FOR INFORNATION
SiMON FRASER UNIVERSITY
MEMORANDUM
To ......... FIJt.. .Ey.an.s,.Secretary.....................
From.
..N..Jjeath.,.Assistant..to..the
S.enate .................................. .......
I
?
... Dean..of.Science..............................
Subect ..... Rpor.t.
n. Special. Topic. Courses
.....
.
4 ?
Date... 1978-12
.
J9 ....................................
Details of the selected topics courses offered in the
Faculty of Science in the semesters 77-3, 78-1, 78-2 and 78-3
are attached for the information of Senate. The courses included
are:
77-3 Biological Sciences
?
471 Experimental Aquatic Biology
472 Advanced Developmental Biology
473 The Echinoderms
Mathematics ?
495 Non Parametric Statistics
Physics ?
198 Introductory Astronomy
78-1 Biochemistry ?
420 Contemporary Biochemistry
Biological Sciences ?
471 Introduction to Mammajogy
472 Anatomy, Biology and Taxonomy of the
Araneae of Canada
473 Physical and Chemical Aspects of the
Terrestrial Environment
Mathematics ?
291 Mathematical Model Building
292 Principles of Mathematics for Teachers TI
496 Experimental Design
78-2 Biological Sciences
?
471 Limnology
78-3 Biological Sciences
?
471 Ornithology
471 Biology of fishes
472 Toxicology
472 Environmental Physiology
473 Experimental Ecology of Benthic Marine
Algae
.12
1
0
?
H.M. Evans
?
-2-
?
...... ?
. ?
1978-12-19
?
78-3 Chemistry
?
472 Theoretical Chemistry
Mathematics
?
292 Introduction to Actuarial Mathematics
Physics
?
493 Nonlinear Problems in the Physical
World
N. Heath
NH: km
Attach.
0
Department of Biological Sciences
.
?
Course Outline
Fall 1977
(at Kelowna)
?
BiSc. 471-3
(2-0-4)
?
Dr. L.D. Druehi
Special Topics
in Biology:
Experimental
Aquatic Biology
Prerequisites:
BiSc. 204 (or 0knagan Coil., BiSc. 222).
Recoumeflded BiSC. 326 be taken concurrently.
Theories and techniques for the evaluation of aquatic biological
processes
will be explored. Emphasis will be on local waters.
Ofle field trip to the Bamfièld Marine Station is planned. Each
student will conduct a research project.
Enrollment: 4
.
? /
1
Department of
Biological Sciences
S
?
Course Outline
Fall
1977
?
BiSc. 472-3
(2-2-0)
?
Drs. Baillie & Smith
Special Topics
in Biology: ADVANCED DEVELOPMENTAL BIOLOGY
Prerequisites: RiSc. 201, 202 and 203. BiSc. 301 recommended.
This course is designed to. bring the advanced undergraduate
student up to date in modern studies of developmental biology.
The lectures are concerned with major topic areas such as
cytoplasmic localization phenomena, maternal versus embryonic
transcriptional events, nuclear totipotency, etc. The lectures
cover the classical experiments in these areas followed by an in
depth examination of recent experiments at the molecular and
biochemical
level.
The student is expected to be well grounded
in basic embryology,
biochnistry, and cell biology in preparation
for this course.
urse texts: Molecular Biology of Eucaryotic Cells by Hod,
Wilson & wood.
Enrollments 4
U
S ?
2
Department of Biological. Sciences
?
Course Outline
Fall 1977
?
RiSc. 473-3
(0 - 0 - 9)
?
Dr.
P.V.
Fankboner
Special Topics in Biology: The Echinoderms
Prerequisites: BiSc. 306
Objecti
ve
of the course: Further study and training by advanced
students of invertebrate zoology
on the
microanatomy, ecology and
taxonomy of echinoderms living in coastal waters of British
Columbia.
Course Text: Starfishes and their relations by Clark.
Enrollment: 14
is
3
Selected Topics in Mathematics
MATH
495-4
Instructor: Dr. P. De Jong
Title:
?
'
?
'
?
Vector: ?
4-1-0
Enrolment:' ?
10
NON PARAMETRIC STATISTICS
1.
PROBABILITY THEORY
1.1 Preliminary Remarks
1.2 Counting
1.3 Probability
1.4 Random Variables
13 Some Properties of Random Variables
1.6 Continuous Random Variables
2.
STATISTICAL INFERENCE
2.1 Populations Samples, and Statistics
2.2 Estimation
2.3 Hypothesis Testing
2.4' Some Properties of Hypothesis Tests
2.5 NonparametricStatiStiCS
3 SOME TESTS BASED ON THE BINOMIAL DISTRIBUTION
3.1 The Binomial Test
3.2 The Quantile Test
3.3 Tolerance Limits
3.4 The Sign Test and Some Variations
4. CONTINGENCY TABLES
4.1 The 2 x 2 Contingency Table
4.2 The r x c Contingency Table
4.3 The Median Test
4.4 Measures of Dependence
4.5 A goodness of Fit Test
4.6 Cochran's Test for Related Observations
S. THE USE OF RANKS
5.1 The One-Sample or Match Pairs
,
Case
5.2' A Confidence Interval for the Median
5.3 Two Independent Samples
5.4 A Confidence interval for the Difference Between Two
Means
5.5 Measures of Rank Correlation
5.6 Several Independent Samples
5.7 Several Related Samples
5.8 The Balanced Incomplete Block Design
5.9 Tests with Efficiency of One or More
6. STATISTICS OF THE KOLMOGOROV-SMIRNOV TYPE
( •
?
6.1 Tests of Goodness of Fit
,,.,,. ?
2
-
?
4
-2-
6'. STATISTICS OF THE KOL*)GOROV-SMIRNOV TYPE (cont'd)
6.2 Tests for Two Independent Samples
6.3 Tests for Several Independent Samples
7. SOME MISCELLANEOUS TESTS
7.1 Some Quick Tests
7.2 A Slippage Test for Several Independent Samples
7.3 Tests Based on Runs
7.4 Fisher's Method of Randomization
Recoended Text:
Practical NonpaTametric Statistics by W.J. Conover,
John Wiley Sons Inc., New York, London, Sydney,
Toronto
S
. ?
5
Periphysical Topics 1.11
PHYSICS
198-3
STITLE:
?
I N I R 0 D U C T 0 R Y
?
A S T R 0 N 0 M Y
FALL SEMESTER
1977
INSTRUCTOR: ?
Leigh Hunt Palmer
TEXTBOOK: ?
Exploration
of
the Universe, Third Edition,
by George 0. Abell
TIME & PLACE:
7:30 - 9:30 p.m. Monday and Wednesday,
Room 9002
Introductory Astronomy will be a quantitative survey
of the subject with mathematical treatment at the level
of simple algebra. Lectures will be supplemented with
planetarium sessions and optical observation sessions.
Relevant physics from the areas of optics, mechanics,
relativity and nuclear physics will be included. The
astronomical topics will be selected from among those in
the textbook and will include the motions of the earth,
moon, sun, planets, and stars, methods and
instruments
of observational astronomy, stellar and galactic evolution,
and cosmogony..
Questions regarding the course should be directed to
Leigh Palmer at 291-4844.
Vector: 3-1-0
Prerequisites: B.C. High School Physics 11 and Math 12 or equivalent
Enrolment: 46
6
SIMON FRASER UNIVERSITY
?
MEMORANDUM
N. Heath ?
A.M. Unrau
To.
?
From
.....................................................
....................................................
?
...
BIOCHEMISTRY 420-3 ?
18 December, 1978
Subject.....
l
... 78.......
Spri .ng
............................
Date
- ?
Semester
"Selected Topics in Contemporary Biochemistry"
Topic
Physical and Biochemical Properties of Model and Cell Membranes
1.
Historicland modern concepts of membrane structure. Electron micro-
scopic examination of membrane structure. Chemical composition of
biotnembranes;
2.
Comparison of synthetic model monolayer and bilayer vesicles with blo-
membranes;
3.
