MA1S11: JF Mathematics for Scientists
What is where in the textbook
This refers to Elementary linear algebra : with supplemental applications / Howard A. Anton, Chris Rorres Publisher: Wiley, Hoboken, NJ 2011. [Hamilton, Counter Reserve 512.5 L32*9-2;29; Hamilton, Lending S-LEN 512.5 L32*9-2;6]
- Chapter 1: Vectors
-
They
deal with vectors from a geometrical point of view
(arrows) first. Then a more algebraic approach (with components).
Equations of lines and planes in space.
Basic ideas about higher dimensions.
Anton & Rorres, Chapter 3 excluding last 2 sections.
(See also Chapter 11 of Anton's Calculus) - Chapter 2: Linear Equations
- These notes deal with Gaussian elimination and Gauss-Jordan
elimination, as ways of solving systems of linear equations.
Anton & Rorres, sections 1.1, 1.2 - 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.
Anton & Rorres, sections 1.3 - 1.7 and 10.6 - Chapter 4: A little on Spreadsheets
-
Some basic uses for spreadsheets.
(No special book - there is online Help in Google Docs that may help if the notes don't.) - 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.
No special book - the notes mention a number of online sources of information, some of which go into more detail than we did: