# 32: Math Chapters

- Page ID
- 38822

- 32.2: Probability and Statistics
- A random variable X can have more than one value x as an outcome. Which value the variable has in a particular case is a matter of chance and cannot be predicted other than that we associate a probability to the outcome. Probability p is a number between 0 and 1 that indicates the likelihood that the variable X has a particular outcome x . The set of outcomes and their probabilities form a probability distribution.

- 32.3: Vectors
- In this chapter we will review a few concepts you probably know from your physics courses. This chapter does not intend to cover the topic in a comprehensive manner, but instead touch on a few concepts that you will use in your physical chemistry classes.

- 32.4: Spherical Coordinates
- Understand the concept of area and volume elements in cartesian, polar and spherical coordinates. Be able to integrate functions expressed in polar or spherical coordinates. Understand how to normalize orbitals expressed in spherical coordinates, and perform calculations involving triple integrals.

- 32.5: Determinants
- The determinant is a useful value that can be computed from the elements of a square matrix

- 32.6: Matrices
- Learn the nomenclature used in linear algebra to describe matrices (rows, columns, triangular matrices, diagonal matrices, trace, transpose, singularity, etc). Learn how to add, subtract and multiply matrices. Learn the concept of inverse. Understand the use of matrices as symmetry operators.

- 32.8: Partial Differentiation
- The development of thermodynamics would have been unthinkable without calculus in more than one dimension (multivariate calculus) and partial differentiation is essential to the theory.

- 32.9: Series and Limits
- Learn how to obtain Maclaurin and Taylor expansions of different functions. Learn how to express infinite sums using the summation operator ( Σ ) Understand how a series expansion can be used in the physical sciences to obtain an approximation that is valid in a particular regime (e.g. low concentration of solute, low pressure of a gas, small oscillations of a pendulum, etc). Understand how a series expansion can be used to prove a mathematical relationship.

- 32.10: Fourier Analysis
- The Fourier transform converts a function vs. continuous (or descrete) time and maps it into a function vs. continuous (or descrete) frequencies. Hence, the transform converts time-domain data into frequency-domain data (and vice versa). This decomposion of a function into sinusoids of different frequencies is a powerful approach to many experimental and theoretical problems.