School of Health Sciences MATH 1441
Program: Biological Sciences
Option:
Technical Mathematics for Biological Sciences
Service provided by: School of Computing and Academic Studies, Mathematics Dept.
Start Date: September 4, 2002 End Date: December 13, 2002
Total Hours:
Hours/Week:
90 Total Weeks: 15
6 Lecture :
Term/Level:
3 Lab: 2 Shop:
1 Course Credits: 6.0
Seminar: Other: 1
Prerequisites
Course No. Course Name
MATH 12 or equivalent
MATH 1441 is a Prerequisite for:
Course No. Course Name
MATH 2441 Statistics for Biological Sciences

Course Description
Exponential/logarithmic theory and transformations, common and natural logarithms, logarithmic/semilogarithmic graphs. Variation, straight line equation, curve fitting. Delta-process, the derivative, differentiation rules, curve sketching, applied maxima/minima and other applications of the derivative, the differential, antiderivatives, indefinite integral, definite integral and area under a curve. Introduction to microcomputers using Excel.

Detailed Course Description
After a brief review of relevant algebraic topics, the goals of this course are to:
 introduce the student to the properties and applications of exponential and logarithmic functions, the concepts and application of the derivative and the integral, and the use of microcomputers for routine data processing operations.
 solve problems involving an exponential or logarithmic model, including the use of logarithmic scale graphs to estimate model parameters from experimentally determined measurements of systems obeying such models.
 determine derivatives of algebraic functions and demonstrate and explain the principles of applications of derivatives in finding maximum/minimum values of functions, solving related rates problems, sketching graphs of functions, solving general mathematical equations, etc.
 use differential forms to estimate amounts of change in derived quantities, and carry out simple error analyses for quantities computed from experimental measurements.
 determine antiderivatives, indefinite and definite integrals of algebraic functions, and demonstrate the application of definite integrals in computing bulk properties such as area, volume, work done, average values, etc.
 design, create, and print worksheets/workbooks using Excel, including use of formulas, built-in functions, implementation of simple numerical algorithms, and creation of graphics based on data in the worksheet.
D:\726936641.doc 04/20 Format02 1

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)

Evaluation
Final Examination
Term Tests (2)
Quizzes (>10)
Projects/Reports (6)
TOTAL
40%
25%
20%
15%
100%

Course Learning Outcomes/Competencies
Policy: Minimum passing grade for this course is 50%.
Upon successful completion, the student will be able to:
1.
solve simple linear and quadratic equations.
2.
solve simple algebraic word problems, especially involving percent and mixtures.
3.
describe or list the properties of generic exponential functions.
4.
recite and apply the usual formula expressing exponential growth or decay, including being able to explain the meaning of each symbol in the formula, and being able to correctly associate values in growth/decay problems with corresponding symbols in the formula.
5.
explain what is meant by a logarithm and state the three basic properties of logarithms.
6.
use the properties of logarithms to simplify expressions involving logarithms.
7.
use logarithms to solve exponential equations.
8.
use properties of exponentials and logarithms to solve logarithmic equations.
9.
apply the techniques used to solve exponential and logarithmic equations to the solution of problems involving exponential growth and decay, cooling, pH, light absorption, etc.
10.
explain the principles involved in using logarithmic graph scales to linearize plots of exponential or power function data, and apply them to estimate values of constants in the formulas governing such systems.
11.
demonstrate the use of functional notation.
12.
demonstrate the determination of derivatives of very simple algebraic functions using the so-called deltamethod, and explain the meaning of the derivative as an instantaneous rate of change.
13.
explain the concept of a limit, and demonstrate the determination of limits in examples involving algebraic functions.
14.
demonstrate the use of standard procedures for finding derivatives, including the derivative of a power of a function, sums, products and quotients of two functions, the chain rule, implicit functions and higher derivatives.
15.
apply the derivative to determination of slopes and equations of lines tangent and lines normal to given curves
16.
apply the derivative to the determination of maxima and minima, with emphasis on problems involving volumes/surface areas of standard container shapes (cylinders, boxes, etc.), etc.
17.
explain the principles behind the function-value, derivative-value, and second derivative value tests for distinguishing between local maxima and local minima, and apply these principles in actual application problems.
D:\726936641.doc 04/20 Format02 2

