, 9-9.7

Ammonia inversion 11-10, 11-10.1, 11-10.2

Analysis of variance 13-6.6

Analytic Signal 9-10.5

Angular frequency 1-5.2, 6-21.1, 7-14.2, 7-15.2, 8-3, 9-1.2, 9-6.3, 9-6.7, 9-7.4, 9-9.6, 10-11, 11-6.4

Angular momentum 1-8, 1-9.9, 4-12.6, 5-5.3, 5-6.10, 6-2.2, 6-21, 7-, 7-5.3, 7-12.9, 7-15.2 7-16, 7-16.1 8-2, 8-3, 8-4.2, 8-4.3, 9-4.1, 9-8.6, 10-2.4, 10-3.2, 11-3.7, 11-6.4, 13-7.4

Anharmonic oscillator 3-3.16, 5-9, 8-2, 10-3.3, 11-10.1, 12-6.1

Annihilation 10-2.4

ANOVA 13-6.6

Antenna 7-3.1, 7-13.2, 10-15.1, 12-4.1

Anti-bonding 4-12.1, 4-12.5, 6-14

Apodising 9-5.2, 9-5.6, 9-9.7, 9-10.2

Arc length 4-7, 4-13.3, 6-6

Arcsin 1-6,

Argand 2-1, 2-1.4, 2-3.3, 7-2.4, 9-9.1

Arithmetic and Geometric progressions 1-12

Arithmetic mean 1-2.3

Arrhenius 1-9.27, 3-7.1, 10-5.5, 11-5.3, 13-6.1

Arrhenius equation 10-5.5, 11-5.3

Asymmetric boundary conditions 10-16.2

Atomic force microscope 1-9.25, 10-12.1, 10-13.2

Atomic orbital 4-10.2, 6-14, 7-3.2, 7-6.16

Atomic Structure Factors 2-4.2, 9-13.5

Atomic units 4-9.1, 7-3.2, 11-10.1, 11-10.2, 14-1.4

Autocatalytic reaction 10-3.1, 11-7, 12-5

Autocorrelation 9-5.2, 9-8, 9-8.1 to 9-8.7, 13-6.4

Auxiliary equations 10-12.3

Average as a summation 4-8.1

Average as an integration 4-8.2

Average energy 5-4.1, 5-5.1, 5-5.3, 5-9, 9-8.6, 10-12.1, 12-6.1, 12-6.7, 13-3.8

Average of a function 4-8.3, 5-6.10

Average value 1-2.3, 1-9.22, 1-9.27, 4-2.8, 4-8, 4-8.1 to 4-8.4, 5-4, 5-5.3, 5-6.10, 5-8.2, 8-2, 9-6.7, 9-8.2, 10-4.9, 10-10.5, 10-12.1, 11-4.10, 12-1.2, 12-3.1, 12-4.1, 12-6.1, 13-1.1

AX spectra 8-3.1

Back projection 9-14.4, 9-14.6, 9-14.7

Bacteriorhodopsin 6-18, 7-9

Base units 7-15.1

Basis set 4-9.2, 4-12.4, 5-8.1, 6-1.1, to 6-1.3, 6-2.1, 6-2.5, to 6-2.9, 6-4, 6-8.1, 6-9, 6-10.1, 6-12, to 6-15.2, 6-16, 6-18, 7-3.1, 7-3.2, 7-4.4, 7-5.6, 7-6.8, 7-6.9, 7-6.15, 7-7, 7-9, 7-12.4, to 7-12.9, 7-13.4, 7-14.2, 8-1, 8-2.1 to 8-2.4, 8-3, 8-4.1 to 8-4.3, 8-5.1, 9-3, 9-4, 11-5.6, 13-11

Basis sets in molecules 6-14

Basis vectors 6-2.1, 6-2.5, 6-9.1, 6-10, 6-12, 6-16, 7-6.13, 7-6.16, 7-12.8, 7-16, 8-2.1, 8-4.2

Beam scattering 11-3.6

Beam waist 7-10

Beating 1-5.2, 7-14.1, 9-9.5

Bending motion 7-14.5, 7-14.6

Benjamin Franklin 1-13.3

Bernoulli equation 10-9.4

Best plane 6-15.6

Bifurcation 11-1.4

Bimolecular reactions 10-4.1,

Binomial distribution 1-9.16, to 1-9.27, 3-3.13, 12-3.2, 13-8

Binomial expansion 1-9.4, 1-9.16, 5-6.8

Biological membrane 10-16.1

Bisection method 11-2.1, 11-3.8, 11-3.10, 11-10.1

Bjerrum s 11-3.4

Black-body 9-6.6

Bloch equations 10-13.3

Block diagonal 7-5.6, 7-12.9

Body-centred 2-4.2, 9-13.4

Bohr radius 4-12.1, 11-10.2

Boltzmann distribution 3-10, 4-8.1, 5-4.1, 5-5.3, 12-1.3, 12-6.1, 12-6.2, 13-3.8

Bond angle 6-10.1, 7-6.16, 7-14.6

Bond length 1-9.25, 4-12.4, 4-12.5, 6-8.3, 6-10.1, 7-6.14, 7-12.2, 7-14.5, 7-14.6, 7-15.1, 8-2.2, 9-13.5, 9-13.9

Bond rotation 5-5.1

Bonding 4-12.1, 6-14, 6-18, 7-2.4, 7-14.4

Bones 1-4, 3-9

Born-Oppenheimer Approximation 4-12.1, 7-3.2

Boundary value problems 10-1.3

Bra-ket notation 5-8.1, 7-5, 7-5.2, 8-2, 8-4.2

Brachistochrone 3-8.2

Bragg diffraction 9-13.3

Brownian motion 10-12.1

Butadiene 6-14, 7-3

Calculating the structure factors 9-13.8

Calculus of Variations 3-8

CAT scan 9-14.1

Central Limit Theorem 13-2, 13-3, 13-6.2, 13-9

Centre of inversion 7-6.3, 7-6.4, 9-12, 11-10.1, 13-7.4

Centrifugal energy 11-3.7

Centrifuge 4-1.4, 10-6

Centripetal force 10-6

Centroids 4-8.2, 4-10.1

Chain reactions 4-8.1

Chain rule 3-4.1, 3-4.2, 3-11.4, to 3-11.8, 10-3.2, 11-6.2, 11-6.4, 11-7.2

Change of variables 4-11

Chaos 11-1.4, 11-2.1

Character 6-18, 7-4.4, 7-6.1, to 7-6.16

Character table 7-6.1, 7-6.2, 7-6.8, 7-6.9, 7-6.12, 7-6.13

Characteristic equation 7-2.1, 7-3, 7-5.7, 7-10, 7-12.6, 7-13.2, to 7-13.5, 7-14.2, 10-12.1, 10-13.1, 10-13.4, 10-14.1

Chauvenet s criterion 13-3.6

Chemical bond 4-12.4, 4-12.5, 7-, 7-14.2, 8-3, 11-4.7

Chemical kinetics 1-4, 3-1, 3-3.2, 7-4, 7-9, 7-12.4, 7-12.9, 7-13.1, 7-13.4, 10-4, 10-5, 10-12, 10-13.2, 11-5.1, 12-2.2, 13-10.1

Chemical Thermodynamics 3-3.12, 4-14

Chi squared 13-6.2, 13-6.4, 13-7.4

Chromatography 1-9.22, 1-9.25, 4-8.2, 10-15.8

Circulant determinant/matrix 7-3.1, 7-13.2, 9-9.3, 9-11.5

Classical harmonic oscillator 12-6.2

Cofactor 7-2.2, 7-4.9, 7-12.6

Colliding molecules 6-2.10

Comb of delta functions 9-6.6, 9-12

Combinations 1-9.1, 1-9.3, 1-9.4, 1-9.5, 1-9.6, 1-9.8, 1-9.9, 1-9.14, 4-9.2, 5-8.1, 5-9.1, 6-9.1, 6-12, 6-14, 6-15, 7-6.16, 7-12.9, 8-3, 8-4.2, 10-15.5, 10-17, 10-18.2, 12-2.2, 12-3.2, 12-6.1, 12-6.6, 12-6.7, 13-11

Commutation/commutator 7-5.3

Comparison of two means 13-3.5

Complement 1-9.13, 1-9.15

Complementary function 10-12.5 to 10-12.9

Complex conjugate 2-1 to 2-1.5, 2-4.2, 4-8.4, 4-9.2, 4-10.2, 4-12.1, 5-8.1, 5-8.2, 5-9.1, 6-2.9, 7-3.1, 7-3.2, 7-4.6 to 7-4.8, 7-5.2, 7-13.2, 8-1.1, 8-2, 8-4.1, 9-4, 9-6.1 to 9-6.8, 9-8.2, to 9-8.4, 10-18.2

Component of vector 6-6

Compound pendulum 10-11.1

Computed tomography 9-14.1

Concentration of ion pairs 11-3.4

Concentration profile 10-4.8, 10-15.1, 10-15.6 to 10-15.9, 10-16.1, 10-16.3, 10-18.4, 11-4.11