Studies of physical properties of membranes; i.e., fluidity of structure:
(a)
E.S.R. - mobility of polar head-groups and mobility along hydrocarbon
chain of fatty acid;
(b)
N.M.R. - Deuterium label, relaxation phenomena, etc.
4. Transport
properties, theories
of active transport;
5.
Macrolide antibiotic
effect on
membrane
structure;
6.
Correlation of antibiotic resistance with sterol biosynthesis pathways.
AMU
/ ae
Instructor : A.M. Unrau
Vector: ?
3-0-0
Enrolment:
?
4
Prerequisite,: Permission of the Biochemistry Curriculum Committee.
Upper levels standing (with at least 60 semester hours)
in the Biochemistry Program will usually he required.
7
Department
of Biological Sciences
Course Outline
Spring 1978 (at Kelowna)
?
BiSc. 471-3
Dr. R.M. Sadleir
Special Topics in Biology: Introduction to Manunalogy
Prerequisites: Permission of the Department.
A review
of the biology of mammals with special emphasis on the
larger game species of British Columbia and on marine mammals.
urSe, Texts: Mamalogy by Vaughan.
Maxnrnalogy by Gunderson
Mammalian Odours & Pheromones by Stoddart
The Mammals of B.C. by Cowan & Guiget
ro11ment: 6
.
ru
L!J
- ---- ?
- --r
?
- ?
- ?
- ?
-
•
?
Department-of Biological Sciences
Course Outline
Spring 1978 (at Kelowna)
(2-0-3)
BiSc. 472-3
Dr. Turnbull
Special Topics in Biology:
Anatomy, Biology and Taxonomy of the Araneae of
Canada
Pre-requisites: Permission of the Department.
Canadian Spiders (Araneae): A review of the biology, anatocny,
and taxonomy of spiders with
emphasis
on the conucfl spiders of
Canada.
.
Enrollments: 6
- ?
.9
Department of Biological Sciences ?
Course Outline
Spring 1978
?
BiSC. 473-3
(2 - 0 - 4)
?
Drs. Brooke/Lister
Special Topics in Biology: Physical and Chemical Aspects of the
Terrestrial Environment
Prerequisites: 75 semester hours credit in the biological
sciences program.
Students who have credit for BISC 300 may
not take this for further credit.
• The physical
and chemical aspects of terrestrial environment
as related to biological systems; large and small-scale
envirori%ental processes, energy balances and fluxes;
measurement and evaluation.
Enrollments:
17
F_
L
10
Selected Topics in Mathematics
TITLE: ?
MATHEMATICAL MODEL BUILDING
?
INSTRUCTOR: Dr. M. Singh
EVENING COURSE
?
VECTOR: ?
2-1-0
291-2 ?
ENROLMENT:. 11
SPRING 78
An introductory course in applications of the calculus in business,
commerce, and engineering problems. The course includes: approximation
techniques and mathematical modelling applied to problems in ecology,
population dynamics, business management, and related areas; Mathematics
of finance: finite difference methods and their applications in
actuarial science.
The emphasis will be to inquire into practical and realistic problems.
Making appropriate approximations, mathematical models will be constructed,
and then the subsequeit- comparison of theoretical results with available
data shall be made.
(6
PREREQUISITE: MATH 152-3 or 155-3
8/77
(S
11
Selected Topics in Mathematics?
MATH 292-3
78-1
?
Title: ?
PRINCIPLES OF MATHEMATICS FOR TEACHERS II
Instructor: Dr. H.. Gerber
?
Enrolment: 28
Vector: ?
3-1-0.
1.
Ihtegers, Rationals and Reals
A. Integers and rationals
b. Multiplication and division of integers and rationals
C.
Using integers as exponents
d.
Irrationals and reals
e.
Approximations and rational exponents
2. Logic and set theory
a.
Venn Diagrams, complements and intersection
b.
Logical connectives
3. Inform
a.
b.
C.
d.
e.
f.
g.
h.
i.
