MATH 6952 - Analysis of Real Variable Functions
Fall 2026 Syllabus, Section 01, CRN 42767,
Credit hours: 3
Course Meeting Times
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Instructor
Jamal Tartir
Email: jktartir@ysu.edu
Course Description
6952. Analysis of Real Variable Functions. This course covers topics in the analysis of functions, mainly of several variables, and may include uniform convergence of sequences of functions and some consequences, functions on n-space, derivatives in vector spaces, and results such as the mean value theorem, Taylor's formula, inverse mapping theorem, and the implicit mapping theorem. Prereq.: MATH 3751 or MATH 5851 or satisfactory score on a Departmental prerequisite examination. 3 s.h.
Course Readings
| Group | Title | Author | ISBN |
|---|---|---|---|
| Required | Introduction to Real Analysis (4th Edition) | Robert G. Bartle and Donald R. Sherbert | 978-0-471-43331-6 |
| Required | Elementary Real Analysis (2nd Edition) | Brian S. Thomas, Judith B. Bruckner, and Andrew M. Bruckner | 978-1434843678 |
The course readings are subject to change in the event of extenuating circumstances, research developments, current events, and/or to ensure better learning.
Assignments/Assessments
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Schedule of Topics and Assignments
| Week of | Reading(s) | Proposed Topic | Due/To Prepare for Class |
|---|---|---|---|
| 8/24 | Chapter 7 of BS | Review of the Reimann Integral | |
| 8/31 | Chapter 7 of BS | The FToC and the Darboux Integral | |
| 9/7 | Chapter 7 of BS | The Darboux Integral and It's comparison to the Reimann Integral | |
| 9/14 | Chapter 8 of BS, Chapter 9 of TBB | Sequences of Functions and Series | |
| 9/21 | Chapter 9 of BS, Chapter 9 of TBB | Series of Functions | |
| 9/28 | Chapter 10 of TBB | Power Series | |
| 10/5 | Chapter 10 of TBB | Power Series and Functions | |
| 10/12 | Chapter 10 of TBB | Properties of Power Series | |
| 10/19 | Chapter 11 of BS, Chapter 11 of TBB | Topology of Euclidean Spaces | |
| 10/26 | Chapter 11 of TBB | Sequences and Functions in Euclidean Spaces | |
| 11/2 | Chapter 11 of TBB | Limits and Continuity of Multivariable Functions | |
| 11/9 | Chapter 11 of TBB | Properties of Continuous Multivariable Functions | |
| 11/16 | Chapter 12 of TBB | Differentiability of Multivariable Functions | |
| 11/23 | Chapter 12 of TBB | Properties of Differentiable Multivariable Functions | |
| 11/30 | Chapter 12 of TBB | Properties of Differentiable Multivariable Functions Continued | |
| 12/7 | Final Exams Week |
The course schedule, policies, procedures, and assignments in this course are subject to change in the event of extenuating circumstances, by mutual agreement, and/or to ensure better learning.