Zarqa University Instructor: Dr. Shaza Zorba
Faculty of Science Lecture’s time: 9.30 – 11 M. W.
Department: Serves Courses Unit Semester : First
Course Title: Real Analysis 1 Course No. (0301211)
Office Hours: 12 – 13 S. T. Th.
8 - 9.30 M. W.
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. Knowledge and Understanding
A1. Concepts and Theories:
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. Modeling and Design:
Prove related theorems.
B3. Application of Methods and Tools:
Prove a selection of related theorems.
C. Critical-Thinking Skills C1. Analytic skills: Assess
Classify real space R and its properties using separation axioms and connectedness.
C2. Strategic Thinking:
Constructing a proof of theorems.
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C3. Creative thinking and innovation:
Constructing a proof of theorems and describle 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
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(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 intervals 5.2- 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
6.1- Definition of derivative
Lectures, Cooperative Learning and
Exams and Homeworks
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C1,C2 D1,D2
6.2- Chain rule Discussion
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:
Introduction to Real Analysis - Ropert G. Bartle , Second Edition , Eastern Michigan University , University of lllinois , 1992.
Assessment Methods:
Methods Grade Date
1st exam 25% 15 / 11 / 2015
2nd exam 25% 20 / 12 / 2015
Final exam 50%
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