Conditional probability 1-9.14, 1-9.15

Confidence intervals 13-3, 13-3.5, 13-6.5

Confidence limits 13-3, 13-3.1, 13-3.2, 13-3.5, 13-6.2, 13-6.5, 13-7.6

Configuration 1-9.9, 5-5.1, 6-19, 6-19.1, 7-14.3, 12-6.1, to 12-6.5, 12-6.10

Confocal beam length 7-10

Conservation of momentum 6-1.5, 9-13.1, 10-10.4

Continuous basis set 8-4.3, 8-5.1

Convergence 1-2.2, 5-1.1, 5-3, 5-6.7, 5-7, 9-1.8, 10-8.1, 11-3.1, 11-3.3

Converting axes 6-9.1, 6-10.1

Convolution 9-5.6, 9-7.1 to 9-7.5, 9-8.2, 9-8.3, 9-10.1, 9-10.4, 9-12, 9-14.4, 10-16.1, 10-18.4

Convolution by fourier transform 9-7.4

Correlation coefficients 13-6.7

Cosh 1-5.6, 1-6, 3-3.10, 3-8.1, 4-2.7, 4-2.14, 4-8.3, 10-11.2, 12-6.9

Cosine and tangent 4-2.6

Cosine integral 4-2.6, 9-1.6

Coulomb integral 4-12.3

Coulomb potential 7-14, 7-14.2, 11-3.9, 11-4.5, to 11-4.7, 11-5.1, to 11-5.5, 11-6.3, 11-7, 11-9.1

Coupled springs 10-13.4

Coupling between two spins 7-12.9

Crank-Nicholson 11-4.12, 11-4.13

Critical point 3-11.2

Critical temperature 3-11.2, 11-5.4

Cross product 3-4.10, 6-2.2, 6-2.3, 6-2.4, 6-5, 6-15, 6-15.1 to 6-15.4, 6-16, 6-17, 6-21, 7-15.2, 7-16.1

Cross-correlation 9-8, 9-8.2

CT scans 7-13.2, 9-5.4

Cycloid 3-8.2

Cylindrical coordinates 1-7, 4-10

Damped oscillator 10-12.1

Damped simple harmonic motion 10-12.1

Data Analysis 4-8.5, 5-4, 7-4.12, 9-6.7, 9-8, 9-10.1

Data fitting 13-8

Dating minerals 3-7.1

De Moivre s theorem 2-3, 2-3.2, 2-3.3, 9-6

Decoding 9-11.1, 9-11.2

Decomposition of borane carbonyl 10-2.2

Definite integral 3-1, 4-1.1, 4-1.2, 4-1.3, 4-2.1, 4-3.3

Definite integrals with substitution 4-3.3

Degeneracy 1-9.9, 4-8.1, 5-5, 5-5.2, 5-5.3, 5-6.10, 7-15.1, 8-3, 12-6.1

Degree of freedom 5-5.3

Del 10-15.5

Delta functions 1-11, 9-6.6, 9-7.4, 9-9.1, 9-12

Determinants 1-9.8, 4-11, 6-15.1, 7-1, 7-2 to 7-3.2, 7-4.13, 7-13.2

DFT via a Circulant Matrix 9-9.3

Diagonal matrix 6-9.1, 6-9.2, 7-4.3, 7-4.12, 7-5.4, 7-5.5, 7-12.6, 7-12.9, 7-13.2, 7-13.4, 7-14.2 to 7-14.5, 7-16.1, 13-11

Dielectric constant 11-3.4

Differential equations 4-1.4, 6-14, 7-8, 7-13.1, 7-13.3, 7-14.2, 8-1, 9-4.1, 9-5.4, 9-6.8, 10-1.1, 10-2.5, 10-10, 10-10.1, 10-12, 10-14.1, 10-14.2, 10-15.1, 10-15.2, 10-16.4, 10-17, 11-1.3, 11-2.1, 11-4.11, 11-5.1, 11-5.5, 11-5.6, 11-6.1, 11-7.6, 11-8.3, 11-9.1, 12-2.1, 12-3.1

Differential operator 3-3.1, 7-5.3, 10-11.5, 10-12.1

Differentiating and summing series 9-2

Differentiating constants 3-3.5

Differentiating dot and cross products 3-4.10

Differentiating exponentials 3-3.2

Differentiating integrals 3-3.15, 4-5.2

Differentiating logarithms 3-3.12

Differentiating by parts 3-5

Differentiating parametric functions 3-4.8

Differentiating powers 3-3.3, 3-3.4

Differentiating ratios of functions 3-4.5

Differentiating sine and cosine 3-3.9

Differentiating by substitution 3-3

Differentiating vectors 3-4.9, 3-4.10

Differentiating with Sympy 3-3.6

Differentiating x as a power 3-3.13

Differentiation 1-2.4, 1-9.23, 3-1 to 3-11 4-1.1, 4-2, 4-2.1, 4-8.2, 4-9, 4-9.1, 4-11, 5-8.2, 7-14.2, 10-12, 10-12.1, 10-12.6, 10-12.8, 11-5.6, 13-4

Differentiation summary 3-5

Differentiation with respect to a function 3-4.6, 3-8

Diffraction 1-5.5, 2-3.3, 2-4.2, 3-6, 5-1.2, 5-1.3, 6-15.4, 9-5.2 to 9-5.6, 9-6.6, 9-7.4, 9-12, 9-13, 9-13.1 to 9-13.8, 9-13.9, 10-18.1, 10-18.5

Diffraction from DNA 9-13.1

Diffraction intensity 2-4.2, 10-18.5

Diffusion 4-2.9, 9-5.4, 9-8.1, 9-8.6, 10-1.1, 10-2.4, 10-4, 10-4.3, 10-4.9, 10-5, 10-5.1, 10-5.3, 10-5.4, 10-5.5, 10-12.1, 10-15.1, 10-15.2, 10-15.6, 10-15.7, 10-15.8, 10-15.9, 10-16.1, 10-16.2, 10-16.3, 10-17, 10-18, 10-18.4, 10-18.5, 11-4.11, 11-4.12, 11-4.13, 11-5.5, 12-3.1, 12-3.2, 12-3.3, 12-4.1, 12-5, 13-6.1

Diffusion across an interface 10-16.1

Diffusion and chemical reactions 10-15.7

Diffusion equation 10-1.1, 10-5.4, 10-12.1, 10-15.1, 10-15.2, 10-15.6, 10-15.7, 10-15.9, 10-16.2, 10-16.3, 10-17, 10-18.4, 11-4.11, 11-4.12, 11-4.13, 11-5.5

Diffusion in a closed tube 10-15.9

Diffusion through a cell wall 10-5.3

Dihedral angle 6-18

Dipole 1-5.1, 6-21, 6-21.1, 7-6.12, 7-6.13, 9-4, 10-12.1, 10-18.5

Dipole-dipole energy transfer 7-13.2, 12-4.1

Dirac delta function 1-11

Direct product 4-8.4, 7-6.10, 7-6.11, 7-6.12, 7-6.13

Direction cosines 6-7

Discontinuous functions 9-1.7

Discrete basis sets 8-4.2

Discrete Fourier transform (DFT) 7-13.2, 9-, 9-5.6, 9-7.4, 9-9.1, 9-9.5, 9-9.6

Disease 4-8.2, 10-4.8, 11-7, 11-7.1, 11-7.2, 11-7.4, 11-7.5, 11-7.6, 12-5, 13-11

Dispersion 1-5.3, 4-8.1, 5-4, 9-5.3, 12-6.7, 13-1.2, 13-3, 13-6.4

Dissociation limit 10-3.3

Dissolution kinetics 10-4.8

Distance from a point to a line 6-15.3

Distance from a point to a plane 6-15.4

Distinguishable objects 1-9.3, 1-9.4, 12-6.7

DNA 1-9.19, 1-9.25, 1-9.27, 5-4.3, 5-5.2, 6-19 6-20, 7-9, 9-5.4, 9-12, 9-13.1, 10-13.2, 11-4.6, 11-5.3, 11-5.4, 13-3.5, 13-8, 13-11

DNA melting 5-5.2

Dot and cross products 3-4.10, 6-15

Dot product 1-1.2, 3-4.10, 6-2.1 to 6-2.11, 6-3 to 6-7, 6-8.1 6-8.3, 6-9.2, 6-10.1, 6-12 to 6-18, 6-21.1, 7-5, 7-5.8, 7-12.2, 7-12.7, 7-12.8, 7-13.4, 7-14.2, 7-16.1, 8-3, 8-4.3, 9-3, 9-9.3, 9-9.4, 9-13.2, 11-5.6, 11-8.4, 11-10.1, 11-10.2, 13-11

Driven simple harmonic motion 10-12.1

Dyadic 7-16.1

Eigenvalue 5-9, 7-2.4, 7-12.3 to 7-12.9, 7-14.2, 7-14.5, 8-2.2, 8-3, 10-1.4, 11-5.6, 11-10, 13-11

Eigenvalue-Eigenvector equation 7-3, 7-4, 7-10, 7-12.1, 7-12.3, 7-12.6, 7-14.2, 7-14.3, 8-2.1, 10-13.1, 13-11

Eigenvalues 6-14, 7-3.1 7-4, 7-4.8, 7-4.12, 7-5.6, 7-5.7, 7-6.16, 7-10, 7-12.3, 7-12.5, 7-12.6, 7-12.7, 7-12.9, 7-13.2, 7-13.4, 7-13.5, 7-14.2 to 7-14.6, 7-16.1, 7-16.2, 8-2, 8-2.1, 8-2.2, 8-2.4, 8-3, 9-9.3, 11-5.6, 11-10, 11-10.1, 11-10.2, 13-11

