SENATE
COMMITTEE
ON UNDERGRADUATE
From ?
S
TUDI
ES
To
?
SENATE
SiMON FRASER UNIVERSITY
?
S
.74-ii
MEMORANDUM
Subject MATH 154-3 AND 155-3
?
Date ?
SEPTEMBER 17, 1974
MOTION: "That Senate approve, as set forth in
S.74-119,
the Revised Proposal for MATH 154-3 and 155-3."
.
.
SiMON FRASER UNIVERSITY
S-
744
/
9
MEMORANDUM
To. ?
SENATE ?
.
?
...
?
From
Senate Committee on Undergraduate Studies
Subject..
Math.
.1.5.47.3....
and 155-3 ?
Date ?
September 17, 1974
At its meeting of September 10, 1974 the Senate
Committee on Undergraduate Studies considered the attached
revised proposal for Math 154-3 and 155-3. It is now
transmitted to Senate for its consid ation with the
Committee's recommendation that it b a proved.
I. Ilugridge
att.
cp.t
A
..
0
SiMON FASER UNIVERSITY
?
L'
74a$5
A Ii•&
mm'dIMuIuYIL
Attached for the consideration of SCUS is the revised proposal
for two new Mathematics courses, MATH 154-3 and 155-3. They
have been reapproved by the Faculty Undergraduate Curriculum
Committee and the Faculty of Science Executive Committee
respectively.
1w
cc: A. Lachlan, Mathematics
.
U
SIMON FRASER UNIVERSITY
MEMORANDUM
S
...... ?
..........
Dr.
S. Aronoff ?
.
?
From
.....................................................................................
Dr. A. H. Lachlan, Chairman
Dean of Science
...
?
Mathematics Department
NEW COURSE PROPOSALS - Math 154-3,
?
.
Subject.........
.
M
ath
155-3 and their associated ?
.Date...
July10, 1974
. .
changes in prerequisites for
mathematic courses
?
.
JUL
ftfl
•
1 1
-
DEAN O
?
SCIENCE ofrc
1.
Following discussions with the Department of
this Department agreed to split the first year calculus courses into two
sections. One section was for students in Biology, and the other for
those in Chemistry, Mathematics and Physics. This has been done on an
experimental basis for the past two years and is considered to be worth-
while. One positive result is the reduction of class size, in the case
of Math 151-3 from 250-300 students to lectures with 100-150 students
in each section. For the past year, a textbook different from the one
used in the regular section of Math 151-3 has been adopted and as a
result, there have been syllabus changes. This is one of the reasons
we are making formal proposals for new course numbers. The other reasons
are to ease administrative procedures with respect to pre-registration
in these courses. Without separate course numbers, it is difficult for
' ?
the Registrar's Office to ensure that students register in the appropriate
lecture and tutorial sections. During the experimental period this has
resulted in tutorial assignments for the split calculus courses being
done departmentally. The new course numbers will mean that these courses
can be treated like the others in the pre-registration procedure.
2.
Assuming that Math 154-3, 155-3 are approved by Senate, the following
changes and prerequisites for other mathematic courses should he
,
made.
We are hereby also seeking approval of these changes contingent upon the
approval by Senate of Math 154-3, 155-3. In summary these changes are
as follows:
Math 154-3 and 155-3 are to be equivalent to
Math 151-3 and 152-3, respectively as pre-
requisites for other mathematic courses. A
detailed list of necessary changes is attached.
3.
Below, some of the objections raised in Senate, when these courses
were first considered, are rebutted.
One objection to the new calculus sequence was that the proposed
courses, Math 154-3 and Math 155-3, would give insufficient preparation
for further mathematics courses. Math 151-3 and Math 154-3 are in fact
interchangeable as prerequisites for other mathematics courses. The only
possible difficulty concerning prerequisites arises with Math 155-3 in
• ?
comparison with Math 152-3. These courses are interchangeable as pre-
requisites for all mathematics courses. However, in Math 155-3 more
material is covered than in. Math 152-3, but in 1es detail. Moreover,
infinite
series, covered in, Math 152-3 is not cov'red in Math 155--3.
Thus a student entering certain courses from Math 155-3 (e.g. Math 253-4
Math 371-3) would be well advised to study series on his own.
!
?
A
SDr. S. Aronoff
?
-2- ?