%J
Geometry and MeasuremEnt
Points, lines and planes
Angles and separation
Simple closed curvet
Motion Geometry - flips or reflections
TranslatiOns, rotations and congruence of triangles
Measurement - Metric system
Perimeters, areas and volumes
Functions, relations and graphs
The straight line and the circle
4. COnuting
•
a. Hand calculators
b. Flow charts
PREREQUISITE: MATH 190-3
11/77
(.
12
Selected Topics in Mathematics
'10
MATH 496-4
Title: EXPERIMENTAL DESIGN
Spring 78
Instructor: Dr. P. De Jong
Vector: ?
4-1-0
Enrolment: ?
10
1. Brief review of:
(a)
Distribution of random variables, expected values.
(b)
Sampling from
N(11,0 2
)
with the reneratibn of chi-squares,
F and t distribution.
(C)
Two parameter tests with explanation of fl
0 :
11 l
=
u
2
test
by t or
,
F , and generalization to One-way ANOVA.
(d) Review of P9wer and required sample size.
2. Analysis of variance
(a) One-way analysis (one factor)
(b) Two or more, factors
(c) Fixed, random and nested models
(d) Tuckey's and Scheff's tests
.
3. Analysis of covariane
4.
Multiple regression
5.
Factorial Experiii'ents
(a) 2n models
(h) Latin squares and Greco-Latin squares
(c)
Conformity
(d)
Fractional designs
(e) Incomplete block designs
(f) Response surfaces.
PREREQUISITES: Math 302 or Math 371. Permission will be given to students
from other departments with suitable backgrounds.
RECOMMENDED TEXT: Fundamental Concepts in the Design of Experiments by Hicks
REFERENCE TEXT: ?
Introduction to Linear Models and the Design and
Analysis of Experiments by William Mendenhall
11/77
ii
Department of Biological Sciences
Course outline
Intersession - BISC 471-3
Summer
1978
?
Dr. G.H. Geen
Special Topics
in Biology: Limnology
.Prerequisites: One
of BISC 300, 306 or 424 recommended.
This course will involve a consideration of
fresh waters
with
particular
reference to those in British Columbia. The origin
of
lakes
and streams and the physical and chemical parameters of
particular importance to plant and animal life will be considered.
Much of theemphasis in the lectures, laboratories and field work
will focus on the biology of fresh water organisms.
Recommended Text: Llmnology
by R.G. Wetzel
Enrollment:
5
14
.
Department of Biological Sciences
?
Course Outline
Fall
1978 ?
BiSc. 471 (Group 01)
(2 - 0 - 4) ?
Di:. N. Verbeek
Special
Topics in Biology:. 0inithology
Prerequisite: BiSc.
304 or BiSc. .316.
TO provide advanced undergraduate students with an understanding
of the biology of birds. This will be achieved through a series
of lectures on a wide range of topics. Laboratories will
emphasize
classification, identification, and morphology
of North American
birds, behaviour, and ecology. Field trips will provide practical
experience in
field identification, behaviour studies and ecology
of birds.
Course. texts: Families of Birds by O.L. Austin
The Life of Birds by J.C. Welty
B
i
rds of North America by k,bbins et
al
Enrollment:
14
40
Department of B io log lea 1
Sciences
Course
Outline
Fall 1978 (At
Bainfléld)
?
The Biology of Fishes
?
BiSc. 471
(3 - 0
?
4) ?
Dr. K. J.
Brewer
Three one hour lectures will be given each week. Topics to be covered:
1.
Evolutionary histdry and classification of
the main fish groups.
2. The circulatory
system - anatctny and physiology.
3. Structure
and function of the gills and air bladder.
4.
Reproduction and develozment.
S. Ecology and Zoogeoqraphy.
•
?
1boratory Work - four hours per week
This will be divided into two sections:-
A. Fish
will be collected from a variety of marine habitats (eel grass,
kelp beds etc.) and classified in the laboratory.
B Coho salmon (Oncorhnchis kiutcih) will be maintained in the
laboratory
and subjected to a variety of experimental treatments
eg. increasing or decreasing
photoperiods, differing salinities and
temperatures, so as
to determine optimum conditions for growth.
Treatment
with hormones may also be carried out. Results from this
investigation will be presented as a scientific paper.
