Module Handbook


Module Name:

Real Analysis I

Module Level:


Abbreviation, if applicable:


Sub-heading, if applicable:


Courses   included   in   the

module, if applicable:

The theory of real numbers; sequences and series; continuous functions.


5th / Third Year

Module coordinator(s):

Dr. Mohammad Imam Utoyo, M.Si.


Dr. Mohammad Imam Utoyo, M.Si., Abdulloh Jaelani, S.Si., M.Si.


Bahasa Indonesia

Classification   within   the


Compulsory Course / Elective Studies

Teaching format / class

hours per week during semester:

3 hours lectures (50 min / hour)


3 hours lectures, 3 hour structural activities, 3 hours individual study,

13 week per semester, and total 117 hours per semester   3.9 ECTS

Credit Points:



  Calculus II, Fundamentals of Mathematics II

Learning goals/competencies:

General Competence (Knowledge)

 Can explain the concept of calculus analysis


Specific Competence:

1.           Explains algebraic and order properties of real numbers
2.           Explains Absolute Value and interpretation
3.           Explain concept supremum and infimum
4.           Applications of the supremum property
5.           Explain the concept of sequence and its properties
6.           Determining the sequence convergence
7.           Explain the concept subsequences and Bolzano-Weierstrass theorem
8.           Explaining the criteria Cauchy
9.           Explain the concept of function, limit and continuity
10.        Explain the concept of continuous functions on interval
11.        Explain the concept of uniform continuity


This course covers the fundamentals of mathematical analysis: 
real number system, order properties of real numbers, absolute value, completeness, the concept of supremum and infimum, characterization interval,sequnces, sequence convergence, monotone sequences, Cauchy criterion, convergent series, continuous functions, sequence criterion and uniformly continuous

Soft skill Attribute

 Discipline, honest, and Active

Study/exam achievements:

Students are considered to be competent and pass if at least get 40 of maximum mark of the final score.


Grading Policy




10 %


20 %


10 %

Midterm exams

30 %

Final exam

30 %


Final index is defined as follow:

A      :    75 - 100

AB    :    70 - 74.99

B      :    65 - 69.99

BC    :    60 - 64.99

C      :    55 - 59.99

D      :    40 - 54.99

E       :      0 - 39.99

Forms of Media:

Slides and LCD projectors, whiteboards

Learning Methods:

Lecture, quiz, and assessments


1.       Bartle, Robert  G. and Sherbert, Donald R., 2000, Introduction to Real Analysis, 4th ed, John Wiley & Sons,Inc., New York.

2.       Rudin, Walter., 1976. Principles of Mathematical Analysis (International Series in Pure and Applied Mathematics). 3rd ed, McGraw-Hill.


In order to pass the course, you do have to satisfy the minimum requirements for 75 % attendance.