Course Syllabus

Department of Mathematics and Computer Science, Lincoln University



      Gordon, Russell. Real Analysis, A First Course. Pearson: Boston. 2002


***To be provided for each section***


      This is the second semester course in a one-year sequence that is designed as a rigorous development of fundamentals of analysis for Mathematics majors. The following topics will be covered in this course: differentiation of functions, integration of functions, infinite series, and sequences and series of functions.

PREREQUISITE:             MAT-421 (Analysis I)


      To prepare students with the theoretical foundation needed for further study in higher mathematics.

       At a minimum, upon completion of this course, students will be able to present accurately mathematical definitions and concepts, and provide rigorous mathematical proofs of basic facts in the following topics:

  1. The differentiations of functions. This includes:
    1. A rigorous definition of the derivative of a function and rigorous proofs of rules and theorems about derivatives that are presented in Calculus.
    2. A special focus on the mean-value theorem and its popular applications.
  2. The theory of Riemann integration, which includes:
    1. The construction and definition of the Riemann integral.
    2. Theorems on conditions for Riemann integrability of functions.
    3. A rigorous revision of the Fundamental Theorem of Calculus.
  3. The notions of infinite series. This includes:
    1. The notions of convergence and divergence of series.
    2. The comparison tests.
    3. The notion of absolute convergence, the root test and the ratio test.
  4. The notions of sequences and series of functions. This includes:
    1. The notions of point-wise convergence and uniform convergence.
    2. The properties of functions inherited through uniform convergence.
    3. The notion of power series and Taylorís formula.


CH 4: Differentiation (Weeks 1 to 3)
      Section 4.1: The Derivative of a Function.
      Section 4.2: The Mean Value Theorem.
      Section 4.3: Further Topics on Differentiation.

CH 5: Integration (Week 4 to 8)
      Section 5.1: The Riemann Integral.
      Section 5.2: Conditions for Riemann Integrability.
      Section 5.3: The Fundamental Theorem of Calculus.
      Section 5.4: Further Properties of the Integral.

CH 6: Infinite Series (Weeks 9 to 12)
      Section 6.1: Convergence of Infinite Series.
      Section 6.2: The Comparison Tests.
      Section 6.3: Absolute Convergence.
      Section 6.4: Rearrangements and Products.

CH 7: Sequences and Series of Functions (Weeks 13 to 16)
      Section 7.1: Pointwise Convergence.
      Section 7.2: Uniform Convergence.
      Section 7.3: Uniform Convergence and Inherited Properties.
      Section 7.4: Power Series.
      Section 7.5: Taylorís Formula.


At least 4 collections of home assignments will be given The students may discuss the assignments with each other only before they start their assignments. While they are doing their assignments the university rule on academic integrity applies.


        Participation 20%
        Assignments 80%

The grading scale guideline: **
A       92-100%
A-       88-91%
B+      85-87%
B      82-84%
B-      78-81%
C+       75-77%
C       72-74%
C-      68-71%
D+      65-67%
D      58-64%
F      0-57%


1) Attendance:

Lincoln University uses the class method of teaching, which assumes that each student has something to contribute and something to gain by attending class. It further assumes that there is much more instruction absorbed in the classroom than can be tested on examinations. Therefore, students are expected to attend all regularly scheduled class meetings and should exhibit good faith in this regard. For the control of absences, the faculty adopted the following regulations:

  • Four absences may result in an automatic failure in the course.
  • Three tardy arrivals may be counted as one absence.
  • Absences will be counted starting with whatever day is specified by the instructor but not later than the deadline for adding or dropping courses.
  • In case of illness, death in the family, or other extenuating circumstances, the student must present documented evidence of inability to attend classes to the Vice President for Student Affairs and Enrollment Management. However, in such cases the student is responsible for all work missed during those absences.
  • Students representing the University in athletic events or other University sanctioned activities will be excused from class (es) with the responsibility of making up all work and examinations. The Registrar will issue the excused format to the faculty member in charge of the off- or on-campus activity for delivery by the student(s) to their instructors.
2) Statement on Academic Integrity:

Students are responsible for proper conduct and integrity in all of their scholastic work. They must follow a professor's instructions when completing tests, homework, and laboratory reports, and must ask for clarification if the instructions are not clear. In general, students should not give or receive aid when taking exams, or exceed the time limitations specified by the professor. In seeking the truth, in learning to think critically, and in preparing for a life of constructive service, honesty is imperative. Honesty in the classroom and in the preparation of papers is therefore expected of all students. Each student has the responsibility to submit work that is uniquely his or her own. All of this work must be done in accordance with established principles of academic integrity.

An act of academic dishonesty or plagiarism may result in failure for a project or in a course. Plagiarism involves representing another person's ideas or scholarship, including material from the Internet, as your own. Cheating or acts of academic dishonesty include (but are not limited to) fabricating data, tampering with grades, copying, and offering or receiving unauthorized assistance or information.

3) The Student Conduct Code:

Students will be held to the rules and regulations of the Student Conduct Code as described in the Lincoln University Student Handbook. In particular, excessive talking, leaving and reentering class, phones or pagers, or other means of disrupting the class will not be tolerated and students may be asked to leave. Students who constantly disrupt class may be asked to leave permanently and will receive an F.

4) The Core Curriculum Learner Competencies:

All courses offered through the Department of Mathematics and Computer Science require students to meet at least the following out of the 8 Core Curriculum Learner Competencies:

(1) Listen and effectively communicate ideas through written, spoken, and visual means;
(2) Think critically via classifying, analyzing, comparing, contrasting, hypothesizing, synthesizing, extrapolating, and evaluating ideas;

(6) Apply and evaluate quantitative reasoning through the disciplines of mathematics, computational science, laboratory science, selected social sciences and other like-minded approaches that require precision of thought;

(8) Demonstrate positive interpersonal skills by adhering to the principles of freedom, justice, equality, fairness, tolerance, open dialogue and concern for the common good.


* The instructor of a given section of the course may make some modifications to the evaluation as well as to the rest of the syllabi including but not limited to; the grade weights, number of tests, and test total points.

**The grading scale guideline includes a 2-point flexibility.

Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this page _ last updated 9/10/2007.

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