Zarqa University Instructor
Faculty of Science Lecture’s time:
Department: Mathematics Semester:
Course title: Introduction to
Functional Analysis.(0301414) Office Hours:
Course description:
The course gives an introduction to functional analysis, which is a branch of analysis in which one develops analysis in infinite dimensional vector spaces. The central concepts which are studied are metric space, normed spaces with emphasis on Banach and Hilbert spaces, and continuous linear maps (often called operators) between such spaces. Spectral theory for compact operators is studied in detail.
Aims of the course:
1. Define metric space and related concepts and illustrate them with typical example.
2. Understand the theory of inner product spaces and prove their properties.
3. Understand the theory of normal spaces, Banach spaces, and the theory of linear operators.
4. Know examples of linear functional, finite dimensional spaces, and dual space.
5. Derive and apply the basic properties of Hilbert spaces.
Intended Learning Outcomes: (ILOs)
A.
KnowledgeandUnderstanding A1.ConceptsandTheories: New theories and concepts.
Analytical procedures for solving Problems.
A2.Contemporary Trends, Problems and Research:
Serve to understanding topics in the course.
A3.Professional Responsibility:
Prove theorems concerning functional analysis.
B.
Subject-specific skills B1. Problem solving skills: Students will be able to apply the fundamental of functional analysis that they have learned in this course to solve problems.
Students will develop the ability to think independently and solve problems.
B2. Modeling and Design:
Teaching strategies to be used to develop these cognitive skills
Lectures are followed by numerous examples, some of which are practical in nature, to illustrate the application of learned theories.
Problem classes are used to explain further the theories and to help the students apply them in solving problems.
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B3.ApplicationofMethodsandTools:
Exams and homework will include problems, solution of which requires critical thinking and identification of correct formulas.
Class discussion.
C.
Critical-Thinking Skills C1. Analytic skills: Assess
Responsibility to solve given assignments on their own and submit the solution on time.
Time management in study of course materials.
Use of university library and web search for collecting information C2.Strategic Thinking:Participation of students in classroom discussion
.
C3.Creative thinking and innovation:
Constructing a proof of theorems and describe different examples.
D.
General and Transferable Skills (other skills relevant to employability and personaldevelopment) D1.Communication:Description of the skills to be developed in this domain .
Ability of the students to apply basic knowledge of mathematics in solving Problems .
D2.Teamwork and Leadership:
Test questions and assignments that require students’ knowledge in mathematics and their computational capabilities for solving problems
.
Course structures:
Wee k
Credit
Hours ILOs Topics Teaching
Procedure
Assessment methods
1 3 A1 Metric Space, Examples of metric
Spaces.
Lectures and discussion
Participation question, quiz and homework
2 3 A1, B1, C1, D1 Open Set, Closed Set,
Neighborhood.
Lectures and discussion
Participation question, quiz and homework 3 3 A1, B1, C1, D1 Convergence, Cauchy Sequence,
Completeness.
Lectures and discussion
Participation question, quiz and homework 4 3 A1, B1, C1, D1 Completion of Metric Space,
Completeness proofs.
Lectures and discussion
Participation question, quiz and homework 5 3 A1, B1, C1, D1 Vector Space, Normed Space and
Banach Space.
Lectures and discussion
Participation question, quiz and homework 6 3 A1, B1, C1, D1 Subspaces, Compactness. Lectures and Participation question,
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discussion quiz and homework
7 3 A1, B1, C1, D1 Linear Operators. Lectures and
discussion
Participation question, quiz and homework 8 3 A1, B1, C1, D1 Continuous Linear Operators,
Linear Functionals.
Lectures and discussion
Participation question, quiz and homework 9 3 A1, B1, C1, D1 Normed Spaces of Operators,
Dual Space.
Lectures and discussion
Participation question, quiz and homework 10 3 A1, B1, C1, D1 Inner Product Space, Hilbert
Space.
Lectures and discussion
Participation question, quiz and homework 11 3 A1, B1, C1, D1 Orthonormal Sets and Sequences,
Hilbert Adjoint Operator.
Lectures and discussion
Participation question, quiz and homework 12 3 A1, B1, C1, D1 Self Adjoint Operator, Unitary
Operators.
Lectures and discussion
Participation question, quiz and homework 13 3 A1, B1, C1, D1 Normal Operators, Bounded and
Continuous Linear Operator.
Lectures and discussion
Participation question, quiz and homework 14 3 A1, B1, C1, D1 Hilbert Space Operators, Unitarily
Invariant Norms, Total Orthonormal Sets.
Lectures and discussion
Participation question, quiz and homework
References:
A.
Main Textbook:IntroductoryFunctional Analysiswith Applications, by Erwin Kreyszig.
B.
Supplementary Textbook(s):
Functional Analysis by Walter Rudin.
Functional Analysis by F. Riesz and B.SZ. Nagy.
Elements of functional analysis, A. L. BrownAssessment Methods:
Methods Grade Date
First Exam 25
Second Exam 25
Final Exam 50
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