| EC18A:
Calculus I for Business and Social Sciences |
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| Lecturer:
Office:
Timetable:
Tutorials:
Office Hours:
Phone:
Email:
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Winston Vassell
Room 13
Wednesday 12:00pm -1:00pm, Friday 1:00pm - 3:00pm
Once per week (Attendance compulsory)
(876) 512-3282
winston.vassell@uwimona.edu.jm
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Course
Objective:
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| To provide an opportunity
for students to explore some of the mathematical processes
that are required to access the quantitative elements of
Economics and Management SciencesTo expose students to concepts
and rules of the Differential Calculus that is prerequisites
to the optimization process.To introduce students to concepts
of the Calculus that are necessary for understanding the
Quantitative Methods employed by economists in the decision
making process. |
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Assessment:
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- One hour mid-semester examination consisting of (20)
multiple choice questions - 20%
Two hours final examination consists of six questions to do
any four. - 80% |
PRESENTATION
Lectures and tutorials
including class discussion. |
Reading
List:
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- Hoffmann, L. D. Calculus For Business, Economics,
and the Social Science, McGraw-Hill Companies, New
York, Six Edition, 1996.
- Ayres, Frank & Mendelson, Elliott Differential
and Integral Calculus, 3rd ed. New York,
McGraw-Hill, 1990
- Varberg, Dale & Purcell, Edwin Calculus,
7th ed. Upper Saddle River, N.J, Prentice-Hall, 1997
FURTHER REFERENCES:
http://www.netsrq.com/nhahn/calculus.html
http://archives.math.vtk.edu/ |
| You may download all the information
on this course web site here.(Pdf document) |
CALCULUS
1. LIMITS
§ Definition of limits
§ Properties of limits
§ Techniques for finding limits
§ Finding limits of functions (Polynomials, rationales
and irrational)
2. CONTINUITY
§ Conditions for continuity
§ Determination of continuity of polynomials, rational
and irrational functions.
§ Determination of continuity over an interval
§ Types of discontinuities
§ Point of discontinuity
3. DIFFERENTIATION (REVISION)
Students are expected to know the following concepts listed
below in order to apply them in finding derivatives of trigonometric
functions and other functions. These concepts will not be
tested in any of the examinations.
§ Steps for obtaining a derivative
§ Rules for differentiation:- Polynomial, logarithmic
and exponential functions.
4. TRIGONOMETRIC FUNCTIONS
Identities, limit concepts of sine and cosine, derivatives
of trigonometric functions (sine, cosine, tangent, cosecant,
secant, cotangent using the various rules of differentiation)
5. DIFFERENTIATION OF LOGARITHMIC FUNCTIONS
6. DIFFERENTIATION OF EXPONENTIAL FUNCTIONS
7. INTEGRATION
§ Indefinite integration:-
§ Standard form
§ Methods of Integration: substitution, By Parts; Partial
Fractions
§ Definite Integrals:
§ Definition; Properties; Application
§ Integral of trigonometric ratios
§ Double Integrals
8. MULTI-VARIATE CALCULUS
§ Partial differentiation of functions with two variables
§ Determination of relative maximum and minimum of functions
with n variables.
§ Determination of relative maximum and minimum of functions
with n variables subject to a constraint.
§ Total Differential; Total derivative; Partial total
derivative
9. APPLICATION OF PARTIAL DERIVATIVE
Demand functions:- revenue and profit functions
10. PARTIAL DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
11. TOTAL DIFFERENTIAL OF TRIGONOMETRIC FUNCTIONS
12. TOTAL DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
13. PARTIAL TOTAL DERIVATIVE OF TRIGONOMETRIC FUNCTIONS
14. IMPLICIT DIFFERENTIATION
15. LINEAR HOMOGENEOUS FUNCTIONS
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