MA1S11: JF Mathematics for Scientists
Notes
Some (not all) parts of the course notes will be in the form of a handout or will be available here. All will be in PDF format and require a programme such as Adobe Acrobat Reader to read them.
- Chapter 0. What is Linear Algebra?
- Some short introductory remarks.
- Chapter 1. Vectors
- This deals with vectors from a geometrical point of view (arrows) first. Then a more algebraic approach (with components). Equations of lines and planes in space. Cross products. Basic ideas about higher dimensions.
- Chapter 2: Linear Equations
- Here we deal with Gaussian elimination and Gauss-Jordan elimination, as ways of solving systems of linear equations.
- Chapter 3: Matrices
- These notes deal with matrix operations (addition, muliplication by scalars, matrix multiplication). They continue with expressing elementary row operations via matrix multiplication by elementary matrices, inverses, how to find inverses. Next special kinds of square matrices (diagonal matrices, upper triangular matrices, strictly upper triangular, nilpotent matrices, lower triangular). Transposes. Traces of (square) matrices. An application: directed graphs and their vertex matrices.
- Chapter 4: A little on Spreadsheets
- Some basic uses for spreadsheets.
- Chapter 5: Binary, octal and hexadecimal numbers
- First, what are binary, octal and hex, how to convert between them and how to convert to/from decimal. Relationship with computers, storage of (signed) integers. Limits arising from the usual systems (use of approximation $2^{10} \cong 10^3$). Floating point. Idea of relative errors and use of condition numbers.