If
time allows,
a
visit
to salmon spawning beds will also be carried out.
ALLOCATION OF MARKS
1.
Fiflal exam
?
40%
2.
Mid-term exam ?
35%
3.
Coho paper
?
25%
TEXTS
1.
Pacific Fishes of
Canada - J.L. Hart.
Is
F.R.B. of C. 1973.
2. Ichthyology - K.F. Lagler et al. 1977.
Enrollment: 13
?
16
Department of Biological Sciences
Course Outline
Fall 1978
?
RiSc. 472 (GroupOi
(2 - 1
?
0)
?
Dr. C. van Netten
Special Topics in Biology: Selected Topics in Toxicology
Prerequisite: RiSc. 201 or permission of the Department.
This course will investigate the available information regarding
the modern chemical environment and its effect on living organisms.
Topics dealt with will include heavy metals, pesticides, PCBs,
food additives, synthetic hormones, and drugs. Special attention
will be given to the physiological and biochemical principles
involved and their relationship to cancer.
Enrollment: 46
Department of Biological Sciences
Course Outline
Fall
1978 (at
Bamfield)
?
Environmental Physiology
?
BiSc. 472
(3 - 0 - 4)
?
Dr. K. Brewer
Three
one hour lectures will be given each week. Thpics to be covered:
1.
Diving in vertebrates - whales, seals, otters, amphibians and reptiles.
2.
Animal rhythms.
Photoperiodimu.
3.
Life at high
altitudes.
4.
Thermal relations - endothermy and
ectothérmy.
Life in hot and cold
environments. Hibernation.
5.
Regulation of salt and water levels in vertebrates and invertebrates.
Life in hypo-and hyperosmotic environments.
.
?
Laboratory work.
-
Four hours per week.
The theme of the course will be ono - and
ionorequlation
in different
animal groups. Two projects from the following will be carried out
and results preseted as scientific papers.
1.
Ion
levels and osmotic pressure will be monitored in a variety of
experimental
situations in an invertebrate species. Depending on
availabilityi annelids,
crustaceans or molluscs will be used.
2. The
ability
of euryhaline and stenohalne fish species to withstand
charges in the ambient medium. If possible, beach fish will be
collected at various times after the tide has receded and plasma
samples analysed for various ions. Oxygen concentrations and water
temperatures in tidal pools will be recorded.
3.
The
marine green
turtle, Che].Onia mydas, has modified orbital glands
which function to rid the body
of
excess salt.
A
study of
thT role +
played by the salt gland
and
the kidney/cloacal complex in Na and K
homeostasis will be carried out.
ALLOCATI
ON CF MARKS
1.
Final exam
?
-
40%
2.
Mid-term
exam - 30%
• ?
3. Project ?
- 30%
TEXTS - Comparative Physiology of Animals - an environmental approach.
R.W. Hill.
Enrollment! 13
flWAflT?1flNT OF BIOLOCICAL
.
SCIENCES
Course Outline
Semester: 78-3
?
Vector: 3-0-4
Rls(:. 473-3, Special
Topics: ?
Prof. Dr. L. Druehi
ExperiflCfltal Pcology of Renthic Marine Algae
Lectures, RadiugS and Laboratory exercises dealing with
various biological functions of seaweed particularly as they relate
to
ecology.
Text:
Selected
re prints
Evaluation technique:
2 Papers and an examination.
Enrollment: 18
... ?
19
p
Ci-IEM 472-3
?
Selected Topics "in Theoretical Chemistry
Course Outline for Chem
472
Fall 1978
?
S
Prof. C. Maui
Texts:
(I) F.A. Cotton: Chemical Applications of Croup Theory. Wiley
lnterscicnce Second Edition 1971.
(II) E.G. Kaplan: Symmetry of Many-Electron Systems:
Academic
Press 1975.
Course Contents: 1. Groups: Subgroups, Classes,
?
. Some examples of groups.
2. Molecular Symmetry and Symmetry groups,: Finite groups,
classification of molecular symmetry groups. Proper axes
and rotations. Improper axes and rotations. Symmetry point
groups.
• '
?