Eigenvectors 7-3.1, 7-4, 7-4.8, 7-5.7, 7-6.16, 7-12.3 to 7-12.9, 7-13.2, 7-13.4, 7-14.2 to 7-14.6, 7-16.1, 7-16.2, 8-2, 8-2.1 to 8-2.4, 8-3, 9-9.3, 13-11

El-Sayed Rules 7-6.12

Elastic 6-1.5, 6-2.1, 6-2.10, 9-8.5, 10-12.1, 11-3.6, 11-3.10, 11-3.11

Elastic scattering 6-1.5, 6-2.10, 11-3.6, 11-3.10

Electric dipole transition 7-6.12, 7-6.13

Electrochemical cell 3-3.8, 3-4.2, 10-16.2

Electrochemical potential 3-3.8

Electron spin 7-12.9, 10-2.4, 12-6.7

Encoding 9-11.1, 9-11.2, 9-11.4

Energy equation 4-12.4, 7-2.4, 7-13.2, 7-14.6, 9-9.3, 10-2.4, 10-10.2, 10-16.4, 11-5.3, 12-4.1

Energy Integral 7-3

Energy transfer 7-3.1

Enthalpy 3-3.8, 3-3.12, 3-4.6, 3-11.1, 3-11.5, 3-11.9, 4-14

Entropy 1-4, 1-9.23, 1-9.24, 3-3.8, 3-4.2, 3-11.1 to 3-11.9, 4-14, 4-14.1, 5-5, 5-5.3, 5-6.10, 7-13.5, 12-6.1, 12-6.5 to 12-6.9

Epidemic 11-7.1 to 11-7.6

Equilibrium 1-4, 1-4.5, 1-5.2, 1-8.1, 1-9.22, 3-3.12, 3-4.6, 3-6, 4-8.4, 5-5, 5-5.3, 5-9, 6-1.4, 7-6.12, 7-13.2, 7-14.2 to 7-14.6, 8-2.2, 9-5.3, 9-6.6, 9-8.6, 10-2.2, 10-2.5, 10-3.2, 10-3.3, 10-4.2 to 10-4.6, 10-6, 10-10.6, 10-11.2, 10-11.3, 10-12.1, 10-13.3, 10-13.4, 10-15.8, 10-15.9, 10-16.2, 11-4.6, 11-5.3, 11-6.4, 11-8.1, 11-8.4, 12-6.2 to 12-6.7, 13-7.4

Equilibrium constant 1-4.5, 3-3.12, 3-4.6, 10-2.2, 10-4.2 to 10-4.6, 10-15.8

Equilibrium points 10-2.5, 11-8.1

Equipartition Theorem 10-12.1, 12-6.2, 12-6.3

Error function 4-2.9, 10-9.3, 10-16.1, 13-3.6

Error propagation 13-4.1, 13-6.4

Estimation 1-2.2, 1-13, 1-13.2, 1-13.4, 9-8.4, 11-4.8, 12-6.2, 12-6.3, 13-1.2, 13-5

Ethanol 6-1.4, 7-7, 7-16.1, 7-16.2, 10-2.4

Euler angles 7-7

Euler or Cauchy eqns 10-14.1

Euler’s … 2-1.5, 2-3.3, 2-4.2, 3-11.8, 7-3.1, 9-10.5, 10-13.3, 10-14.1, 11-4.1, 11-4.3, 11-5.1

Euler’s chain rule 3-11.8

Euler’s equation 2-4.2, 9-10.5

Euler’s method 11-4.3, 11-5.1

Euler’s theorem 2-1.5, 2-3.3, 2-4.2

Euler-Lagrange equation 3-8

Euler-Maclaurin 5-6.7, 5-7, 11-3

Euler–Cromer 11-6.5

Exact and non-exact differentials 3-11.1

Exact equations 10-9.2

Examples of molecules 6-18, 7-6.4

Examples of Point Groups 7-6.5

Exchange integral 4-12.4

Excited state 1-3, 1-9.14, 1-9.25, 4-8.2, 5-9, 7-6.12, 7-9, 7-13.1, 7-13.2, 9-6.7, 9-7.1, 9-8.1, 10-2.3, 10-2.4, 10-3.1, 10-4.3, 10-18.5, 11-4.11, 12-2.3, 12-2.4, 12-3.1, 12-3.4, 12-4.1, 13-7.4

Excited state forming triplet 12-2.4

Exclusive events 1-9.14

Expansion coefficients 5-8.1, 7-12.8, 9-1.2

Expectation values 4-8.4, 5-8.1, 6-12, 7-4.8, 7-6.16, 8-2.1, 8-2.3, 8-3

Exponential decay 7-13.1, 9-5.6, 9-6.3, 9-6.7, 9-9.6, 9-9.7, 9-10.3, 10-12.1, 10-18.1, 12-3.4, 13-10.1

Exponential expansion 5-6.6, 7-13.3, 9-3

Exponential representation 9-1.4, 9-3

Exponential series 1-3, 2-3.3, 5-3, 9-9.5

Exponentials 1-5.6, 2-4.2, 3-3.2, 3-3.7, 4-2.5, 4-2.7, 4-7.2, 4-12.1, 5-1.2, 5-4.1, 9-6.3, 9-8.6, 9-9.2, 9-9.3, 9-9.4, 9-10.5, 10-11.2, 10-11.5, 10-12, 10-12.1 to 10-12.8, 10-13.3, 10-16.1, 10-16.2, 11-1.3, 12-6.10, 13-6.1, 13-10.1

Extent of reaction 4-8.1

Factorials 1-1.3, 1-3, 1-8.1, 1-9.16, 1-9.18, 1-9.23, 1-9.25, 3-3.7, 3-3.13, 3-3.16

Fast Fourier transform (FFT) 7-13.2, 9-7.3, 9-7.4, 9-8.7, 9-9.2 to 9-9.6, 9-10.3, 9-10.5, 9-12, 9-14.7, 10-18.4

Feedback 7-10, 10-3.1, 10-5.5, 10-12.1, 11-7.5, 13-6.1

Femtosecond 5-9, 7-9, 7-13.1, 9-5.7, 9-7.4, 9-8.4, 9-11.4, 10-15.1, 10-18.5

Fermion 1-9.9

Feynman’s Trick (Integration) 4-5.4,

Fick’s first law 10-5.3, 10-15.6, 10-15.7

FID (Free induction decay) 9-5.3, 9-9.5, to 9-9.8, 9-10.5, 10-13.3

Filtering 9-5.4, 9-9.7, 9-10, 9-10.2, 9-10.3, 9-14.4

Filtering and apodising 9-10.2

Finite wave train 9-6.3

First-order 1-2.4, 1-3, 1-4, 3-3.2, 4-1.4, 5-8.1, 5-8.2, 7-13.1, 7-13.2, 10-1.4, 10-2.4, 10-4.7, 10-5.5, 10-9.2, 10-9.3, 10-12.3, 10-13.3, 10-15.1, 11-4.1, 11-5.5, 11-8.1, 12-2.1, 12-3.4, 12-6.8

Fitzhugh-Nagumo equations 11-8.1, 11-8.3

Flow 1-9.22, 9-4.1, 9-5.3, 9-5.4, 9-8.5, 9-11.4, 9-11.5, 10-4.7, 10-5.1 to 10-5.5, 10-15.5, 10-15.8, 11-4.11, 11-4.12, 11-6.3, 11-7.3, 12-2.1, 12-5

Flow and chemical reaction 10-15.8

Fluorescence decay 13-8

Fluorescence lifetime 10-2.3

Fluorescence yield 1-9.14, 10-2.3, 10-4.3, 11-5.3, 12-2.4

Flux 10-5, 10-5.3, 10-15.6, 10-15.8, 10-16.2, 11-4.12

Forster & Forster energy transfer 7-13.2, 11-5.3, 12-4.1

Forward transform 9-5.1, 9-6, 10-18

Four point DFT 9-9.2

Fourier Series 1-5.2, 1-5.5, 7-3.2, 7-13.2, 8-5.1, 9-1.1 to 9-1.8, 9-2.1, 9-3 9-4, 9-5.3 to 9-5.7, 9-6.3, 9-8.5, 9-9.2, 10-15.2, 10-15.5, 10-17, 13-7.3

