Course: Analyse 1

Topic outline

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Institute : Science and Technology

Department: Common Core Department of Science and Technology.

Target public: First year engineering (civil engineering, mechanical engineering, process engineering)

Fields of Specialization: Mathematics

Course title: Analysis 1

Credit: 6

Coefficient: 3

Duration: 15 weeks

Weekly timetable: 1h 30 min of course and 3 hours for tutorial group

Place of teaching: Lecture hall 2

Teacher: Hocine RANDJI

Contact: randji.h@centre-univ-mila.dz

Evaluation methods: A final exam , short tests.

Target skills:
The aim of this course is to bridge the knowledge in analysis acquired in high school with the foundations that will be a cornerstone in the mathematical analysis training at the undergraduate level. Given that admission to the first year of analysis will be exclusively for holders of a technical mathematics baccalaureate, it seems prudent to start by revisiting elementary concepts that will be used throughout this course, to ensure that nobody gets lost along the way.

Recommended Prerequisite Knowledge:

Elementary Mathematics from High School.

Any questions, please send me an email.
- Annonces Forum
Chapter 01: Properties of the set of real numbers R
The main topics 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 02: Sequences of real number
The main topics in this chapter are:
- Convergent sequences.
- Comparison theorems.
- Monotone convergence theorem.
- Extracted sequences.
- Adjacent sequences.
- Special sequences (arithmetic, geometric, recurrent).
Chapter 3: Real-valued functions
The main topics in this chapter are:
Definitions (monotony, parity, periodicity).
Limits.
Continuity.
Differentiability.
Chapter 4: Series expansion and Taylor series
The main topics in this chapter are:
1. Comparison relations
2. 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
3. Series expansions in the vicinity of a point, in the vicinity of infinity and generalized Series expansions.
4. Applications of Series expansions (calculation of limits, equations of tangent and asymptote)
Chapter 05: Integral
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The main topics in this chapter are:
1. Definitions and properties (primitive, integral, and definite integral)
2. Integration methods
(a) Integration by parts
(b) Integration by change of variable
References:
:بالعربية
.بابا حامد، بن حبيب، التحيل 1 تذكير بالدروس و تمارين محلولة عدد 300 ترجمة الحفيظ مقران، ديوان المطبوعات الجامعي *
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.
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