July 10, 1974
Another objection voiced in Senate was that the proposed calculus
sequence for biologists would limit the flexibility of students to pick
Alternate programmes. Only a minimal amount of difficulty will arise
if the student wishes to change from Biology to Chemistry, Physics,
Mathematics, Bio-Chemistry or Kinesiology. Math 154-3 and Math 155-3,
while they provide adequate background for these subjects do not provide
optimal background for them. Thus Biology students who feel that there
is any significant likelihood of their changing into any of
.
the above
mentioned fields or taking additional mathematics beyond first year
calculus should take Math 151-3 and Math 152-3. We must emphasize that
Biology students who take Math 154-3, Math 155-3 and who decide to take
additional mathematics will certainly be able to do so.
Although the topic of infinite series has been omitted from the
Math 154-3, Math 155-3 sequence, introductory treatments of ordinary
differential equations and of functions of several variables have been
included in Math 155-3. These topics do not appear in either Math 151-3
or Math .152-3. Thus the proposed sequence is not a "watered-down" ,version
of Math 151-3, Math 152-3. The proposed sequence is obtained from the old
one by the substitution of topics which biologists find more useful. In
. ?
traditional calculus courses there is a great emphasis on examples in
Physics and Geometry. In this sequence there will be far more examples.
from Biology. Finally, there is a stronger emphasis in Math 154-3,
Math 155-3 on applications than in Math 151-3, Math 152-3.
It has been argued that all Science students should take the same
first year calculus courses. But to include the topics and applications
desirable for Biology students, as well as those needed by students in
the other Sciences, in two 3 credit courses of only three semester hours
credit each would necessitate a pace intolerable to students and faculty
alike. Thus such courses usually short-change the Biology student.
Attached are copies of the Course Proposal Forms for Math 154-3,
Math 155-3 together with copies of supporting letters from Dr. GeeTi,
Biology Department, Dr. Pate, Chemistry Department, and Leigh Hunt Palmer,
Physics Department.
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Appendix B3
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
Calendar Information
Department: ?
Mathematics
Abbreviation Code:
?
Number: 154
?
Credit Hours: 3
?
Vector: 3-1-0
Title of Course: CALCULUS I FOR THE BIOLOGICAL SCIENCES
Calendar Description of Course:
The logarithmic, trigonometric and exponential functions. Limits and continuity.
The derivative and techniques of differentiation. Maxima, minima, the mean value
theorem. Applications for the Biological Sciences.
Nature of Course
?
Lecture/Tutorial.
Prerequisites (or special instructions): Math 12 (B.C. Schools) or Mathematics 100-3.
Students with other qualifications must consult an advisor in the Mathematics Department
before they can be admitted to the course. Students who have received credit for either
Mathematics 150-3 or 151-3 cannot receive credit for Mathematics 154-3.
What course (courses), if any, is being dropped from the calendar if this course is
approved: ?
None
2.
Scheduling
How frequently will the course be offered? Twice per year; Fall and Spring Semester.
Semester in which the course will first be offered?
Fall
1974
Which of your present faculty would be available to make the proposed offering
i
spossible: All faculty
,
members.
3.
ObjectivesoftheCourse
?
The objective of the course is to make the study of
calculus more relevant to students in Biological Sciences. The difference between
the topics discussed in Math 154-3 and those discussed in Math 151-3 is very small.
The emphasis in Math 154-3 is placed on the application of techniques learned in
calculus to problems in the Biological Sciences, wherever it is possible.
4.
Budgetary and Space Requirements
,
(for information only)
What additional resources will be required in the following areas:
Faculty ?
There will be no net increase in faculty teaching time required for this course.
Staff ?
For the past two years, the Department has offered separate sections of Math
151-3 in the Fall Semester. One section has been for Biology students; and the
Library ?
other for Chemistry, Mathematics and Physics students. This experiment has
Audio Visual proved to be successful and as a result, the Department has rearranged its
upper level course offerings so that it can afford to offer this course in
Space ?
Spring Semesters.
None
Equipment
5.
pprova1
Date: ?
ji.
VI,
Department Chairman ?
Dean ?
Chairman, SCU
SCUS 73-34b:- (When completing this form, for instructions see Memorandum SCtIS 73-341.
Attach course outline).
S
.
MATHEMATICS 154-3
Calculus, for Biology Students
I.
Real Number, Sets, Functions and Limits
Section 1.0 Real Numbers, Order, Absolute Value
1.1 Sets, Set Notation, Operations with sets
1.2 Functions (Polynomial Functions, Rational
Functions)
1.3 Addition, Multiplication, Division and Composition
of Functions
1.4 Limits
1.5 Increments and Rate of Change
1.6 Review of Trigonometry (3 lectures)
1.7. Limits of Trigonometric Functions
1.8 Limit as x tends to Infinity
II.