Fourier Slice Theorem 9-14.6

Fourier Synthesis 9-13.2, 9-13.6 to 9-13.9

Fourier transform equations 9-5.1, 9-6

Fourier Transform method 9-7.5, 10-18

Fourier transforms 9-, 9-1.8, 9-5 to 9-14, 10-18, 10-18.4

Fractional derivatives 3-3.16

Franck-Condon 1-9.25, 5-9, 7-6.12

FRAP 10-16.1, 11-4.13

Free energy 1-4.5, 3-4.6, 3-11.9, 5-5, 7-13.5, 11-8.1, 12-6.5

Frequency doubling 9-8.4

FRET 12-4.1

FTIR spectrometer 9-5.2, 9-6.3, 9-8.1, 9-8.7

Function-of-a-function 3-4.1, 3-4.2

Functions of matrices 7-5.5

Gain 7-6.12, 7-10, 9-5.7, 9-13.8, 10-1.4, 10-3.1, 10-5.5, 10-12.1, 12-6.5

Gamma function 1-8, 4-8.2, 13-6.4

Gaussian distribution 1-9.25, 4-8.2, 5-9, 12-1.1, 12-3.3, 13-6.2

General Equation of Motion 10-10.2

Generalized Fourier series 9-3, 9-4

Generating functions 9-4.1

Genes 1-9.1, 1-9.27

Genetics 1-9.1, 1-9.27, 1-9.27

Geometric mean 1-2.3

Geometrical progression 1-12

GFG matrix 7-14.4, 7-14.6

Gibbs energy 3-11.9, 6-1.4, 10-4.6

Gibbs phenomenon 9-1.7, 9-1.8, 9-3.1

Gibbs-Helmholtz equation 3-4.6

Gillespie method 11-4.10, 12-2.1, to 12-2.4, 12-3.4

Golden ratio 1-2.4, 10-13.4

Golden section 1-2.4

Gradient Expansion method 13-7.1

Gravitational potential 3-11.1, 10-18.2

Green s function 4-14.2

Group theory 4-1.3, 4-8.4, 6-14, 7-4.4, 7-4.12, 7-5.3, 7-5.6, 7-6.1 to 6.8, 7-6.15, 7-12.3, 7-13.4

Group velocity 1-5.3, 10-16.4

Hadamard transform 9-11.1, 13-1.3

Haemoglobin 6-2.2, 6-15.6

Hamilton’s Equations of Motion 10-3.4

Hamiltonian operator 4-12.1, 5-8.1, 5-9, 7-12.3, 8-2.2, 10-16.4

Hard sphere potential 4-5.1

Harmonic mean 1-2.3

Harmonic oscillator 1-5.2, 1-8.1, 1-9.25, 4-8.4, 4-8.5, 5-5, 5-8.1, 5-9, 6-12, 6-13, 7-14.3, 8-1.1, 8-2, 8-2.1 to 8-2.4, 9-3, 9-4.1, 9-6.6, 9-6.7, 10-1.1, 10-3.2 to 10-3.4, 10-10.2, 10-10.5, 10-11.4, 10-11.5, 10-12, 10-14.2, 10-18.2, 11-5.6, 11-6.4, 11-10, 12-6.1, to 12-6.4

Hartree 7-3.2, 11-10.2

Heat capacity 3-3.8, 3-11.2, 3-11.5, 4-14.1, 5-5.2, 5-6.10, 10-5.5, 12-6.1 to 12-6.8, 12-6.9, 12-6.10

Heisenberg uncertainty principle 7-5.3, 9-5.6, 9-6.6, 10-11.4, 10-11.5

Helix-coil transition 7-13.5

Herd immunity 11-7.4

Hermite equation 10-14.2

Hermite polynomial 1-8.1

Hermitian 7-3, 7-4.8, 7-12.7, 7-12.9, 7-13.2, 7-13.4, 7-14.2, 7-16.1, 8-2.4, 8-3, 8-4.1

Hermitian matrix 7-4.8

Herzberg-Teller 7-6.12

Heterozygous 1-9.27

Heun’s method 11-4.4, 11-4.11

Hilbert Transform 9-10.5

Homogeneous equations 10-9.1

Homogeneous solution 10-12.1, 10-12.5

Homozygous 1-9.27

Horizontal mirror plane 7-6.3

How the Fourier transform works 9-6.4

Huang-Rhys 1-9.25

Huckel 6-14, 7-3, 7-6.16, 7-13.2, 9-9.3

Hybrid orbitals 6-12, 6-14

Hydrogen atom 4-10, 4-12.1, 4-12.3, 8-5.1, 10-11.4, 10-14.2, 11-10.1

Hydrogen iodide equilibrium reaction 10-4.5

Hyperbolic functions 1-5.6, 1-6, 2-3.1, 3-3.10, 4-2.7

Hypothesis testing 13-3.4

ijk vectors 6-4, 6-15.1

Ice forming 10-5.2

Ideal gas 1-1.1, 1-4, 1-9.24, 3-11.1 to 3-11.8, 4-1.2, 4-12.6, 4-14.1, 5-5.3, 5-6, 10-6

Identical objects 1-9.3

Identity 1-9.27, 1-10.1, 3-8, 4-12.6, 5-1.3, 5-9, 6-6, 6-15, 6-17, 7-3, 7-4.2, 7-4.5, 7-5.3, 7-6.3, 7-6.6 to 7-6.16, 7-10, 9-9.4, 9-10.5, 10-4.5

Identity matrix 7-4.2, 7-6.8, 7-10, 9-9.4

Identity operation 7-6.8, 7-6.9

Im 5-9, 7-14.3 to 7-14.5, 7-15.4, 9-14.7, 10-2.1, 10-13.3, 11-4.13

Impact parameter 6-1.5, 11-3.7, 11-3.9, 11-3.10, 11-3.11, 11-4.10

Implicit differentiation 3-4.7

Importance sampling 12-1.3, 12-1.3

Improper and undefined integrals 4-2.10

Improper rotation 7-5.3, 7-6.3

Inclusive probability 1-9.13, 1-9.14

Indefinite and Definite Integrals 4-1.2

Independent events 1-9.14, 7-3.2, 10-4.9

Indexing 7-1, 7-14.3, 9-13.4

Indistinguishable 1-9.3, 1-9.9, 1-9.13, 7-6.2, 7-6.3, 9-9.7, 9-12, 10-15.9, 12-2.2, 13-9

Indistinguishable objects 1-9.9

Indistinguishable state 7-6.3

Inelastic 6-1.5

Inertia tensor 7-16.1

Infection 4-8.2, 10-4.8, 11-7.2 to 11-7.5

Infinite basis set 6-12

Inflection 3-7, 3-7.1

Inflection points 3-7, 3-7.1

Initial value problems 10-1.2, 11-9.1

Inner product 6-2.9, 8-4.1, 8-4.3

Inner products 4-2.2, 6-2.9, 8-4.3

Integral powers of square matrices 7-5.4

Integrals with infinite limits 4-2.11

Integrating exponentials 4-2.5

Integrating factors 10-9.3

Integrating powers of x 4-2.1

Integrating sine 4-2.6

Integration 3-1, 3-3.15, 3-5, 3-8, 3-8.1, 3-8.2, 3-11.1, 4-, 5-4, 5-5.3, 5-6.7, 5-8.1, 5-8.2, 7-3.2, 7-6.12, 7-13.1, 7-13.2, 7-15.3, 8-1, 9-1.1, 9-1.5, 9-1.6, 9-2, 9-3.1, 9-4, 9-5.5, 9-6, 9-6.2, 9-6.3, 9-6.5, 9-6.6, 9-6.7, 9-7.1, 9-7.4, 9-8.4, 9-8.7, 9-14.1, 9-14.2, 10-1.1, 10-1.2, 10-1.4, 10-5.3, 10-5.4, 10-9.1, 10-10.1 to 10-10.5, 10-11, 10-12.1, 10-12.5, 10-14.2, 10-15.1, 10-15.5, 10-16.1, 10-16.4, 10-17, 10-18.1, 10-18.4, 11-, 11-1.3, 11-2.1, 11-3.1 to 11-3.10, 11-4.3 to 11-4.13, 11-5.1, 11-5.5, 11-6.2, 11-6.4, 11-7, 11-7.6, 11-8.1, 11-9.1, 11-10.1, 12-1.1, 12-1.2, 12-1.4, 12-6.2, 13-3.1, 13-9

Integration by parts 4-2, 4-5, 4-5.1, 9-1.6

Integration with SymPy 4-2.13

Interferometer 9-5.2, 9-8.1, 9-8.4, 9-8.7, 9-8.8

Internal energy 1-9.24, 3-11.1, 3-11.7, 3-11.9, 4-14, 5-5.2, 5-5.3, 5-6.10, 6-1.5, 12-6.1, 12-6.5

Intersystem crossing 1-9.14, 7-6.12, 7-13.2, 10-2.3, 10-2.4, 12-2.4

Inverse functions 1-1.5, 1-6, 3-3.10

Inverse matrix 7-4, 7-4.9, 7-13.4

Inverse of a square matrix 7-4.9

Inverse operators 10-12.5, 10-12.6, 10-12.7, 10-12.8, 10-12.9

Inversion 4-8.1, 7-5.3, 7-5.5, 7-6.3, 7-6.4, 7-6.15, 7-12.2, 9-11.5, 9-12, 10-3.1, 10-12.1, 11-10.1, 11-10.2, 13-7.4, 13-11

Inverted pendulum 10-11.2

Iodine recombination 10-2.1

Irrational numbers 1-2

Irreducible representation (irreps) 4-8-4, 7-5.6, 7-6.2, 7-6.9 to 7-6.16

Ising spin 12-6.1, 12-6.5, 12-6.6, 12-6.8, 12-6.9, 12-6.10

2D Ising spin 12-6.10

Ising spin energy 12-6.6

Isocline 11-6.3

Isoclines 11-6.3, 11-6.4, 11-7.3

Isotherm 1-9.21, 3-4.6, 3-11.2, 4-11, 4-12.2, 6-2.10, 7-8, 7-16.1, 9-14.4

Jacobians 4-11, 7-8

Kittel 5-5.2, 11-5.3

Kronecker delta 1-11, 4-9.2, 5-8.1, 6-13, 8-1.1, 8-3, 10-15.7

L Hopital s rule 3-6, 5-1.3, 5-6.10, 6-21.1, 9-6.3, 9-8.6, 10-13.2, 10-13.3, 10-15.5

