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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:
Mr. Rosenstein Ori
Coordinator Office Hours:
Tuesdays 1015-1115
Teaching Staff:
Mr. Shmuel Berger,
Dr. Rosenstein Ori,
Mr. Ackermann Benjamin,
Mr. Matan Tal
Course/Module description:
Differential and Integral Calculus, focused on (but not restricted to) one-dimentional calculus.
The course is largely computational but with an emphasis on mathematical technique and writing.
Course/Module aims:
To acquire computational and mathematical capability in the context of differential and integral calculus.
Learning outcomes - On successful completion of this module, students should be able to:
Define basic notions of calculus.
Calculate derivatives and integrals.
Draw graphs of functions.
Expand functions in Taylor series.
Calculate various approximations.
Solve seperable differntial equations.
Solve autonomic differntial equations.
Investigate population dynamics models.
Attendance requirements(%):
/
Teaching arrangement and method of instruction:
Frontal lectures, live lesson and exercise. The lectures are recorded.
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:
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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 80 %
Presentation 0 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 10 %
Reports 0 %
Research project 0 %
Quizzes 10 %
Other 0 %
Additional information:
Other or additional topics may be studied.
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