Discipline / Real and Complex Analysis I / Course ID / OB.101F
Year of Study / I / Semester / I / Assessment and Evaluation / E
Formative category: FDS-Fundamental Discipline of Scientific Type
Type of discipline: Ob.-Mandatory / Number of ECTC / 6
Total number ofinstructional hours / 84 / Total number ofhours allocated to individual study / 92 / Total number ofhours per semester / 176
Faculty / PHYSICS / Total number ofhours incurriculumper semester

Department

/ Theoretical Physics and Mathematics / 84=14 weeks x 3 hours course +14 weeks x 3 hours tutorials

Main Domain

Science, arts, culture / Science

Bachelor Study Program

/ Physics /

Total**

/

C

/

S

/

L

/

P

Branch of Study

/ Physics, Biophysics,
Medical Physics,
Physical Engineering,
Information Physics / 84 / 42 / 42

** C-Course, S-Recitation, L-Lab work, P-Project, or Practical work

Prerequisite Disciplines / Required
Recommended
SYLLABUS / 1. MULTIDIMENSIONAL SPACES. Metric spaces.Normed spaces. Spaces with scalar product. Real and complex Euclidean spaces.
2.SEQUENCES AND SERIES. Sequences in Rn. Convergent and fundamental sequences. Complete spaces. Series in normed spaces. Number series.Convergence tests.
3. LIMITS AND CONTINUITY. Global, iterated and directional limits. Continuous functions. Uniform continuity. Compact and connected sets.
4. MULTIVARIABLE DIFFERENTIAL CALCULUS. Differentiable functions.Partial derivatives. Jacobi matrix. Directional derivatives. Differential operators. Applications to physics. Higher order differentials. Taylor’s formula. Implicit functions. Inverse functions. Local extrema.
5. SEQUENCES AND SERIES OF FUNCTIONS. Pointwise and uniform convergence. Power series. Taylor series. Trigonometric series. Applications to physics.
6.INTEGRABLE FUNCTIONS. Improper integrals.Parameter- dependent integrals. Improper integrals depending on parameters. Euler’s functions.
References / 1.D. Stefanescu,“Real Analysis”, Editura Universitatii din Bucuresti, 1990 (in Romanian).
2. C. Timofte, ‘’Differential Calculus‘’, Editura Universitatii din Bucuresti, 2009.
3. G. Arfken, H.Weber, “Mathematical Methods for Physicists”, Elsevier Academic Press, 2005.
4. P.Bamberg, S. Sternberg, “A Course in Mathematics for Students of Physics”, CambridgeUniversity Press, 1990.
5. R. Courant, “Differential and Integral Calculus”, Wiley, New York, 1992.
6. S. Lang,“Analysis I”, Addison-Wesley Publ. Co., Reading, Massachusetts,1968.
7. L.H. Loomis, S. Sternberg, “Advanced Calculus”, Addison-Wesley Reading,1968.
8. W. Rudin, “Principles of Mathematical Analysis”, McGraw-Hill, New York, 1964.
Equipment List / Computer
The final evaluation will include: /

Percent in %

{Total=100%}

-Examination (final evaluation). / 40%
- Hands-on Lab test quiz. / 0%
- Final answers tomid-termexamination (written). / 20%
- Homework, essays, written tests and quizzesduring recitation classes. / 30%
- Other activities: attendance. / 10%
Final evaluation methods, E/V. {ex: Written test, Oral examination on topics covered by lectures, Individual Colloquium, or Group Project, etc.}.
Written test Oral examination

Minimal requirements for mark 5

(10 point scale)

/ Requirements for mark 10
(10 point scale)
- Mandatoryattending:50% lectures and 70%recitation classes.
- At least 50% for each criterion of the final evaluation / - Mandatoryattending:most lecturesand most recitation classes.
- At least 90% for each criterion of the final evaluation.
Date: Titular signature:

18.04.2011 Prof. dr. Claudia TIMOFTE