The Derivatives
Section 2.1 Slope and Equation of Straight Lines
2.2 Continuous Functions
2.3 The Derivative of a Function (Geometric and Physical
Interpretation, Rate of Growth)
2.4 The Derivative of Polynomials
2.5 The Derivative of Products and Quotients
2.6 The Derivative of Composite Functions
2.7 The Derivative of sin u and cos u
2.8 Derivatives of tan u, cot u, sec u and csc u
2.9 Higher order Derivatives
2.10 Exponential and Logarithmic Functions (See Seeley's
Approach)
III.
More About Derivatives and Their Applications
Section 31 Curve Analysis
3.2 Maxima - Minima
3.3 Applications of Maximum - Minimum
3.4 The Differential
3.5 Implicit Differentiation and Applications
3.6 Inverse Functions
3.7 DerivativeS of the Inverse Trigonometric Functions
3.8 Geometric Interpretation of Rolle's Theorem and the
Mean Value Theorem
TEXT: Calculus for Business, Biology and the Social Sciences
by Crowdis, Shelley and Wheeler
Nv'mber 1973
.
C'
??
Appendix B3
SENATE COMMITTEE ON UNDERGRADUATE STUDIES
COURSE PROPOSAL FORM
Calendar Information
Department: ?
Mathematics
Abbreviation Code:
?
Number:
155
- Credit Hours:
3 ?
Vector:3-1-0
Title of Course: CALCULUS II FOR THE BIOLOGICAL SCIENCES
Calendar Description of Course:
The integral. Techniques of integration. Differential equations,
partial differentiation. Applications to the Biological Sciences.
Nature of Course: Lecture/Tutorial
Prerequisites (or special instructions):
Mathematics 150-3 (with a grade of A or B) or Mathematics 151-3 or 154-3. Students
who have received credit for Mathematics 152-3 cannot receive credit for this course.
What course (courses), if any, is being dropped from the calendar if this course is
approved: ?
None
2.
Scheduling
How frequently will the course be offered? Once per year in the Spring Semester.
Semester in which the course will first be offered?
?
Spring 1975
.
Which of your present faculty would be available to make the proposed offering
possible: All faculty members.
3.
Objectives of the Course
The objective of the course is to make the study of calculus more relevant to students
in Biological Sciences. The syllabus has been prepared on the assumption that those
students who take the course will probably not take further courses in Mathematics.
For this reason a greater variety of topics are discussed in Math 155-3.
4.
Budgetary and Space Requirements for information only)
What additional resources will be required in the following areas:
Faculty ?
There will be no net increase in faculty teaching time required for this
course. For the past two years, the Department has offered separate
Staff
?
sections of Math 152-3 in the Spring semesters, with one section being
Library ?
primarily for students in Biological Sciences.
Audio Visual)
Space
?
NONE
Equipment
J
5.
Approval
Date: ?
July 15, 1974
Department Chairman ?
Dean ?
Chairman, SCUS
;cti 73-34b:- (When completing this form, for instructions sco Memorandum SCUS 73-34a.
Attach course outline).
MATHEMATICS 155-3
Calculus for Biology Students
IV. ?
Introduction to the Integral
Section 4.1
4.2
4.3
4.4
4.5
Area Bounded by a Curve
Sigma Notation
Properties of the Integral
The Indefinite Integral
Indefinite Integrals - Trigonometric Functions
V.
Integration
Section 5.1 The Fundamental Theorem of Calculus
5.2 The Natural Logarithm
5.3 The Exponential Function
5.4 Integration by Parts
5.5 Trigonometric Substitutions
5.7 Improper Integrals
5.8* Use of semi-log and log-log graph papers, curve fitting
VI.
Applications of Integration
Section 6.1 Areas
6.2 Probability
6.3 Families of Curves, Parameters, Moments
6.4 Normal Curve Areas, Areas with Tables
6.8t Natural Growth and Decay
VII.
Functions of Several Variables
Section 7.1 Functions of Several Variables
7.2 Three-Dimensional Coordinate Geometry
7.3 Partial Derivatives
7.4 Extrema for Functions of Two Variables -
Maximum and Minimum
75* Curve Fitting - Least Square Method
VIII Introduction to Ordinary Differential Equations
Section 8.1 Differential Equations
8.2 First Order Differential Equations
8.3t Natural Growth and Decay
8.4 Systems of First Order Linear Differential Equations -
Species Competition
S ?
2
-2-
IX ?
Matrices and Vectors
Section 9.1 Matrix Notations
9.2 Matrix Algebra
9.3 Applications
* Materials which have to be supplemented by the instructor from
sources other than the current textbook.
t This topic is covered twice.
1 .. ?
1,
TEXT: Calculus for Business, Biology and the Social Sciences
by Crowdis, Shelley and Wheeler
November 1973
I
S
- ? r
(JUN 1 71974
M&T't. 4 7I(5
• ?
