Discipline
Real and Complex Analysis I
Course ID
OB.101F
Year of Study
Semester
Assessment and Evaluation
I
I
E
Formative category: FDS-Fundamental Discipline of Scientific Type
Number of
Type of discipline: Ob.- Mandatory
6
ECTC
Total number
Total number of instructional
Total number of hours
84
92 of hours per
176
hours
allocated to individual study
semester
Faculty
Total number of hours in curriculum per semester
PHYSICS
Theoretical
84=14 weeks x 3 hours course +14 weeks x 3
Department
Physics and
hours tutorials
Mathematics
Main Domain
Science
Science, arts, culture
Physics
Total**
C
S
L
P
Bachelor Study
Program
Physics, Biophysics,
Medical Physics,
Physical Engineering,
Information Physics
Branch of Study
84
42
42
** C-Course, S-Recitation, L-Lab work, P-Project, or Practical work
Prerequisite
Disciplines
Required
Recommended
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
SYLLABUS
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”,
Cambridge University 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%}
40%
0%
20%
- Examination (final evaluation).
- Hands-on Lab test & quiz.
- Final answers to mid-term examination (written).
- Homework, essays, written tests and quizzes during recitation
30%
classes.
- 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)
- Mandatory attending: 50% lectures and 70%
recitation classes.
- At least 50% for each criterion of the final
evaluation
Requirements for mark 10
(10 point scale)
- Mandatory attending: most lectures and most
recitation classes.
- At least 90% for each criterion of the final
evaluation.
Date:
Titular signature:
18.04.2011
Prof. dr. Claudia TIMOFTE