Download שמ הקורס: פונקציות מרוכבות(01313701 , 01313702)

1. Course
Code of the course: 2-7221610-1
Name of the course: ‫ מתמטיקה מתקדמת‬/Advanced Mathematics
Faculty: Faculty of Natural Sciences
Department: Biological Chemistry
Degree: BSc
Semester: first semester
Year: second year
Semester hours: 3 h. lecture in the week/1 h. practical work in the week
2. Schedule
Class schedule: Sunday,9:00-12:00, classroom 6.2.20
Tutorial schedule: Sunday, 13:00-14:00, classroom 2.2.03
3. Lecturer
Name: Ass.Prof. Gershon Kresin
Office location: 11.2.16
Tel. number : 03-9758690
E-mail address: [email protected]
Office hours: Sunday, 15:00-16:30; Tuesday, 13:00-14:30
4. Teaching assistent
Name: Ms. Svetlana Reznikov (MSc)
Office location: 11.2.16
Tel. number : 03-9758960
E-mail address: [email protected]
Office hours: Tuesday, 15:00-16:00
5. Course goal
The goal of the course is: to prepare the students by learning of special
subjects of Mathematics for studying of professional courses
6. Prerequisites
Successful studying of courses:
Differential and Integral Calculus-1
Differential and Integral Calculus-2
7. Method of instruction
Frontal lecture (3 h. in the week), practical work (1 h. in the week)
8. Course requirements
Exercise list (every week), exam (at the end of semester)
9. Date of examination
At the end of semester
10. Course grading
Selected themes of Mathematics for second year students of Biological
Chemistry
11. Main textbook
.2000 ,‫ בק‬,‫ פונקציות מרוכבות‬,‫ ציון קון‬-‫ בן‬.1
2. D.M. Hirst, Mathematics for chemists, Chemical Publ., New York, 1979.
3. M.L. Boas, Mathematical methods in the physical sciences (all ed.)
12. Additional text books
.2000 ,‫ האוניברסיטה הפתוחה‬,'‫ב‬/ '‫ חלק א‬,‫ חשבון דיפרנציאלי ואינטגרלי‬,‫ הוורד אנטון‬.1
.1996 ,‫ תיאוריה ותרגילים‬,2 ‫ חשבון דיפרנציאלי ואינטגרלי‬,‫ סמי זעפרני‬,‫ ציון קון‬-‫ בן‬.2
3. G. B. Arfken and H.J. Weber, Mathematical methods for physicists,
Academic Press, 2001.
4. Y. Pinchover and J. Rubinstein, An introduction to partial differential
equations, Cambridge Univ. Press, 2005.
13. Required material for the examinations
List of formulas enclosed to exam
14. Sample of examination
Enclosed
15. Course plan
Subject
Week
Complex numbers and functions
Complex numbers: rectangular form, polar form, complex algebra, Euler’s formula,
exponential form, powers and roots
Power series and elementary functions in the complex plane: properties of power
series, exponential function, logarithms, complex powers, trigonometric functions,
hyperbolic functions, inverse trigonometric and hyperbolic functions
1-4
Triple integral in curvilinear coordinates
Change of variables in the triple integral, Jacobian. Triple integral in the cylindrical and
spherical coordinates.
5-6
Vector analysis
Vector algebra, differentiation of vector valued functions. Scalar field, gradient. Vector
field, divergence, curl. Operator  . Operators of the second order of vector analysis.
Differential operators of vector analysis in the cylindrical and spherical coordinates.
Solenoidal, potential and harmonic fields.
7-10
Special differential equations
Solution of differential equations by generalized power series (Frobenius method).
Hermite equation and polynomials. Laguerre equation, polynomials and associated
Laguerre polynomials. Legendre equation, polynomials and associated Legendre
functions.
11-13