3. Group Representations - Matrix Representation of Groups:
Character, Irreducible representations, Group representations
4.
Group
Theory and Quantum Mechanics: Wavefunctions as bases
for (IR's).. Direct Product. Symmetry adopted Linear
• ?
Combinations (SALC). Projection operators.
5.
Application of Group Theory: Molecular orbital theoretical
methods and group theory. LCAO/MO/ISCF - Scheme of
Roothaan, CI. Hybrid orbitals, Ligand Field Theory
Molecular Vibrations. Selections Rules.
Instructor:
?
Dr. C. Maui
Vector:
?
3-1-0
Prerequisite: CHEM 361-3
Enrolment: ?
1
V ?
20 ?
.
I'
Selected Topics in Mathematics
MATH 292-3
4FALL
Title: ?
INTRODUCTION TO ACTUARIAL MATHEMATICS
78
?
Vector: 3-4-0
(Evening)
Instructor: Mr. R. Norman
?
Enrolment: 7
An introduction to the theory of interest
}
life insurance and pensions.
Topics to be covered include mortgages,
annuities, life
insurance, registered
retirement savings plans and the funding of pension plans.
1.
Introduction - what is an actuary?
- where do actuaries work?
- training of actuaries.
2.
Compound Interest
- accumulation with interest: (1 + i)
- discounting: v
1
' , the present value
- annuity certain a
nj
- accumulation s-
-(12)
- payment in advance, and more frequently than annual a
?
, a-
- use of compound interest tables
- finding effective rate of interest
3.
Payment schedules (loans, mortgages, etc.)
- equivalence, of two sets of payments
- relationship between a and aj:j_rn
- repayment of loans.
- mortgage schedules
4.
Life annuities
- life tables. 1 , d , p ,
q
X
x x x
- expectation of life t ,
x x
- present value of life annuity; definition of
D,
N
- ?
= ?
other modes of payment
- guaranteed annuities, use of tables
- relationship between
a ?
and
ax+l:
the reserve
5.
Life insurance
- value of whole-life insurance, definition of
M
,
A =
MID
-
Ax = 1 -
?
net premiums for whole life assurance, endowment,
• ?
term assurance
(• ?
...2
21
-2-
5.
Life insurance - cont'd
(I ?
-
office premiums for insurances and annuities
- policy reserves (no expenses) for whole life, endowment,
term, annuities
- loans against policies, surrender values, paid up policies
6. Pensions ?
- types of pension plans, final earnings, money purchase,
career average, fixed benefit.
- funding of pension plans (e.g. Canada Pension Plan,
Registered Retirement Savings Plans, etc.)
Additional topics, as time permits.
7.
Accounts and Investments.
- development of balance sheet and income and expenditure
- accounts, from a common sense point of view.
- equity and fixed interest capital, the stock exchange,
book values and market values.
- valuation of investments for actuarial purposes.
8. The Actuarial Valuation.
.( •
? . ?
- types of valuation (i.e. reason for valuation)
- the valuation basis
- valuation of life insurance companies - solvency and
distribution of surplus.
- valuation of pension funds - solvency and funding.
Prerequisites: (1) Math 101 (with a grade of A or B) and
one
of Math 151, 154,
or Math 157
or (2) Math 371
or (3) (with permission of the Department) equivalent experience.
2? ?
.
1
S
Special Topics in Physics
PHYSICS 493-3
R.H. Enns, Instructor
"Nonlinear Problems in the Physical World"
Text: Chapter 10 of "An Introduction to
the Methods and Tools of Theoretical
Physics" by R.H. Enns and
S.S. Rangnekar (a text in preparation)
Outline attached.
Vector: 3-0-0
Prerequisite: Permission of the Department
Enrolment: 7
RECEIVED \
L
?
23
?
DEC
Dw 0
1978
LJ.
N
Chapter.10 - Nonlinear Problems in the Physical World
10.1
?
Introduction (
pp
1-3).
10.2 ?
Some Interesting Nonlinear Systems (pp 3-36)..
A. ?
Nonlinear Mechanics,
(Simple pendulum, Jaáobian elliptic functions, the
eardrum, nonlinear damping.)
