UCU Science course 111, year 2004 (Spring)
The lectures of this course (on Thursdays) are taught by Frits Beukers. The
training of Mathematica (on Mondays) and the "help" function while you are
working on the assignment is taken care off by Yaroslav Kondratyuk (kondraty@math.uu.nl)
and Jan Kuiper
The SCI111 course is not a full fledged calculus course. This would take
far more time than the weeks we are allotted. Instead we have selected a
few topics which occur at many places in mathematics and its applications,
e.g. physics, chemistry, econometrics. To some extent we shall develop
a minimal technical skill in these topics, so that you know how
the calculations should be performed with pencil and paper. But more
importantly we shall make you acquainted with the mathematical
package Mathematica. This computer programme contains an enormous treasure of mathematical
knowledge, beautiful graphics capabilities and a very user friendly interface
(although not every beginning student might attest to this). With some skill in
it, Mathematica can be a powerful tool to study mathematical phenomena which
otherwise would far beyond your capabilities.
Every week there will be a training
session in Mathematica. These sessions are an integral part of
the course. They complement and illustrate the lectures, and they allow
you to do your own computations on the topics involved. This skill is
of utmost importance when you work on the assignments, in which much
of the work can only be done using Mathematica.
The course is divided into four periods of comparable size. Each
period is ended
by a small written examination. At the beginning of each period a home work
assignment is distributed which has to be handed in before the beginning
of the next period. Both the assignments and written examinations are graded
and contribute equally to the final grade, which is also determined by them.
The only condition is that you must have scored a C or more on at least three
written exams.
There is no homework in the strict sense of the
word (except the assignments), but you are expected to know the
subjects discussed in class. This means that you should read the
notes that go with the lectures and work out the exercises at the end
of each chapter of these notes. Moreover, you should have worked
through the Mathematica Notebooks, since they are supposed to
enhance your understanding (once you have understood how to deal
with Mathematica).
The Course material will consist of
- Selected Chapters from D.W.Jordan, P.Smith: Mathematical Techniques,
Oxford University Press, 3rd edition, ISBN 0 19 924972 5. This book is
an introduction to techniques for engineers and for the physical and
mathematical sciences. It also contains excellent material for those who
need to repair deficiencies in their mathematical background.
- Lecture notes, to be distributed in the first week.
Below you find a schedule of the activities for Science course 111, listed
by the week. The Mathematica Notebooks can be found in the home-directory of
the Science 111 course at UCU on the P-drive (P:\Science\Math\111). But you
can also download them from this page (right click and choose "Save link
as...").
- Monday, 26/01:
- Thursday, 29/01:
- Lecture on Taylor series
Material: Lecture Notes Ch.1, Book: Ch.5 and Problems
5.1 to 5.7
Here is the Mathematica demo that was
shown in class.
- Monday, 2/02:
- Thursday, 5/02:
- Lecture on Equation Solving
Material: Lecture Notes Ch.2, Book: Ch.4.6 (for Newton-Raphson)
and Problems 4.13, 4.14, 4.15
Here is the Mathematica demo that was
shown in class.
- Monday, 9/02:
- Thursday, 12/02:
- Lecture on Complex Numbers
Material: Lecture Notes Ch.3, Book: Ch.6.1-6.5
and Problems 6.1-6.14
Here is the Mathematica demo that was
shown in class.
- Monday, 16/02:
- Finish last week's lecture, exercises complex numbers.
- Mathematica session,
Complex Numbers
- Thursday, 19/02:
- First hour: Written examination 1 on Chapters 1,2,3
of the Course Notes and the corresponding Chapters in Jordan-Smith
- Hand in Assignment 1 (written or printed)
before the start of the Exam!!
- On special request, here is the
answer to Problem 2.7.6.
- Second hour: Lecture on Functions in several variables
Material: Lecture Notes Ch.4,
- Monday, 23/02:
- Thursday, 26/02:
- Functions in several variables, continued and
(local) extrema in several variables
Material: Lecture Notes Ch.4, Ch.5, Jordan-Smith: 28.1-28.7
- Here is Assignment 2, to
be handed in before the second examination on March 25.
- Monday, 01/03:
- Thursday, 04/03:
- Extrema in several variables, Lagrange multipliers
Material: Lecture Notes Ch.5, Jordan-Smith: 28.1-28.7
and 30.2 (Lagrange multiplier)
- Here is the Mathematica Demo
used in class.
- Monday, 08/03:
- Thursday, 11/03:
- Introduction to vectors
Material: Lecture notes Ch.6, Jordan-Smith: 9.1-9.4, 9.6, 10.1-10.4
- March 15,18 SPRING BREAK
- Monday, 22/03:
- No Mathematica session this time, we
continue with Vectors and Matrices
- Thursday, 25/03:
- Hand in ASSIGNMENT 2
- First hour EXAM 2 on chapters 4,5 of the reader and
the corresponding chapters in Jordan-Smith.
- Second hour: lecture on matrices, determinants
- Monday, 29/03:
- Thursday, 1/04:
- Lecture on determinants and computation of eigenvectors
- Material: Lecture notes Ch 8, 9. Jordan-Smith: 8.1, 8.2, 13.1,
13.2.
- Monday, 5/04:
- Thursday, 8/04:
- Lecture on Eigenvectors and Markov chains
- Material: Lecture notes Ch 10
- Monday, 12/04 SECOND EASTER DAY
- Thursday, 15/04:
- Lecture on Markov chains, dominant eigenvalues
- Material: Lecture Notes Ch 10
- Monday, 19/04:
- Thursday, 22/04: EXAM No 3 (first hour). Chapters 6-10
of the course notes and corresponding chapters in Jordan-Smith.
DEADLINE of Assignment 3.
- Monday, 26/04:
- Lecture on Differential equations.
- Material: Jordan-Smith Ch 18, 22.1
- Thursday, 29/04:
- Lecture on Differential equations.
- Material: Jordan-Smith Ch 18, 23.1-23.2
- Monday, 3/05:
- Thursday, 6/05:
- Lecture on Differential equations.
- Material: Jordan-Smith Ch 23.1-23.6
- Monday, 10/05, 4 PM:
- EXAM 4 on Jordan-Smith Chapters 18, 22.1, 23.1-23.6