Laser cavity 7-10, 9-6.3, 10-3.1, 10-12.1

Laser gain 10-3.1

Laser pulses 5-9, 9-8.1, 9-8.4, 9-11.4, 10-12.1, 10-15.8

Lattice 1-5.5, 2-4.2, 6-15.4, 6-15.5, 6-16, 9-5.4, 9-5.7, 9-12, 9-13.1 to 9-13.3, 12-6.1, 12-6.5, 12-6.10

Least absolute deviation 13-6.1, 13-10.2

Least squares 6-15.6, 9-1.2, 9-3, 9-7.2, 9-8.6, 9-10.1, 9-10.3, 9-13.2, 9-13.4, 9-13.7, 11-3.5, 13-1.2, 13-4, 13-6.1 to 13-6.7, 13-7.1 to 13-7.4, 13-8, 13-10.1, 13-10.2, 13-11

Least squares fit to a plane 13-7.2

Least squares method for a polynomial 13-7.3

Legendre polynomial 9-4, 9-4.1

Leibniz’s rule 3-3.15, 3-5

Leibniz’s formula 4-5.2

Length of a curve 4-, 4-13.4

Lennard-Jones potential 6-1.5, 11-3.7, 11-3.10, 11-4.3, 11-4.10

Levenberg-Marquardt method 13-7.1, 13-10.1

Limit-cycles 11-8.4

Line integrals 4-13.1, 4-14.2

Linear combination of atomic orbitals 4-12.1

Linear first-order equations 10-9.2, 10-9.3

Linear kinetic schemes 7-13.1

Linked pendulums 7-14

Lock-in amplifier 9-6.5

Log expansion 5-6.7

Logarithms 1-4, 3-3.12

Longitudinal wave 1-5.2

Lotka-Volterra 11-8.3

Luminescence heating curves 3-7.1

Maclaurin series 5-6.1, 5-6.2, 5-6.5, 7-5.5, 9-1.1

Magnetic dipole 1-5.1, 6-21, 6-21.1

Magnetisation 5-6.10, 6-21.1, 7-5.5, 9-5.3, 10-13.3, 12-6.1 to 12-6.10

Magnitude of a vector 6-2.7

Mantissa 11-1.1

Master equation 7-13.2

Mathematical Group 7-6.1, 7-6.6, 7-6.7

Matrices 1-1.2, 1-9.27, 4-1.3, 6-2.5, 6-2.8, 6-2.9, 6-2.10, 6-4, 6-6, 6-9.1, 6-10.1, 6-11, 6-14, 6-15.6, 7-1 to 7-16.2, 8-1, 8-2, 8-3, 8-4, 9-4, 9-5.5, 9-9.2, 9-9.3, 9-9.4, 9-9.6, 9-11.2, 9-11-3 to 9-11.5, 9-14.1, 10-13.4, 11-4.12, 11-5.6, 12.5, 13-7.1 to 13-7.6, 13-10.1, 13-11

Matrix diagonalization 7-12.6

Matrix elements 7-6.16, 8-2, 8-2.2, 8-2.4, 8-3

Matrix multiplication 6-2.9, 6-13, 6-14, 7-4.5, 7-5, 7-5.2, 7-6.6, 7-6.8, 7-7, 7-12.2, 9-9.3, 9-9.4, 9-9.6, 13-7.6, 13-11

Matrix sum 7-5.1

Matrix transpose 7-4.5, 7-4.12

Maxima 3-4.8, 3-6, 3-7, 5-1.3, 9-13.1, 11-8.1

Maximum Likelihood Method 13-5, 13-6.2

Maxwell distribution 12-6.4, 12-6.6

Maxwell-Boltzmann distribution 1-9.26, 13-2

Mean distance diffused 10-15.8, 10-16.1

Mean free path 4-8.2, 9-6.7, 10-4.9

Mean or Average value 13-1.1

Mean value 1-9.16, 1-9.22, 1-9.25, 4-2.8, 4-8.1c to 4-8.5, 4-10.1, 5-9, 9-8.4, 9-10.1, 12-1.1 to 12-3.3, 13-1.1, 13-1.2, 13-3, 13-3.1 to 13-3.5, 13-4, 13-5, 13-6.2, 13-8, 13-10.1, 13-11

Mean value theorem 4-2.8

Mean value theorem for integrals 4-2.8

Mean-value method 12-1.1 to 12-1.3

Metropolis algorithm 12-1.3, 12-6.1, 12-6.2, 12-6.6, 12-6.7, 12-6.10

Michaelis-Menten scheme 11-4.12, 11-5.4

Michelson interferometer 9-5.2, 9-8.4, 9-8.7

Microchannels 11-4.12, 11-5.4

Mid-point rule integration 11-3.2

Miller indices 2-4.2, 9-13.1 to 9-13.5

Minima 3-7, 5-5.1, 11-8.1, 11-10.2, 13-6.2, 13-10.1

Mirror planes 7-6.3 to 7-6.6, 7-6.15, 7-6.16, 9-12

Mixed derivatives 3-11.3

Modal matrix 7-13.5, 7-14.2, 7-16.2, 9-5.7

Modulo 1-1.8, 1-10.1 to 1-10.4

Modulus 1-10.4, 2-1, 2-1.4, 2-1.5, 2-3.3, 5-9.1, 9-8.6, 9-9.6, 10-11.1

Modulus and Argument 2-1.4

Mole fraction 4-8.1

Molecular beam 6-1.5, 11-3.6, 11-3.11

Molecular orbitals 1-9.8, 4-8.4, 4-12.1, 6-9, 6-12, 6-14, 7-3, 7-6.1, 7-6.2 to 7-6.16, 7-12.5, 7-14.4

Molecular vibrations 1-5.2, 7-6.1, 7-6.12 to 7-6.16, 7-14.2, 11-10.2

Moment of inertia 4-10.1, 6-21.1, 7-12.2, 7-15.1 to 7-15.4, 7-16.1, 7-16.2, 10-11.1, 10-11.5

Monoclinic crystal 6-8.3, 6-10.1, 6-11, 6-16

Monolayer 1-13.3, 6-1.4, 12-5

Monte Carlo methods 11-7.1, 12-1.2, 12-2.1, 12-3.1

Monte Carlo simulations 12-2.2

Monte-Carlo integration 12-1.1

Morse potential / oscillator 5-9, 5-9.1, 8-1 8-2.1, 10-3.3, 10-18.2, 11-4.3, 11-10.1, 13-7.4

Most probable state 1-9.23

Motion with a constant force 10-11.3

Moving average 7-6.9, 9-7.1, 9-10.4

Multinomial distribution 1-9.26

Multiple integrals 4-10, 4-11

Multiplying and dividing complex numbers 2-1.3

Nearest neighbours 4-5.3

Nerve impulses 11-8.3

Newton Diagrams 6-1.5, 6-2.10

Newton s law of cooling 10-5.5

Newton s laws 7-14.3, 10-8, 10-10.1, 11-4.6, 11-4.9

Newton-Raphson 3-4.8, 3-7.1, 3-9.1 to 3-9.3, 7-3, 10-8.1, 11-1.1, 11-2.1, 11-7.4, 11-10.1

NMR 1-5.1, 1-9.21, 5-5.1, 6-1.2, 6-18, 6-21.1, 7-5.5, 7-12.9, 8-1, 8-2 8-3, 9-, 9-5.1 to 9-5.7, 9-8.5, 9-8.6, 9-9.5, 9-9.6, 10-13.3, 13-11

NMR spectrum with two spins 8-3

Noise 1-3, 1-9.27, 9-5.2 to 9-5.7, 9-6.5, 9-7.2, 9-8, 9-8.4 to 9-8.6, 9-9.3, 9-10, 9-10.1 to 9-10.4, 9-11.3, 9-11.4, 9-14.4, 10-15.4, 13-1.3, 13-3.6, 13-9, 13-10.1, 13-11

Non-integrability 4-2.9

Non-linear equations 7-14, 11-6.4

Non-linear least squares 13-7.1, 13-10.1, 13-11

Non-orthogonal axes 6-8.2, 6-9.1

Non-orthogonal vectors 6-8.2

Norm 2-1.4, 9-8.4, 13-3.1, 13-3.3, 13-6.4

Normal distribution 1-9.25, 12-3.3, 13-1.1, 13-2, 13-3.1, to 13-3.6, 13-5, 13-8, 13-9

Normal mode vibration 11-10.2

Normal mode vibrations 7-6.1, 7-6.14 to 7-6.16

Normal modes 1-5.2, 4-8.4, 5-5.3, 7-4.9, 7-6.14 to 7-6.16, 7-14.1 to 7-14.6, 10-15.4, 10-17