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)
 Course Learning Outcomes/Competencies (cont’d)
18.
produce sketches of major features of graphs of mathematical functions based on analysis of derivatives, and other features of the formula generating the graph.
19.
use differentiation and integration to relate position, velocity and acceleration of an object to each other.
20.
derive the differential form of a mathematical relation, and apply it to the estimation of small changes in computed values, or absolute and relative errors in values computed from experimental measurements with given uncertainties.
21.
apply Newton’s method to the solution of general mathematical equations.
22.
explain the relationship between a derivative, antiderivative and indefinite integral.
23.
demonstrate calculation of the value of a definite integral of an algebraic function.
24.
demonstrate the calculation of areas between two curves using definite integrals.
25.
demonstrate the method of substitution for determining indefinite/definite integrals.
26.
demonstrate the use of tables of integral formulas.
27.
demonstrate the calculation of various bulk properties (volumes, average values, work done) using the definite integral.
28.
describe the concepts of disks, directories, and files and their naming rules, as implemented in MS-DOS and
MS-Windows environments.
29.
demonstrate the launching of MS-Excel in Windows.
30.
demonstrate the use of file saving/opening commands in Excel.
31.
define the concept of a cell in a worksheet, explain how cells in a worksheet are identified or distinguished, and explain the concept of ranges in a worksheet.
32.
demonstrate entry of string and numerical data manually into spreadsheet cells, and the use of the autofill feature.
33.
demonstrate the entry of formulas into worksheet cells.
34.
demonstrate techniques for copying data and formulas from one range in the worksheet to another, including copying to and pasting from the Windows clipboard, and explain the implications of the difference between relative and absolute cell references or addresses.
35.
demonstrate the use of the Function Wizard to access built-in functions in Excel in constructing cell formulas
(including use of Help to determine how a prospectively useful function works).
36.
demonstrate use of the Chart Wizard to create and format graphical representations of data stored in the worksheet.
37.
demonstrate the selection of ranges, including noncontiguous ranges.
38.
demonstrate the use of the Format menu command to alter the appearance of worksheets, including control of fonts, sizes, colors, borders, justification, etc.
39.
demonstrate the process of preparing printed reports based on information in worksheets, including use of the
Page Setup command.
40.
demonstrate the use of Excel to produce xy-graphs of given mathematical expressions, to produce reference tables of values, and to implement simple iterative or cumulative mathematical algorithms.
D:\726936641.doc 04/20 Format02 3

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)

Verification
I verify that the content of this course outline is current.
Authoring Instructor
I verify that this course outline has been reviewed.
Date
Program Head/Chief Instructor (Math)
Program Head/Chief Instructor (Technology)
I verify that this course outline complies with BCIT policy.
Dean/Associate Dean (Math)
Date
Date
Date
Note: Should changes be required to the content of this course outline, students will be given reasonable notice.
D:\726936641.doc 04/20 Format02 4

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)

Instructor(s)
David W. Sabo

Learning Resources
Text(s) and Equipment:
Required:
Office Location: SW2-231
Office Hrs.:
Office Phone: 604-432-8698
E-mail Address: dsabo@bcit.ca
Office Fax:
Internet:
604-432-9173 apples.soe.bcit.ca
A hand-held electronic calculator with logarithmic, exponentials and trigonometric functions (statistical functions highly recommended for students intending to continue on into MATH 2441). If you do not already have a calculator, delay purchase of a new one until after the first class. Also, students must have a supply of 3.5 inch,
1.44 MB capacity diskettes for use with an IBM-compatible microcomputer (minimum 5 recommended, such diskettes are most economically purchased in boxes of 10 or more).
Recommended:
A suggested reference for the mathematical portion of the course is:
Technical Mathematics with Calculus , 3rd edition or newer, by Paul Calter, published by Prentice-Hall (available in the BCIT Bookstore).
(Notice that only about five of 37 chapters in this book are covered in the course, and those chapters themselves would require considerable supplementary material provided in class!)
References:
None.

