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HU Credits:
4
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
prof. Y. Itin
Coordinator Office Hours:
Sundays, 12-13 am
Teaching Staff:
Mr. Shmuel Berger
Mr. Bar-Yoda Avigdor
Mr. Ohana Barak
Mr. Livne Gil
Course/Module description:
Differenciation, integration and applications.
Population dynamics models.
Course/Module aims:
To obtain ability to calculate derivatives and integrals and use them for various purposes.
Learning outcomes - On successful completion of this module, students should be able to:
Calculate derivatives and integrals.
Draw graphs of functions.
Expand functions in Taylor series.
Calculate various approximations.
Solve seperable differntial equations.
Investigate population dynamics models.
Attendance requirements(%):
/
Teaching arrangement and method of instruction:
Lecture and exercise.
Course/Module Content:
- The real line: Natural, whole ,rational and real numbers. Absolute
value. Distances on the line. Domains on the line.
- The elementary functions: Power
functions. Exponential and trigonometric functions. The
absolute value function.
- The inverse function. Root functions. Logarithmic and inverse trigonometric
functions.
- Polynomials and rational functions.
- Limits and one sided limits of functions. Basic limit theorems.
- Continuity. Basic continuity theorems. The mean value theorem
and the theorem of Weierstrass.
- The derivative. High order derivatives. The tangent. Basic
derivative theorems.
- The theoretical basis of curve plotting: The theorems of Fermat
And Rolle, the mean value theorem and L'Hopital's rule.
- Curve plotting: Intervals of increase and decrease. Minimum
and maximum points. Intervals of convexity and concavity.
Inflection points. Vertical and non-vertical asymptotes.
The integral. The primitive function. Indefinite integral. -
Integration by parts. Integration by substitution. Integration of
rational functions. Definite integral. The integral as a function of
its upper limit. Area computation. Improper integrals.
Geometric and physical meanings of the derivative and the integral.-
Infinite series. Maclauren and Taylor series. Approximations. -
- Differential equations. First order seperable equations.
Investigation of population dynamics models(one species): Exponential growth.-
Restricted growth. Logistic growth. Critical threshold. Logistic
Growth with critical threshold.
Required Reading:
/
Additional Reading Material:
Howard Anton: Calculus. John Wiley. -
Beni Goren: Differential and integral calaulus, 4 and 5 units (Hebrew).-
Frank Ayres: Calculus. Shaum series. -
Murray Spiegel: Advanced calculus. Shaum series. -
Course/Module evaluation:
End of year written/oral examination 70 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 15 %
Reports 0 %
Research project 0 %
Quizzes 15 %
Other 0 %
Additional information:
None
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