1Ma
Mathematics for Chemists
The algebra, calculus, linear algebra and statistics that every other branch leans on.
My level
1.1 Numbers, units and functions
- SI units and dimensional analysisGCSEA-LevelUndergradBase and derived SI units, prefixes, significant figures and checking equations by their dimensions.
- Logarithms and exponentialsA-LevelUndergradLaws of logs, natural vs base-10 logs, and why exponentials appear in decay, kinetics and Boltzmann factors.
- Graphs and linearisationGCSEA-LevelUndergradStraight-line plots, gradients and intercepts, and rearranging laws (Arrhenius, Beer-Lambert, Lineweaver-Burk) into linear form.
1.2 Calculus
- DifferentiationA-LevelUndergradRates of change, standard derivatives, product/quotient/chain rules and locating maxima and minima.
- IntegrationA-LevelUndergradAntiderivatives, definite integrals, substitution and integration by parts, applied to work, rate laws and areas under spectra.
- Partial derivatives and exact differentialsUndergradPhDFunctions of several variables, total differentials and the identities behind Maxwell relations.
- Power series and approximationsUndergradPhDTaylor and Maclaurin series and the small-x approximations used throughout physical chemistry.
1.3 Differential equations
- First-order differential equationsA-LevelUndergradSeparable equations and their solution; the mathematics of first-order decay and growth.
- Second-order differential equationsUndergradPhDLinear equations with constant coefficients, the harmonic oscillator and boundary conditions in quantum problems.
- Partial differential equationsUndergradPhDDiffusion and wave equations and the method of separation of variables.
1.4 Linear algebra
- VectorsUndergradComponents, scalar and vector products, and their use for dipoles, forces and crystal lattices.
- Matrices, determinants and eigenvaluesUndergradPhDMatrix algebra, determinants, and eigenvalue problems such as the secular equations of molecular orbital theory.
1.5 Complex numbers and transforms
- Complex numbersUndergradPhDArgand diagrams, polar form and Euler's formula; why wavefunctions are complex.
- Fourier transformsUndergradPhDMoving between time and frequency domains; the basis of FT-IR, FT-NMR and diffraction.
1.6 Statistics and data
- Errors and uncertaintyGCSEA-LevelUndergradRandom and systematic error, mean and standard deviation, and propagating uncertainty through calculations.
- Least-squares fittingA-LevelUndergradLinear regression, residuals and goodness of fit for calibration curves and kinetic plots.
1.7 Symmetry mathematics
- Group theory and character tablesUndergradPhDGroups, representations, character tables and the reduction formula used in spectroscopy and bonding.