Information for Students
(This is general information regarding all mathematics courses at BCIT. Some exceptions exist for MATH 1441.)
Assignments: Late assignments, lab reports or projects will not be accepted for marking. Assignments must be done on an individual basis unless otherwise specified by the instructor.
Makeup Tests, Exams or Quizzes: There will be no makeup tests, exams or quizzes. If you miss a test, exam or quiz, you will receive zero marks. Exceptions may be made for documented medical reasons or extenuating circumstances. In such a case, it is the responsibility of the student to inform the instructor immediately .
Ethics: BCIT assumes that all students attending the Institute will follow a high standard of ethics. Incidents of cheating or plagiarism may, therefore, result in a grade of zero for the assignment, quiz, test, exam, or project for all parties involved and/or expulsion from the course.
Attendance: The attendance policy as outlined in the current BCIT Calendar will be enforced. Attendance will be taken at the beginning of each session. Students not present at that time will be recorded as absent.
Illness: A doctor’s note is required for any illness causing you to miss assignments, quizzes, tests, projects, or exam . At the discretion of the instructor, you may complete the work missed or have the work prorated.
Attempts: Students must successfully complete a course within a maximum of three attempts at the course. Students with two attempts in a single course will be allowed to repeat the course only upon special written permission from the Associate Dean.
D:\726936641.doc 04/20 Format02 5

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences
Students who have not successfully completed a course within three attempts will not be eligible to graduate from the appropriate program.
(cont’d.)
 Information for Students (cont’d)
Course Outline Changes: The material or schedule specified in this course outline may be changed by the instructor. If changes are required, they will be announced in class.
Course Credit: Applications for course credit or course exemption on the basis of previously completed mathematics courses are assessed on a case-by-case basis by the BCIT Mathematics Dept. taking into account all of the following:
 the correspondence between topics, content and level
 recency (generally no more than 3–5 years)
 the grade (generally at least a C+ or 65%)
 the context (course taken as part of a university or college science or engineering program, rather than, for example, an arts or social science program).
Course Makeup Equivalents: In most cases, students who fail a math course or withdraw from a math course may make up the course by taking makeup courses. These courses may be BCIT evening or correspondence courses, or equivalent courses from another institution. In some cases, students may be required to take more than one course or several distance education modules to gain credit. In some cases, students may be required to achieve a mark of greater than 50% in the makeup course in order to achieve credit for the failed course. If a student fails a course, a makeup letter signed by the mathematics program head will be sent to the student, the technology program head, and to Student Records. Any course substitutions would require prior written approval of the mathematics program head.
Learning Disabilities : BCIT is committed to providing opportunities for students with disabilities to meet their educational, career, and personal goals within the context of the Institute’s training mandate. For further information, contact the Disability
Resource Centre.
I.D. Required in Examination Centres: In order to write exams, students will be required to produce photo identification at examination centres. Photo I.D. must be placed on the desk and must remain in view on the desk while writing the exam, for inspection by invigilators. Students should bring a BCIT OneCard or alternatively two pieces of identification, one of which must be government photo I.D. such as a driver’s licence. Please see BCIT Policy #5300, Formal Invigilation Procedures.

Assignment Details
One hour per week is scheduled in a microcomputer laboratory. During that time, students are asked to complete six assignments involving MS-Windows, and Excel. Assignments require submission of written work and diskettes containing results of work with a microcomputer. Work on assignments is done on an individual basis. Availability and due dates for each assignment will be announced in class.
D:\726936641.doc 04/20 Format02 6

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)
Week
1
2
3
4
5
Topics
 simple equations and word problems
 quadratic equations and applications
Reference/Reading
Chapter 3
Chapter 14
 discussion of compound interest, and generalization to the exponential growth model
 properties of exponentials and exponential functions
 solving simple problems in exponential growth and decay, interpretation of data and solutions
 definition of logarithms, description of the basic properties of logarithms , antilogarithms
 range of values for base, logarithms, exponentials
 relationship between logarithms with respect to different bases

