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:

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:

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 ofMathematics 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

Exerciselist (every week), exam (at the end of semester)

9. Date of examination

At the end of semester

10. Course grading

Selected themes of Mathematicsfor second yearstudents of Biological

Chemistry

11. Main textbook

1. בן- ציון קון, פונקציות מרוכבות, בק, 2000.

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

1.הוורד אנטון, חשבון דיפרנציאלי ואינטגרלי, חלק א' /ב', האוניברסיטה הפתוחה, 2000.

2. בן- ציון קון, סמי זעפרני, חשבון דיפרנציאלי ואינטגרלי 2, תיאוריה ותרגילים, 1996.

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

Week / Subject
Complex numbers and functions
1-4 / 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
Triple integral in curvilinear coordinates
5-6 / Change of variables in the triple integral, Jacobian. Triple integral in the cylindrical and spherical coordinates.
Vector analysis
7-10 / 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.
Special differential equations
11-13 / Solution of differential equations by generalized power series (Frobenius method). Hermite equation and polynomials.Laguerre equation, polynomials and associated Laguerre polynomials. Legendre equation, polynomials andassociated Legendre functions.