Zarqa University Instructor:
Faculty of Science Lecture’s time:
Department: Mathematics Semester:
Course Title: Real Analysis 1 Course No. (0301211)
Office Hours:
Instructor:
Course description:
This course gives the analysis and theorems which has already given in Calculus, and put the first step for mathematical student in theoretical sense.
Aims of the course:
1 - This course will investigate many roles that are very important for students.
2 - Also give an idea for topology on real line and some prosperities of real line.
3 - This course will present and emphasize many topics in mathematics in particular Real Analysis, in order to aid the student in his future mathematical studies.
Intended Learning Outcomes: (ILOs) A. KnowledgeandUnderstanding
A1.ConceptsandTheories:
Prepare freshmen for higher level courses in mathematics.
A2. Contemporary Trends, Problems and Research:
Serve to understanding topics in mathematics.
A3. Professional Responsibility:
Prove a selection of theorems concerning real analysis.
B. Subject-specific skills B1. Problem solving skills:
Prove a selection of related theorems.
B2.ModelingandDesign:
Prove related theorems.
B3.ApplicationofMethodsandTools:
Prove a selection of related theorems.
C. Critical-Thinking Skills C1. Analytic skills: Assess
Classify real space Rand its properties using separation axioms and connectedness.
C2.Strategic Thinking:
Constructing a proof of theorems.
:رادإصلا خيرات 24
ناريزح 2015 :رادإصلا 01ZU/QP07F018
C3. Creative thinking and innovation:
Constructing a proof of theorems and describe different examples about real analysis.
D. General and Transferable Skills (other skills relevant to employability and personal development)
D1.Communication:
Engage students in solving problems in real analysis to build deep thinking and to become active in the communications in the future.
D2. Teamwork and Leadership:
Discussion of how to practically apply the theorems of real analysis and skills development partnership and cooperation to work in a spirit of collective action.
Course structures:
Wee k
Credit
Hours ILOs Topics Teaching
Procedure
Assessment methods
1 3 A1,A2
B1,B2
1.1-Real
Numbers& sets 1.2-Axioms of ordering
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
2 3 A1,A2
B1,B2 C1,D1
1.3-Bounded subsets of real numbers
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
3 3 A1,A2
B1,B2 D2
1.4-dense of rational numbers
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
4 3 A1,A2
B1,B2 C1,C2 D1,D2
2.1-Definitions of limits
2.2- Convergent of sequences by using limits
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
5 3 A1,B1 2.3- Algebraic
structures of sequences 2.4-
subsequences increasing
&decreasing
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
:رادإصلا خيرات 24
ناريزح 2015 :رادإصلا 01ZU/QP07F018
(monotonic) sequences 2.5- limits points
6 3 A1,A2
B1,B2 D2
3.1- Bolzano – Weierstrass theorem 3.2- Limits theorem
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
7 3 A1,A2
B1,B2 C2
3.3- Cauchy sequence 3.4- Nested interval 3.5-
Compactness
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
8 3 A1,A2
B1,B2 C1,C2 D1,D2
4.1- Definition of continuous function
4.2- composition of continuous function
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
9 3 A1,A2
B1,B2 C1,C2 D1,D2
4.3- algebraic operation for continuous functions
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
10 3 A1,A2
B1,B2 C1,C2 D1,D2
5.1- Open and closed
intervals5.2- Types of point in R Clustor points
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
11 3 A1,A2
B1,B2 C1,C2 D1,D2
5.3-
Interiorpoints exterior points 5.4-Boundary points
5.5-
Accumelationpo ints
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
12 3 A1,A2
B1,B2 C1,C2
6.1- Definition of derivative 6.2- Chain rule
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
:رادإصلا خيرات 24
ناريزح 2015 :رادإصلا 01ZU/QP07F018
D1,D2
13 3 A1,A2
B1,B2
6.3- Rolls theorem
6.4- Mean value theorem
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
14 3 A1,A2
B1,B2 C1,C2 D1,D2
6.5-Lhopitals rule theorem
Lectures, Cooperative Learning and Discussion
Exams and Homeworks
15 Final Exams
References:
Main Textbook:
Elements of real analysis- Charles G. Denlinger, Student Edition, Jones & Bartlett Supplementary Textbook(s):
Introduction to Real Analysis - Ropert G. Bartle , Second Edition , Eastern Michigan University , University of lllinois , 1992.
Assessment Methods:
Methods Grade Date
1st exam 25%
2nd exam 25%
Final exam 50%
:رادإصلا خيرات 24
ناريزح 2015 :رادإصلا 01ZU/QP07F018