Simplifying expressions involving logarithms; avoiding common misuses of properties of logarithms; use of logarithms in numerical computation
Section 20-1
Section 20-2
Section 20-3
Section 20-4
 solving logarithmic equations
 solving exponential equations
 applications to exponential growth/decay, Newtonian cooling, pH, light absorption, etc.
Section 20-5
Section 20-6
 review of basic analytic geometry, (graphs, equation of the straight line)
 semi-log and log-log plots; determining parameters in exponential and power function formulas from experimental data
Section 22-1
Section 20-7 and lecture notes

 review of functional notation concepts of average and instantaneous rates of change
 limits
Chapter 4
Section 27-1
D:\726936641.doc 04/20 Format02 7

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)
Week
6
7
8
9
10
11
12
Topics
 the derivative
 simple examples using the “delta-method” (low powers of x, a constant times a power of x, etc)
 formulas for finding the derivatives of sums, differences, products and quotients of functions (examples restricted to algebraic functions)
Sections 27-2, 27-3, 27-5
 the chain rule for derivatives (derivatives of powers of functions)
 higher-order derivatives
Reference/Reading*
Section 27-4
Section 27-7

 tangents and normals maxima/minima of functions (local and global), points of inflection, distinguishing between local maxima and local minima, application to problems involving minimum surface area, maximum volume, etc.
Section 28-1
Section 28-2
Section 29-4
 sketching, verifying and interpreting graphs Section 28-3


 approximate solution of mathematical equations using
Newton’s method
 motion of a point in one and two dimentions (relationship between position, velocity and acceleration) related rates differentials; application of differentials to estimation of small changes, volumes of thin layers, error analysis
Section 28-4
Section 29-2
Section 29-3 lecture notes
 antiderivatives
 relationship between antiderivatives, areas under a curve, and the definite integral
 indefinite integrals; the constant of integration

 method of substitution for finding integrals use of tables of integral formulas
Section 30-1
Section 30-3 - 30-6
Section 30-2 lecture notes
D:\726936641.doc 04/20 Format02 8

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)
Week
13
14
15
Topics Reference/Reading*
 application of the definite integral to determination of areas of plane regions
 application of the definite integral to determination of average values
 application of differentiation and integration to understanding the relationship between position, velocity, and acceleration
 other applications of the definite integral (as time permits)
Section 31-3 lecture notes
Section 31-1
Review
Final Examination
*Section references are relative to the suggested reference text, Calter, third edition.
D:\726936641.doc 04/20 Format02 9

Course Outline
MATH 1441 Technical Mathematics for Biological Sciences (cont’d.)
Assignment/
Project
1
2
Title — Description
Creation of four worksheets in an Excel workbook, all involving producing a conversion table for specific physical quantities, requiring entry of text and numbers into cells, development of formulas, copying cell content to ranges of cells, use of autofill, use of the worksheet formatting menu, file save, use of absolute and relative cell references, etc.
Creation of a worksheet to duplicate the computations of a gravimetric analysis experiment; requiring use of SUM(..) and AVERAGE(..) functions, further design and formatting of a worksheet,
3
4
5
Creation of a worksheet duplicating the calculations in a physics experiment measuring the force constant of a spring; requiring creation of several simple xy-charts, setting up the calculation of the slope and intercept of the best-fit straight line, comparison with results of
Excel’s regression tool, printing a worksheet.
Creation of a worksheet summarizing simple financial and related information; and the production of a variety of charts summarizing and illustrating various aspects of the numerical information; indepth look at Excel’s chart wizard and facilities for formatting and annotating charts.
In depth examination of the Excel function wizard and library of built-in functions; production of graphs of mathematical equations, solution of mathematical equations, comparison of results from Excel’s Solver tool, and related topics.
D:\726936641.doc 04/20 Format02 10