Résumé de section
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Institute : Science and TechnologyDepartment : Common Core Department of Science and Technology
Target LearnersFirstYear Common Core of Science and Technology(LMD).
Field of Specialization : Mathematics.
Course Title : Analysis1
Credit : 6
Coefficient : 3
Duration: 13 weeksWeeklyt Time table: 1h 30 min of course and 3 Hours for tutorial group
Teacher : Dr Nadjet BOUDJERIDA
n.boudjerida@centre-univ-mila.dz
boudjnadj1843@google.comEvaluation Methods:
A final exam,short tests.
Objectives of the teaching :This course is intended for university students enrolled in their first year of LMD (Bachelor's degree) - Science and Technology .
The "Analysis 1" course illustrates the basic concepts of mathematics to help students acquire and understand the foundations of mathematical reasoning essential for understanding subsequent mathematics courses. The concepts covered are fundamental and among the most widely used in the field of Science and Technology.
Objectives :
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Consolidation: Review and deepen the calculation and analysis concepts learned in secondary school.
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Reasoning: Establish the foundations of mathematical rigor essential for technical disciplines (mechanics, electronics, civil engineering, etc.).
Recommended prerequisite knowledge:Basic high mathematics concepts.
Chapter One: Field of real numbers.
The main topics that will be covered in this chapter are:
Upper bound,lower bound,bounded set. Maximum element, minimum element. Supremum(least upper bound), infimum(greatest lower bound). Absolute value, integer part(floor function).
Chapter Two: Numerical Sequences
The main topics that will be covered in this chapter are :
Convergent sequences.
Comparison theorems. Monotone convergence theorem.
Extracted sequences .Adjacent sequences.
Special sequences (arithmetic,geometric,recurrent).Chapter Three: Real-valued functions
The main topics that will be covered in this chapter are:
- Definitions (monotony, parity, periodicity).
- Limits.
- Continuity.
- Differentiability.
Chapter Four : Series expansion and Taylor series
The main topics that will be covered in this chapter are:
- Comparison relations
- Series expansions in the vicinity of zero
(a) Definitions of Series expansion and Taylor-Lagrange theorem
(b) Usual Series expansions
(c) Operations on Series expansions - Series expansions in the vicinity of a point, in the vicinity of infinity and generalized Series expansions.
- Applications of Series expansions (calculation of limits, equations of tangent and asymptote)
Chapter Five : Integrals
The main topics that will be covered in this chapter are:
- Definitions and properties (primitive, integral, and definite integral)
- Integration methods
(a) Integration by parts
(b) Integration by change of variable
References and Bibliography:
بالعربية
بابا حامد بن حبيب ترجمة عبد الحفيظ مقران التحليل 1: تذكير بالدروس وتطبيقات (أو تمارين محلولة عدد 300)
In English
Murray R. Spiegel, Schaum's outline of theory and problems of advanced calculus, Mcgraw-Hill (1968).
Terence Tao, Analysis 1 (3rd edition), Springer (2016).
Glyn James, Modern Engineering Mathematics, Pearson (2020).
Bill Cox, Understanding Engineering Mathematics, Newnes, (2001).
Murray R. Spiegel, Schaum's Outline of Advanced Mathematics for Engineers and Scientists, Mcgraw-Hill (1971).
James Stewart, Calculus - Early Transcendentals (6th edition), Thomson Learning, (2008).
En français:
BOUHARIS Epouse, OUDJDI DAMERDJI Amel, Cours et exercices corrigés d’Analyse 1, Première année Licence MI Mathématiques et
Informatique, U.S.T.O, 2020-2021.
Benzine BENZINE, Analyse réelle cours et exercices corriges, première année maths et informatique (2016),
N. Piskounov, Calcul differentiel et integral T1 (8ème édition), 2 édition mir. Moscou -
