Mathematics Course 1S3 for JF Science students
Notes
Some (not all) parts of the course notes will be in the form of a handout or will be available here.
- How to use the Mathematics computers
- These notes offer a few basic ideas about how to use the Maths (UNIX - FreeBSD and Linux) computer system (here as a pdf file that may print better).
- Chapter 1: Binary, octal and hexadecimal numbers
- These notes are in PDF format and require a programme such as Adobe Acrobat Reader to read them. They deal with elementary matters about base 2, base 8 and base 16, how these relate to one another and to the way computers store numbers (integer and floating point storage). The limitations on size and accuracy of the standard methods computer use are considered.
- Chapter 2: Mathematica
- These notes are here as a PDF file. They give a very quick introduction to how to use the computer programme Mathematca.
- Chapter 2: appendix
- These notes are here as a PDF file. They deal with the idea of a function, the graph of a function, parametric graphs, and hyperbolic functions. Examples include circles, standard ellipses and standard hyperbolae.
- Chapter 3: Graphing, maxima and minima
- These notes are here as a PDF file. They cover the Intermediate Value theorem, Rolle's theorem, Mean Value Theorem, graphing, max/min problems.
- Chapter 4: Linear approximation and applications
- These notes are here as a PDF file. They cover the linear approximation formula (a consequence of the definition of the derivative), relative errors, condition numbers. Also the intermediate value theorem, its application to the bisection method for root finding, and Newtons method.
- Chapter 5: Numerical integration
- These notes are here as a PDF file. They cover the Trapezoidal rule and Simpsons rule, error estimations for them, and efficient ways of computing integrals with them. There is an additional section here, about how to use spreadsheets.
- Chapter 6: Integration: partial fractions and improper integrals
- These notes are here as a PDF file. The topics covered are partial fractions, improper integrals. There are background sections on integrating powers of tan and sec, on the inverse hyperbolic functions and on inverse trigonometric substitutions. There is an appendix dealing with substitution, integration by parts and more simple trigonometric integrals.
- Chapter 7: Applications of Integration
- These notes cover just 3 applications (fluid pressure on a flat vertical wall caused by a uniform fluid and gravity, work done by a force in one dimension where the strength of the force depends on position, and centre of mass in one domension.
- Chapter 8: An Introduction to Probability and Statistics
- The notes are here as a PDF file. They include some basic concepts of probability (sample space, event, probability, random variable, mean, variance), a very little on data and some of the examples of probability distributions most used in applications (binomial, Poisson and normal). In the normal case we are dealing with a continuous distribution and improper integrals enter in.