School of Mathematics
School of Mathematics
Course 1M01 - Mathematical Methods for JF Science
2008-09 (JF Natural Science
)
Lecturer: Dr. R. Levene and Dr. S. Ryan
Requirements/prerequisites: none
Duration: One semester course (10 ECTS).
Number of lectures per week: 8 hours per week total, including 5 lectures, 2 tutorials
and 1 computer practical.
Assessment: Tutorial work and computer practical work will count 25% of
the marks.
End-of-year Examination: One 3-hour exam at in May/June (for 75% of the total marks).
Description:
The syllabus is largely based on
[Bittinger-G-N].
Calculus for Life Scientists
This part will be lectured by Dr. Levene and there will be 3 lectures
plus one tutorail per week.
The syllabus is
approximately
Chapter 1-5 along with a little of Chapter
8 on differential equations (sections 8.1 and 8.2) from
[Bittinger-G-N].
- Functions and graphs. Lines, polynomials, rational functions,
trigonometric functions and the unit circle.
- Differentiation. Limits, continuity, average rate of change, first
principles definition, basic rules for differentiation.
- Graphical interpretation of derivatives, max/min.
- Exponential and log functions. Growth and decay applications.
- Integration (definite and indefinite). Techniques of
substitution and integration by parts. Applications.
- Differential equations and initial value problems, solving
first order linear equations. Some application in biology or ecology.
Discrete Mathematics for Life Scientists
Dr. Ryan will be the lectuer for this part. There will be 2 lectures
per week, one tutorial and, for several of the weeks, a computer
practical.
The syllabus is approximately:
-
Linear algebra. Matrices, solving systems of linear equations,
inverse matrices, determinants, eigenvalues and eigenvectors, solving
difference equations. Population growth. (Chapter 6 of
[Bittinger-G-N].)
- Spreadsheets. Basic concept of programming formulae in a
spreadsheet such as Excel (absolute and relative cell references, some
typical built in functions like sum, count, if). Formula for least
squares fit of a line to points in the plane (without
justification?). Graphs.
Use of log scales.
- Data. Scientific notation, number of significant digits,
relative error. Sample mean, median, sample variance.
- Probability. Basic concepts of probability. The binomial
distribution, expectation and standard deviation for discrete random
variables. (Sections 10.1, 10.3, 10.4 of [Bittinger-G-N].)
Textbook:
- [Bittinger-G-N]
Calculus for the Life Sciences.
Marvin Bittinger, Neal Brand, John Quintanilla.
Pearson Dec 2005
File translated from
TEX
by
TTH,
version 2.70.
On 29 Sep 2008, 23:03.