School of Mathematics
Course 1S  Mathematics for Science students 19992000 (JF Mathematics as a whole subject within the Natural Science
Moderatorships. JF Human Genetics. JF Computational Physics and Chemistry.
JF Medicinal Chemistry.
)
Lecturer: Dr. S. McMurry, Dr. B. Redmond, Dr. R. M. Timoney, Dr.
N. H. Buttimore & Dr. T. G. Murphy
Requirements/prerequisites: None
Duration:
Number of lectures per week: 8 lectures per week including
course 061 (1 lecture per week for part of the year; separate course
description)
Assessment: Those taking the Chemistry, Mathematics and Physics combinatin
take parts 1, 2 and 3 together with 061. Others take parts 1, 3 and 4
together with 061.
The three main sections of the course will count equally towards
the
overall result for the course.
Two endofterm assignments assignment will each
count for 10% of the marks for section 2.
Practical work, assignments, tutorial work and 061 assignment results
will count for 1/4 of the marks for section
3,
with the paper counting for the remaining 3/4.
Endofyear Examination: Three 3hour exams on each section, papers 1, 2, 3 and 4
Description:
Section 1
Dr. S. McMurry
 Differentiation of functions of one variable.
Anton (Calculus): Chapters 23. Chapter 1, sections 1.1, 1.2, 1.4
assumed known.
 Antiderivatives and integration.
Anton (Calculus): 7.17.5, 7.8.
 Trigonometric and hyperbolic functions, and the corresponding inverse
functions; logarithmic function, exponential function.
Anton (Calculus): 3.4 and Chapter 4. Also part of 7.6.
 Introduction to partial derivatives.
Anton (Calculus): Part of 15.3
 Polynomials, sequences and series, including simple convergence tests.
Anton (Calculus): 11.111.6, 11.8.
 Complex numbers.
There is a web page for this part of the course, which is upmydated during
the year. The address is
http://www.maths.tcd.ie/pub/coursework/1S1
Section 2
Dr. B. Redmond
Vectors and linear algebra, differential equations, and applications
to physical examples.
More detailed outline:
 Vectors, addition, scalar product, cross product,
vector equation of a line in 3 dimensions,
triple vector product, differentiation. (Anton (Calculus): 13.113.6)
Parametric equations (Anton (Calculus): 1.7); cylindrical coordinates
(Anton (Calculus): 13.8).
 Matrices, systems of linear equations, determinants.
(Anton&Rorres: Chapters 12)

Ordinary Differential Equations of first and second order.
Linear differential equations with constant coefficients.
Nonhomogeneous. (Kreysig: from Chapter 12)
 Applications/Examples:
Simple Harmonic motion, with and without resistance.
Electric circuits.
Radiocative decay.
Motion in a resisting 1dmensional medium.
(Anton (Calculus): Chapter 10, Kreysig: from Chapter 12)
Section 3
Dr. R. M. Timoney
 Introduction to computing
Binary, octal and hexadecimal integers;
storage of integers and floating point numbers in computers (via
bits).
 Introduction to symbolic computing
Use of a computer algebra system.
Facilities of the system for elementary number theory and algebra.
Elementary facilities for differentiation, integration and
differential equations.
Plotting and the mathematical basis.
User defined functions.
Anton (Calculus): 1.3, Chapter 5, exercises in Chapter 23, 710
marked CAS or `graphing calculator'. Mathematica book Part 1 (less
than what is in section 1.11.9).
 Differential Calculus
Maxima and minima and plotting (with the aid of symbolic
computation); parametric plots.
Linear approximation, root finding using Newton's method.
Anton (Calculus): Chapter 5 and 3.6.
 Integration
The concept of a definite integral (area or Riemann sum).
Elementary algorithms for computing definite integrals
(trapezoidal and Simpson's rules).
Fundamental Theorem of Calculus and antiderivatives
Techniques of integration and standard applications
(backed up by practical work using computer algebra).
Anton (Calculus): 7.1, 7.57.7, 8.18.4, 8.6.
 An introduction to probability and statistics
The notion of a probability on a sample space, mean and standard deviation
for random variables, sample mean and sample variance, the normal
distribution.
Kreysig: 22.122.3, 22.522.6, 22.8.
There is a web page for this part of the course, which is upmydated during
the year. The address is
http://www.maths.tcd.ie/pub/coursework/1S3
Section 4
Dr. N. H. Buttimore
Vectors and linear algebra, differential equations, and applications
to biological examples.
More detailed outline:
 Vectors, addition, scalar product, cross product,
vector equation of a line in 3 dimensions,
triple vector product, differentiation. (Anton:13.113.6)

Matrices, systems of linear equations, determinants.
(Anton&Rorres: Chapters 12)

Ordinary Differential Equations of first and second order.
Linear differential equations with constant coefficients.
Nonhomogeneous. (Kreysig: from Chapter 12)
 Applications/Examples: TO BE SPECIFIED
Radiocative decay.
Essential Reference
 Howard Anton, Calculus: a new horizon
(6th edition), Wiley, 1998.
Recommended references
 Howard Anton and Chris Rorres, Elementary Linear Algebra
applications version, (7th edition) Wiley 1994.
 Erwin Kreyszig, Advanced Engineering Mathematics, (7th
edition) Wiley, 1993.
 Kenneth A. Stroud,
Engineering mathematics : programmes and problems, (4th edition)
Macmillan, 1995.

S. Wolfram, Mathematica a system for doing mathematics by computer,
AddisonWesley (3rd edition) 1996, published by Wolfram Media and
Cambridge University Press.

G. B. Thomas & R.L. Finney, Calculus and Analytic Geometry (9th
edition), Addison Wesley, 1996.
Oct 8, 1999