Normalization constant 1-8.1, 4-10.2, 5-9.1, 6-3, 7-12.9, 8-4.3, 9-4

Normalized vectors 6-18

Null matrix 7-4.1, 7-4.10, 7-5.3, 7-12.6

Nullcline 11-6.1, 11-6.3, 11-6.4, 11-7.2, 11-7.3, 11-8.1, 11-8.3

Number average 5-4.2

Numerical accuracy 5-6.2, 8-2, 11-2.1

Numerical approximation 11-4.1

Numerical integration 5-6.7, 8-1, 10-11, 11-1.3, 11-3.1, 11-4.7, 11-5.5, 11-7.6, 11-10

Numerical integration of the Schroedinger equation 11-10

Numerical solution 7-13.2, 10-1.4, 10-18.5, 11-, 11-4.1, 11-4.11, 11-4.13, 11-5.1, 11-5.5, 11-5.6, 11-6.2, 13-10.1

Numerical solution of the Diffusion equation 11-4.11

Numerically calculating a Fourier series 9-3.1

Numerov algorithm 11-5.5, 11-5.6

Nyquist Critical Frequency 9-9.5, 9-9.7

Object-image 3-10.2, 7-9.1

Odd and even functions 4-1.3, 9-1.5, 9-1.6

One-dimensional diffusion 10-15.6, 10-15.9, 12-3.3

Operators 6-12, 7-5.3, 7-6.1 to 7-6.16, 7-12.3, 8-3, 8-4.4, 10-12.1, 10-12.5 to 10-12.9, 11-5.1

Optical autocorrelator 9-8.4

Orbit 10-2.4, 10-3.4, 11-1.4, 11-3.7, 11-3.11, 11-4.10

Orthogonal matrices 7-4.12, 7-7

Orthogonal polynomials 1-8.1, 8-5.1, 9-4, 9-4.1

Orthogonal unit vectors 6-2.5, 6-14

Orthogonal vectors 6-8.2, 7-6.15, 9-3

Orthonormal 5-8.1, 6-2.3, 6-4, 6-5, 6-6, 6-8.1, 6-9, 6-12, 6-13, 6-14, 7-3.2, 7-4.12, 7-12.8, 8-3, 8-4.1, 8-4.2, 9-3

Orthonormal basis set 6-12, 6-14

Orthorhombic 2-4.2, 6-15.5

Outer products 8-4.4

Outliers 1-2.3, 13-3.6, 13-6.1, 13-10.2

Overlap integral 4-12.1 to 4-12.4

Overtone 1-5.4, 10-17

Para-hydrogen 10-4.6

Parallel vectors 6-2.4

Paramagnetic spins 5-6.10

Parametric equations 3-4.8, 3-4.9, 4-, 4-6

Parseval 9-6.6

Partial derivatives 3-3.8, 3-11.1 to 3-11.9, 4-11, 4-13.6, 4-14.1, 13-4, 13-4.2

Partial Derivatives in Thermodynamics 3-11.9

Partial differential equations 10-1.1, 10-15.1, 10-17

Partial differentiation 3-3.8, 3-11.3

Partial fractions 1-5.4, 4-2, 4-2.4, 4-8.5, 5-5.3, 5-8.2, 8-1, 8-2.2 to 8-2.4, 8-5.1, 9-13.4, 10-3.1, 10-3.3, 10-4.1, 10-4.8, 10-11.4, 10-15.4, 11-10, 11-10.1, 13-8

Particle in a circular well 10-15.4

Particle in a gravitational potential 10-18.2

Particle in a one-dimensional box 5-8.2, 10-11.4, 10-15.3

Particle on a Ring 7-8, 10-11.4, 10-11.5, 10-15.4

Particular integral 1-9.1, 5-5, 5-5.3, 5-6.10, 10-12.1, 10-12.5 to 10-12.9

Path independent integrals 4-13.6

Path integrals 4-13, 4-14

Pauli exclusion principle 1-9.9

Principal compoent analysis (PCA) 1-9.3, 5-4.3, 5-8.2, 6-18, 6-20, 9-4.1, 11-4.12, 11-5.3, 11-5.4, 13-6.1 13-7.2, 13-11

Pendulum 1-5.2, 5-6, 7-14.1 to 7-14.3, 10-1.1, 10-3.2, 10-10.2, 10-10.7, 10-11.1, 10-11.2, 10-12.1, 11-6.4, 11-6.5

Percolation 12-5

Periodic boundary conditions 10-15.1, 12-6.10

Permutations 1-9.1 to 1-9.3, 1-9.4, 1-9.9, 1-9.16, 1-9.23

Perpendicular axis theorem 7-15.4

Perpendicular vectors 6-2.3

Perturbation calculation 5-8.2

Perturbation theory 5-8

Pfaffians 3-11.1

PH 9-1.6, 9-14.7, 10-4.3, 11-4.13, 11-8.3

Phase and group velocity 1-5.3

Phase angle 9-13.7, 9-13.8, 10-2.5, 10-3.2, 10-10.5, 10-13.4, 11-6.1 to 11-6.4, 11-7.2, 11-7.3, 11-8.1, 11-8.3

Phase portrait 10-2.5, 10-3.1, 10-3.2, 11-6.2, 11-6.3

Phase problem 2-4.2, 9-13.2

Phase sensitive detection 9-6.5

Phenotype 1-9.27

Phosphorescence 3-7.1, 7-13.2, 9-6.7, 10-2.4, 12-4.1, 13-3.8

Phosphors 3-7.1

Photograph 51 9-13.1

Photon and particle counting 13-8

Photon counting 2-4.2, 12-3.4, 13-3.8, 13-5, 13-6.4, 13-8

Photosynthesis 7-3.1, 7-13.2, 12-4.1

Plancherel 9-6.6

Plane polar coordinates 1-7, 4-7, 4-11, 4-13.4, 7-8, 10-11.5, 10-15.4

Pochhammer symbol 1-8

Point group 7-, 7-5.3, 7-6.1 to 7-6.16, 7-14.6, 11-10.2, 13-7.4

Poisson distribution 1-9.22, 1-9.25, 4-8.2, 10-13.2, 12-2.1, 12-2.2, 13-2, 13-3.7, 13-5, 13-8

Polar angle 1-7, 2-1.4, 2-1.5, 2-3.2, 4-10.2

Polar coordinates 1-7, 4-7, 4-7.1, 4-9, 4-10.2, 4-11, 4-13.4, 6-6, 6-9, 7-8, 9-12, 9-14.2, 9-14.4, 10-11.5, 10-15.4

Polarizability 7-6.12

Polarizers 13-6.1

Polyene 7-3, 10-11.4

Polymerase Chain Reaction 11-5.3

Polymers 5-4.2, 11-4.6

Polynomials 1-8.1, 4-2.11, 4-8.5, 7-3, 8-5.1, 9-3, 9-4.1, 10-12.1, 10-12.9, 10-14.2, 10-14.3, 10-18.4, 11-1.3, 13-6.1

Population inversion 10-3.1, 10-12.1

Population variance 13-1.2

Position vectors 6-1.3

Power series 3-3.16, 5-1.1, 5-2.1, 5-3, 5-6.1, 7-13.4, 10-14.2

Precession 6-21.1, 10-13.3

Predator-prey 11-5.1, 11-8.1, 12-2.1

Principal axis 7-, 7-6.3, 7-6.4, 7-6.8, 7-6.13, 7-6.15, 7-13.4, 7-16.1, 13-7.4, 13-11

Principal value 2-3.2, 2-4.2

Probability 1-3, 1-9.1 to 1-9.27, 3-3.15, 4-2.3, 4-8, 4-8.1, 4-8.2, 4-10.2, 4-12.1, 5-4.3, 5-5, 5-5.1, 5-9, 5-9.1, 7-3.2, 7-6.12, 7-13.2, 8-4.3, 10-4.9, 10-10.5, 10-13.2, 10-16.4, 10-18.2, 10-18.5, 11-10, 12-2.1, 12-2.2, 12-3.2 to 12-3.4, 12-6.1, 12-6.4, 12-6.6, 13-3, 13-3.1, 13-3.6, 13-5, 13-6.2, 13-6.4, 13-7.4, 13-7.5, 13-8, 13-9, 13-10.1

Probability amplitude 8-4.3

Probable error 13-3.1

Product rule 3-4.3, to 3-4.7, 3-7.1, 3-11.1, 6-21, 7-6.7, 7-6.8, 10-14.1

Projection operators 7-6.16, 8-4.4

Projections 6-4, 6-6, 6-7, 9-4, 9-13.9, 9-14.4

Prolate spherical coordinates 4-12.1, 4-12.3

Properties of eigenvalues and eigenvectors 7-12.7

Protein 1-9.3, 1-9.10, 1-9.20, 1-9.25, 1-9.26, 6-18, 6-20, 6-21, 7-13.5, 10-5.4, 10-12.1, 10-13.2, 10-15.1, 10-16.1, 10-18.4, 11-4.6, 11-4.13, 11-5.3, 11-8.3, 12-6.1, 13-3.5

Protein data bank 6-18, 6-20

Proteins 1-5.5, 1-9.20, 1-9.25, 6-2.2, 6-15.6, 6-18, 6-20, 7-9, 9-8.6, 10-13.2, 10-16.1, 11-4.6, 12-6.8, 13-11

Pseudo-rotation angles 6-19.1

Punnett square 1-9.27

Pythagoras 1-2.1 to 1-2.3, 3-3.10, 3-8.2, 3-10.2, 4-13.3, 6-1.3, 6-2.9, 7-15.4, 12-4.1