B.
?
Competition Phenomena
(Volterra competition equations (big fish-little fish,
rabbits-foxes, etc.), Eigen's theory of selection and
• ?
.
evolution of biological molecules, interacting laser
beams, arms race between nations.).
C. ?
Nonlinear Electrical Phenomena
(Nonlinear inductance., electronic oscillator circuit
(Rayleigh equation, Van der Pol equation).)
• ?
,
?
,
?
D. ?
Solitons ?
.
?
.
(Water wavésand the KdV. equation, the Sine-Gordon
equation,-self-induc
ed
transparency.)
10.-3
?
Methods of Solution (pp 37-72)
A ?
Exactly Soluble Equations
i) ?
Equations whOse variables, can be separated.
ii) ?
The Bernoulli Equation.
(Laser beam problem, nonlinear diode.)
.
?
.
iii) The Riccati Equation.
•
(competition between two species.)
iv) ?
Equations of the structure d
2 y/dx 2 ?
f(y).
(Simple pendulum, elliptic integrals, elliptic
functions, phase, plane diagram for.pendulum.)
B. ?
Variation of Parameters.
' ?
'
?
(Nonlinear damping, intrOduction to Krylov._BUgOliUbov
S
method.)
?
,, ..,
?
.
?
•
?
.
10 4
?
Topological Analysis and Graphical Solutions (pp 73-138)
A ?
Topological Analysis
(Phase plane diagram, types of singular points (vortex,
saddle point, focal point, nodal point), criteria for
classification of singular points, stability criteria,
higher order singularities:
?
theorem for the
• ?
' .vortex and applications.)
. ?
.
S
B ?
Graphical Methods of Solution
1) ?
The Isocline Method
(Solution of Van der Pol equation, introduction to
limit ?
cycles.)'
?
.
2)
?
The Dólta () Method
• ?
•
?
• '
?
(Nonlinear ?
spring,' Rayleigh
?
equat ion,
?
relaxat,jOfl
. ?
•
oscillations.) ?
.
?
,
24
-4'
10.5
Limit Cycles
?
(pp 139-153).
(Examples of stable, unstable and semi-stable limit cycles,
multiple limit cycles, first.. theorem of Bendixson and
applications, Poincar-Bendixson theorem and examples.)
10.6
. Analytical Methods (
pp
154-203).
A. ?
The Perturbation Method..
1) . Poisson's Method
(Theory, application to nonlinear diode, nonlinear
spring, secular terms.)
ii) Lindstedt's Method
(Theory, removal of secular terms, nonlinear spring,
Van der Pol equation,, introduction to Duff ing's
equation.)
B ?
The Krylov-BogoliubOV (K-B) Method
(Theory, nonlinear spring, nonlinear damping, Coulomb
friction.)
C. ?
Ritz Method.*.
?
.
(Theory, nonlinear diode,' nonlinear spring.)
D. ?
Galerkin's Method
(Theory, applications.)
10.7
Forced Oscillations of Nonlinear Systems (pp 204-232).
A ?
Iterative Solution of Duffing's Equation
B ?
The Nonlinear Response Curve
C
?
Effect of Damping on the Nonlinear Response Curves
D ?
The Jump Phenomenon and Hysteresis
(Stability considerations.)
E.
?
Subharmonic Response
10.8
Ele ?
mentary Soliton Calcul
i
i ?
( pp
233-243)
(Solution of KdV equation, solitary wave solutions of 3-wave
problem in nonlinear optics )
10.9
Numerical Techniques(pp 243-264)
A ?
}inite-Difference Approxinations to Derivatives
B
?
Some Finite-Difference Methods
i)
?
u. er Method
(Application to rabbits-foxes problem )
ii) ?
Modified Euler Method
iii) Runge-Kutta Methods
i) ?
'An Explicit Method of Solving P.D.E.
(Heat ?
flow.),,
v) ?
Crank-Nicolson Implicit Method
vi) ?
Method of Characteristics
(Interacting laser beams,. Sine-Cordon
cquitlOfl
C.
?
(onclusion
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