'LIAR. ?
.4
GHC/ms
SiMON FRASER UNIVERSITY
MEMORArDUM
Dr. A. H. Lachiari
?
..................................From....Dr. C. H. Geen
Mathematics Department
?
.................................
Subject.
Proposed New Courses
Math 154-3 and Math 155-3
Biological Sciences Department..
Date ?
June 14, 1974.
?
.
.......
S
i am in complete agreement with the philosophy and content of the
proposed new courses, Mathematics 154-3 and Math 155-3. I have always
been satisfied that these two courses would be different from, but
not inferior to Math 151-3 and 152-3. It has been a very corron
complaint for many years that the usual University calculus courses
had limited relevance to the needs of Biology students. I would be
the first to applaud your efforts to remedy this situation.
Some years ago the Mathematics Association of America developed a
series of recommendations for the Undergraduate Mathematics Program for
students in the Biological, Management and Social Sciences (BSS). They
recommended that Mathematics Departments offer courses designed to meet
the needs of students in the biological, management and social sciences.
This group recoqnized the problem in providing the varied training in
mathematics in the limited time that biology students have available
for mathematics during their undergraduate years. The Mathematical
Associatior. of America report went on to say:
"it is, therefore, important to recognie that they need
mathematics primarily as a language for scientific reasoning,
and that they do not need as much training in detailed techniques
as mathematics and physical science stuents. Nor is it reasonable
to expend as much time on rigorous proofs for BMSS students as for
mathematics majors. Also, more stress hou1d be placed on applica-
tions which are of special interest in the biological and social
sciences."
I believe this is a very reasonable position and one that is being
tackled very well in the proposed new MatheiaticS courses aimed at the
biology students.
-t--
?
_;_- -
Glen H. Gen,
Chairman.
rN
SIMON FIASER UNIVERSITY
EM
L
.
\ronoff, ?
.
From
?
B. D. Pate
flr of cienee.
?
Department of Chemistry.
Subject ?
.:ATIC l5
and
155 ?
Date ?
June 4th,
1974.
p
oiC•.:D COUi
:
,E ____________________ _____________________________________________________
Th; memorandum is intended to brief you or the Chemistry
Departm it' s po:ition regarding those courses, in time for the
next discussion at senate.
You will recall that the Chemistry Dcpartnent Undergraduate
rtudies Cdmrnitte: and the Department as a ho1.e considered the
cOurse proposal on j. g irlatLng
•
from the Mathematics Department, and,
at -oth levels, supported the proposal. The Undcrg
r
radiiatc Studies
Committee has now reconsidered the proposal, and as a result I
comsont the following:
(a)
The normal Mathematics requirements of the Chemistry
undergraduate program are specified to begin with Mathematics 11
and Mathematics
2.52.
(b)
If a student instead takes the proposed Mathematics 15):.
and Mathematics J, and subsequently decides to transfer into the
Chemis:rv underreduate program, we arc satisfied that the t;?.ansrer-
aI'i i:v from these atheitatics courses to subsequent Mathematics
courses required for the Chemistry program is adequate
.
. The content
ol .1ahematics l:-
M
and Mathematics
155
is also judged adequate for
the preparation of students transferring into the Chemistry program
under these circumstances.
flr
Brian D. Pate, Chairman,
Undergraduate Trudics Committee,
Department of Chemistry.
bdp: smh
C.C. :
D. Ryeburn, Mathematics Department
T
,131ON nsEi UN1VEi.S1fl
MEMORANDUM
S. Arofloff
?
From .
Leigh Hunt Palmer
?
.
Dean
?
Science ....................................................................
?
...
?
Department
of
Physics...................................
................
Date..
?
22 ?
May ?
1974, ?
............................................................
Subject
?
Math 154-3 and 155-3 .. .. ...........
I am the faculty member principally involved in the
counselling of students in the Physics Major and Physics
Honors programs. I am also Chairman of the Physics
Department Undergraduate Studies Committee and also the
Physics represeflttive on the Science Faculty Undergraduate
Studies Committee. I have examined the proposal of the
Mathematics Department for two new calculus courses, MATH 154-3
and 155-3, intended principally for Biological Sciences
students, and I have discussed this proposal with Dr. Ryeburfl
in the Mathematics Department. I judge that any student who
?
.. . -
i.s otherwise well-qualified to change from a Biological
Sciences program to one in Physics will not be precluded
from doing so by having taken the 1543, 155-3 calculus
sequence. He should easily be able to go on with no lost
time or extra courses.
? . ?
.
Leigh Hunt Palmer.
LHP/1'
c.c. Dr. Ryeburfl
I