Q-switching 10-2.4, 10-12.1

Quadratic potential 7-14.3, 8-2.4, 11-10.1

Quantile 13-1.2, 13-3.1, 13-3.3, 13-6.2, 13-6.6

Quantum harmonic oscillator 1-8.1, 10-10.5, 10-14.2, 11-5.6, 12-6.2

Quenching an excited state 10-2.4

Quotient rule 3-4.5

Radian 1-5.1, 1-5.2, 6-21.1, 7-7, 8-3, 9-1.2

Radius of gyration 7-15.4, 7-16.2

Radon Transform 9-14.2

Rainbow scattering 11-3.11

Ramachandran 6-18, 12-6.1

Random digits 1-9.18

Random walk 10-12.1, 12-3.2, 12-3.3, 12-6.2, 12-6.3

Rayleigh-Ritz method 4-9

Re (real part of complex number) 2-3.3, 2-4.2, 10-5.5, 11-3.9, 12-2.2

Reaction and diffusion 10-4, 10-5.4, 11-4.11

Reaction centre 12-4.1

Reaction on a surface 12-5

Reactive scattering 6-1.5, 11-3.11

Reciprocal derivatives 3-3.14, 3-11.6

Recurrence 5-9, 10-13.4

Recursion 1-3, 1-8.1, 5-9, 9-4, 9-4.1, 9-9.4, 9-10.4, 10-14.2, 11-1.3, 11-1.4

Reducible Representations 7-6.13

Reference plane 7-9, 7-9.1, 7-10

Reflection 1-1.7, 1-6, 2-1.1, 2-4.2, 5-1.3, 6-1.5, 7-5.3, 7-6.3 to 7-6.15, 7-9, 9-9.2, 9-13.1 to 9-13.8

Reflection in a mirror plane 7-6.3

Regula-Falsi 3-9

Repeated differentiation 3-3.7, 10-12.1, 10-12.6

Representations based on matrices 7-6.9

Reproductive ratio 11-7.1, 11-7.2, 11-7.5

Residuals 9-8, 9-8.4, 13-6.2 to 13-6.4, 13-7.4, 13-7.5, 13-8, 13-10.1

Resolution 4-8.2, 7-6.12, 9-5.2, 9-6.3, 9-7.1, 9-8.1, 9-8.8, 9-9.5, 9-9.8, 9-11.4, 9-13.1, 9-13.9, 9-14.4, 10-12.1, 12-1.1, 13-3.8

Resonance 4-12.4, 7-3, 7-5.5, 9-6.3, 10-12.1, 10-13.3, 11-5.3, 12-4.1

Resonance integral 4-12.4

Reverse transform 9-5.1, 9-5.5, 9-6, 9-7.4, 9-14.4, 10-18, 10-18.4

Reversible reactions 10-4.4

Rigid Rotor 5-5.3, 5-8, 5-9, 7-12.2, 8-1, 8-3, 10-11.5, 12-6.1

Rockets 10-8.2, 10-10.3, 10-10.4

Rolling average 9-10.1, 9-10.4

Rolling or moving average 9-7.1, 9-10.4

Roots of unity 2-3.2, 2-3.3, 2-4.1, 7-3.1, 7-13.2, 9-9.1, 9-9.2, 9-9.3

Rotation about an axis 7-6.3

Rotation axes 7-, 7-6.15, 7-16

Rotation matrix 6-2.10, 7-2.4, 7-4.11, 7-4.12, 7-6.9, 7-6.15, 7-7, 7-12.3, 9-14.2

Rotation-reflection 7-6.3, 7-6.15

Rotational diffusion 9-8.6, 10-18.5, 11-4.11, 13-6.1

Rotational energy level 5-5.1

Rotational motion of molecules 7-15.1, 9-4.1

Rotational spectrum 7-6.3, 7-6.4, 7-12.3, 7-15.1, 9-12

Rounding errors 11-1.1 to 11-1.4, 11-3.1, 13-6.2

Runge-Kutta 11-4.3 to 11-4.6, 11-4.11, 11-5.2, 11-5.6, 11-10

Sackur-Tetrode 3-11.2

Sample space 1-9.12, 1-9.13, 1-9.15

Sample Standard Deviation 1-9.10, 13-, 13-1.1, 13-1.2, 13-3.1 to 13-3.5

Savitsky-Golay 9-10.1

SAXS 4-5.1

Scalar product 6-2, 6-16

Schroedinger equation 4-9, 4-9.1, 4-9.2, 4-12.1, 5-8.1, 5-8.2, 5-9, 5-9.1, 6-13, 6-14, 7-3.2, 7-8, 7-12.3, 7-12.4, 7-12.9, 8-1.1, 8-2.1 to 8-2.4 9-6.7, 10-1.3, 10-3.3 10-11.4, 10-11.5, 10-12, 10-14.2, 10-15.1, 10-15.3, 10-16.4, 10-18.1, 10-18.2, 10-18.3, 11-5.5, 11-5.6, 11-10, 11-10.1, 11-10.2

Secant method 3-9.3, 11-2.1, 11-9.1

Second and higher order differential equations 11-5.5

Second-order equations 10-13.4, 11-5.5

Secular determinant 7-3, 7-6.16, 7-12.6, 7-12.9, 7-13.2, 7-13.4, 7-14.2, 7-14.3, 7-14.5, 7-16.1

Secular equation 7-3, 7-6.16, 7-12.6, 7-13.2, 8-2

Selection rules 1-9.7, 7-6.1, 7-6.12

Self-adjoint matrix 7-4.8

Self-energy integral 7-3

Semenov’s method 4-8.1

Separable variables 10-1.4

Separation of variables 10-15.1, 10-15.2, 10-15.3

Separatrix 10-3.3, 10-3.4, 11-6.3, 11-6.4

Sequence repeats in DNA 5-4.3

Sequential chemical reactions 10-13.1

Sequential reactions with equal rate constants 10-13.2

Series expansion 1-3, 1-4.4, 5-3, 5-6, 5-6.3 to 5-6.7, 5-7, 8-2.4, 9-1.2, 9-1.7, 9-2, 9-3, 9-4.1, 10-14.1 to 10-14.3, 11-, 11-1.1, 11-3

Series solution of differential equations 10-14.2, 10-14.3

Shannon Sampling 9-9.5

Shooting method 11-5.6, 11-9.1, 11-10.1

Shot noise 9-8.5

SI units 1-4.5, 3-3.8, 4-12.1, 7-14.6, 11-3.9, 11-10.2, 14.1.1

Signal to noise 9-, 9-5.2, 9-5.3, 9-6.5, 9-11.3, 9-11.4, 13-1.3, 13-9

Signals buried in noise 9-6.5, 13-9

Significant figures 1-2.1

Similarity 5-7, 7-6.1, 7-6.10, 7-10, 7-13.2 to 7-13.5, 9-4, 9-6.8, 9-8, 9-12, 9-13.1

Similarity and Classes 7-6.10

Similarity transforms 7-13.4

Simple harmonic motion 1-5.2, 7-14.2, 7-14.3, 10-3.2, 10-10.2, 10-10.5, 10-11.3, 10-12.1, 10-12.7, 11-6.4

Simple pendulum 10-11.1

Simpson’s rule 5-6.7, 11-3, 11-3.4, 11-4.5

Simulation 6-18, 9-13.1, 10-12.1, 11-4.6, 11-4.7, 12-, 12-3.1, 12-3.2, 12-3.3, 12-3.4, 12-4.1, 12-6.2, 12-6.4

Simulation of one-dimensional diffusion 12-3.3

Simultaneous equations 3-10.2, 7-12.1 to 7-12.6, 7-14.3, 7-14.4, 8-1.1, 10-10.1, 10-13.2, 13-6.2, 13-7.3

Single photons 1-3, 7-6.12, 12-3.4, 13-8

Singular matrix 7-4.10, 7-12.6

Sinc 3-6, 5-1.3, 9-5.6, 9-6.5 to 9-6.9, 9-8.8, 9-9.1, 9-12

Sinh 1-5.6, 1-6, 3-3.10, 4-2.7, 4-2.14, 4-13.4, 5-6.10, 10-10.3, 10-11.2, 10-12.8, 12-6.9, 12-6.10

Sinograms 9-14.3

SIR model of infection 11-7 to 11-7.3, 11-7.6, 12-5

Skew lines 6-15.3

Skydiving 10-8.1

Slater determinants 1-9.8

Small angle x-ray scattering 4-5.1

Small sample 13-3.2

Smoothing 9-2, 9-10, 9-10.1 to 9-10.4, 9-14.4, 11-3.5, 13-3.6

Spectral resolution 9-5.2, 9-8.8

Spherical polar coordinates 1-7, 4-10.2, 4-11, 6-6, 7-8

Spin basis set 8-4.2

Spin-orbit coupling 7-6.12, 10-2.4

Spin-spin coupling 8-3, 8-3.1, 11-5.1, 11-7, 12-5

Springs 6-1.3, 7-14.5, 10-10.6, 10-13.4, 11-5.3

Spur 7-4.4

Square Root 1-2.2, 1.3, 1-8.1

Square wave 9-1.7, 9-1.8, 9-4.1, 9-5.6, 9-6.6

Stable points 11-8.4

Standard Deviation in the Mean 13-1.3

Standard normal distribution 13-3.1, 13-9

Standing waves 1-5.4,

State functions 3-11.1, 4-13.6, 4-14, 4-14.1

Steady state 4-8.1, 7-13.2, 10-2.1 to 10-2.5, 10-3.1, 10-5, 10-5.4, 10-12.1, 10-15.5, 11-6.2, 11-6.4, 11-7.3, 11-8.1

