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MATH 0420: Introduction to the Theory of One-Variable Calculus

About the Course

Instructor: Tom Everest (email: [email protected])

Lectures: MoWeFr 02:00-02:50 PM in A719 Public Health-Crabtree

Recitation: Tu 02:00-02:50 PM in Benedum 1045. Instructor: Amber Tindall

Textbook: Jiri Lebl: Basic Analysis, Custom Pitt Edition.

Prerequisites: The course contains the  “theoretical”  One-Variable  Calculus.   Prerequisite is MATH 0413:  Introduction to Theoretical Mathematics.  If you do not feel comfortable with the prerequisite material, please contact the instructor at the beginning of the course.

Core Topics:

1. The Bolzano-Weierstrass Theorem; Cauchy sequences; Cauchy completeness of the real num- bers.

2. Real-valued functions on an interval; limits and continuity.

3. Intermediate Value Theorem; Max-Min Theorem.

4. Uniform continuity;  continuous functions on a closed and bounded interval are uniformly continuous.

5. Differentiable functions.

6. Interior Extremum Theorem; Rolle’s Theorem; Mean Value Theorem.

7. Taylor’s Theorem and Taylor Series.

8. The Riemann Integral on a closed and bounded interval. Increasing functions are Riemann- integrable. Continuous functions are Riemann-integrable.

9. The Fundamental Theorem of Calculus.

10. Definition and examples of pointwise and uniformly-convergent sequences of functions.

11. Continuity of uniform limits of continuous functions.

12. Interchange of uniform limits and integration.

13. Interchange of limits with differentiation.

14. The M-test for uniform convergence of series.

15. Application of power series.


This course fulfills requirements for the following majors:

❼ Bachelor of Science in Mathematics

❼ Bachelor of Science in Applied Mathematics

Bachelor of Science in Mathematics-Economics

❼ Bachelor of Science in Mathematical Biology

Grading Scheme:

Homework Assignments (30%)

❼ Midterm Exam 1 (20%)

Midterm Exam 2 (20%)

❼ Final Exam (30%)

Homework Assignments and Exam Policy: Homework will be assigned weekly.   You are encouraged to work with other students or use resources, but each student must write up their solutions independently.  Copying solutions from another student or an internet resource will be considered cheating and handled accordingly. Late homework will not be accepted, but your lowest homework score will be dropped.

Exams must be taken on the announced dates.  There will be no make up exams.  If you miss an exam for a documented medical reason, your grade on the missed exam will be the prorated grade of your final exam.

Getting Help

Office Hours

Your instructor and TA will announce their office hours.

Disability Services

If you have a disability for which you are or may be requesting an accommodation, you are encour- aged to contact both your instructor and Disability Resources and Services (DRS), 140 William Pitt Union, (412) 648-7890, [email protected], (412) 228-5347 for P3 ASL users, as early as possible in the term. DRS will verify your disabilty and determine reasonable accommodations for this course.

Course Policies

Academic Integrity

Cheating/plagiarism will not be tolerated. Students suspected of violating the University of Pitts- burgh Policy on Academic Integrity may incur a zero score for the assessment in question.  Ad- ditional sanctions may be imposed, depending on the severity of the infraction.  Even during this COVID-19 pandemic, Academic Integrity policies will be enforced. If there is any doubt as to the orginality of a student’s submission for an assessment, they may be asked to explain their work during a one-on-one meeting with their instructor. If the student’s explanations are unsatisfactory, they may receive a zero score for the assessment, or the instructor may choose to administer an alternative assessment in a different format.

Assignments and assessments are designed so that you learn by doing them, and only those re- sources authorized by the instructor may be used to complete them.  Copying graded homework or exam answers from outside sources and other such violations of the academic integrity code will comprimise your learning.  Passing a course without adequately mastering the material may set you up to struggle in subsequent courses.  Also, it is a violation of the academic integrity code to share any question from a graded assignment or an exam in any form. The instructor may choose to post a solution set after the assessment, but these materials written by the instructor are copy- righted, and you are not permitted to distribute them in any way. If you inadvertently have access to a shared exam or graded homework question, then you are obligated to inform the instructor. Academic integrity is not about what you can get away with; it is about personal accountability, honor, ethics, respect, trust, and fairness.

Health and Safety

In the midst of this pandemic, it is extremely important that we all abide by public health regu- lations and University of Pittsburgh health standards and guidelines.  In particular, indoors and within the classroom, we must wear a face covering whenever COVID-19 community levels are HIGH in Allegheny County. For the most up-to-date information and guidance, visit coronavirus.pitt.edu and check your Pitt email for updates before each class.

Diversity and Inclusion

The University of Pittsburgh does not tolerate any form of discrimination, harassment, or retaliation based on disability, race, color, religion, national origin, ancestry, genetic information, marital status, familial status, sex, age, sexual orientation, veteran status, gender identity, or other factors as stated in the University’s Title IX policy. The University is committed to taking prompt action to end a hostile environment that interferes with the University’s mission. For more information about policies, procedures, and practices, visit https://www.diversity.pitt.edu/civil-rights-title-ix/policies- procedures-and-practices.

We ask that everyone in the class strive to help ensure that other members of this class can learn in a supportive and respectful environment. If there are instances of the aforementioned issues, please contact the Title IX Coordinator by calling (412) 628-7860, or emailing [email protected]. Reports can be filled out online.  You may also choose to report this to a faculty/staff member; they are required to communicate this to the University’s Office of Diversity and Inclusion. If you wish to maintain complete confidentiality, you may also contact the University’s Counseling Center (412) 648-7930.

Email Communication

Each student is issued a University email address ([email protected]) upon admittance.  This email adress may be used by your instructor and the University for official communication with students.  Students are expected to read email sent to this account on a regular basis.  Failure to read and react to University communications in a timely manner does not absolve a student from knowing and complying with the content of the communication.

Classroom Recording

To ensure the free and open discussion of ideas, students may not record classroom lectures, dis- cussion and/or activities not already recorded by the instructor, without the advance written per- mission of the instructor, and any such recording properly approved in advance can be used solely for the student’s own private use.

Certain lectures may be recorded by the instructor, and this may include student participation. Students are not required to participate in recorded conversations.  The recorded lecture may be used by the faculty member and the registered students only for internal class purposes and only during the term in which the course is being offered.  Recorded lectures will be made available to all students in the class via Canvas and/or Panopto.

Copyright

Some of the materials in this course may be protected by copyright. United States copyright law, 17 USC section 101, et seq., in addition to University policies and procedures, prohibit unauthorized duplication or retransmission of course materials. See the Library of Congress Copyright Office.