Stimulated emission 7-10, 10-3.1, 10-12.1

Stirling’s formula for factorials 1-8, 1-9.23, 1-9.26, 3-3.13, 5-7

Stokes’ equation 10-18.1

Stokes’ law 10-12.1

Stokes-Einstein equation 10-2.4, 10-4.3, 10-12.1, 10-15.8, 13-6.1

Structure factor 2-3.3, 2-4.2, 9-13.1, 9-13.2, 9-13.7, 9-13.8, 9-13.9

Sugars 6-19, 10-15.8, 13-11

Summary of some Fourier Transform properties 9-6.8

Summation 1-3, 1-5.5, 1-11, 4-1.1, 4-8.1 to 4-8.5, 5-1 to 5-9

Summation of waves 5-1.2

Superposition 1-5.3, 1-5.5, 5-9.1, 9-5.4, 9-6.7, 9-13.7, 10-18.2

Superposition of waves 1-5.5

Surface of revolution 3-8, 3-8.1

Surface Plasmon resonance 10-15.8

Surface tension 6-1.4, 12-5

Susceptible 11-7, 11-7.1 to 11-7.4, 11-7.5, 11-7.6

Symmetry elements 7-, 7-6.1 to 7-6.4, 7-6.10

Symmetry operations 7-6.1 to 7-6.6, 7-6.7, 7-6.8, 7-6.9, 7-6.13, 7-6.15, 7-6.16

Symmetry Operations as matrices 7-6.8

Table of Differentials 3-3.17

Table of integrals 4-2.14

Table of Summations 5-2.1

Table of trig 1-5.1

Tangent 1-5.1, 1-5.6, 3-3, 3-3.10, 3-4.8, 3-9.1, 4-2.6, 4-2.7, 4-7.2

Tanh 1-6, 3-3.10, 4-2.7, 4-2.14, 4-10, 10-3.4, 10-4.5, 12-6.9

Tautochrone 3-8.2

Taylor series 5-3, 5-6.2, 5-6.5, 5-8.1, 7-6.12, 11-4.6, 11-5.6, 13-4, 13-10.1

Temperature Jump 10-4.3

Temperature profile 10-15.5, 10-15.9, 11-5.4

Temperature profile in two dimensions 10-15.5

Tension 1-5.2, 6-1.4, 10-10.6, 10-15.4, 10-17, 12-5

Test statistic 13-3.4, 13-3.5

The Structure Factor 2-4.2, 9-13.1, 9-13.2, 9-13.7 to 9-13.9, 10-5, 10-5.1, 10-18.4

Thermal diffusion 10-4.9, 10-5.5, 11-4.11

Thermodynamic relationships 3-11.9

Thick lens 7-9

Thin lens 3-10.2, 7-9.1

Threshold for an epidemic 11-7.4

Time profile of an epidemic 11-7.6

Time-dependent Schroedinger equation 10-15.1, 10-16.4

Torque 6-2.2, 6-21.1, 9-5.3

Torsion angles in sugars 6-19

Torsional oscillations 10-11.1

Total derivatives 3-11.7, 3-11.9

Trace 7-4.4, 7-5.7, 7-6.8, 7-6.9, 7-6.13, 7-6.15, 7-12.6, 9-8.4, 9-8.5

Transcendental number 1-2.1, 1-2.4

Transient Grating 7-6.12, 10-18.5, 11-4.11

Transpose 6-2.9, 6-10.1, 6-12, 6-18, 7-3.1 to 7-4.8, 7-4.12, 7-5.8, 7-12.6, 7-13.2, 7-14.2, 7-14.5, 8-4.1, 9-11.5, 13-7.2, 13-11

Trapezoidal rule 11-3, 11-3.3, 11-4.12

Trapezoidal rule integration 11-3.3

Travelling wave 1-5.2, 10-17

Trig formulas 4-3.2

Trig functions 1-5.1 to 1-5.6, 1-6, 2-4.2 3-3.10, 3-3.10, 4-2.7 4-3.1 4-8.3, 4-8.3, 5-6.5, 5-6.5

Trigonometric functions 1-5.1, 1-5.6, 4-3.1

Triple integrals 4-10, 4-10.2

Triple products 6-2, 6-16, 7-6.12

Triplet state 7-2.4, 10-2.3, 10-2.4, 12-2.4

Triplet-Triplet annihilation 10-2.4

Trommsdorff-Norrish effect 10-5.5

Truncation errors 11-1.2, 11-4.2

Two pendulums 7-14.1, 7-14.2

Uncertainty Principle 4-8.5, 7-5.3, 9-5.6, 9-6.6, 9-6.7, 10-11.4, 10-11.5

Undefined integrals 4-2.10

Under-damped 10-12.1

Uniform distribution 4-8.1, 4-8.2, 12-1.1, 12-1.2, 12-3.4, 12-4.1, 13-2

Unit cell 1-5.5, 2-4.2, 6-8.1, 6-8.3, 6-9, 6-10.1, 6-11, 6-16, 9-5.4, 9-6.6, 9-12, 9-13.1, 9-13.2, 9-13.3, 9-13.4, 9-13.7, 9-13.8, 9-13.9

Unit cell volume 6-11

Unit vector 6-2.2 to 6-2.5, 6-3, 6-4, 6-6, 6-7, 6-15.1, 6-15.3, 7-6.9, 9-4

Unitary matrix 7-4.11, 7-4.12, 7-6.8, 7-7, 7-9

Unstable 7-10, 10-2.5, 10-11.2, 11-1.3, 11-4.13, 11-6.2, 11-8.4

Unstable equilibrium 10-2.5, 10-11.2

Unstable recursion 11-1.3

Van der Waals 3-11.1, 3-11.2, 4-1.2, 4-14

Van’t Hoff isotherm 3-4.6

Variance 4-8.1 to 4-8.6, 5-4, 9-6.7, 9-7.4, 9-8.5, 12-2.2, 13-1.2, 13-3.1, 13-3.5, 13-3.8, 13-4.1 to 13-5, 13-6.4, 13-6.6, 13-8, 13-11

Variational Method 4-9, 4-9.2

Vector addition 6-1.5, 6-2.8

Vector multiplication 6-2, 6-18

Vector product 6-2, 6-2.2, 6-15

Verlet algorithm 11-4.6, 11-4.8 to 11-4.10

Vertical mirror plane 7-6.3

Vibrational normal modes 1-5.2, 4-8.4, 5-5.3, 7-4.9, 7-6.14, 7-14.1, 7-14.3

Vibrational wavepacket 9-7.4

Vibrations of a linear triatomic 7-14.4

Virial coefficients 5-6

Virial Theorem 4-12.5, 4-12.6

Viscosity 10-2.4, 10-4.3, 10-4.9, 10-5.5, 10-12.1, 10-15.8, 13-6.1

Wave equation 1-5.5, 1-8.1, 1-9.8, 1-9.25, 4-8.4 to 4-9.2, 4-11, 4-12.1 to 4-12.3, 5-8.1, 5-8.2, 5-9, 5-9.1, 6-12, 7-2.4, 7-6.12, 7-8, 7-12.3, 7-12.4, 7-12.9, 8-1, 8-1.1, 8-2, 8-2.1 to 8-2.4, 8-3, 8-4.2, 8-5.1, 9-3, 9-4.1, 9-6.7, 10-11.4, 10-14.2, 10-15.1 to 10-15.4, 10-17, 10-18.2, 10-18.3, 11-1.3, 11-10, 12-6.6

Wavepacket 1-5.5, 5-9, 5-9.1, 9-6.7, 9-7.4, 10-15.1, 10-18.2

Waves 1-5.2 to 1-5.5, 1-13.3, 2-3.3, 3-6, 4-5.1, 5-1.2, 5-1.3, 9-1.1, 9-1.2, 9-5.2 to 9-5.7, 9-6.3, 9-6.6, 9-6.7, 9-7.4, 9-8.7, 9-10.3, 9-12, 9-13.1 to 9-13.8, 9-14.1, 10-11.4, 10-15.4, 10-16.4, 10-17

Weight average 5-4.2

Weighting 4-8.1, 6-1.5, 9-1.2, 9-4, 12-6.1, 12-6.4, 13-3.8, 13-6.2, 13-6.4, 13-7.5, 13-8, 13-10.1

White noise 9-6.5, 9-8.5, 9-8.6

Wiener-Khinchin 9-8.3, 9-8.6

Work done 1-4, 3-11.1, 4-1.1, 4-1.2, 4-14, 6-6, 10-12.2, 10-12.4

X ray diffraction 1-5.5, 2-3.3, 2-4.2, 5-1.2, 9-, 9-5.4, 9-13, 9-13.1, 9-13.2, 9-13.6, 9-13.9

Yield 1-9.14, 10-2.3, 10-4.3, 11-5.3, 12-2.4, 13-3.5, 13-6.1

Zero filling 9-9.8

Zero-point energy 10-11.4

Zimm and Bragg 7-13.5

Zipper model 5-5.2