MINISTRY OF RESEARCH, TECHNOLOGY AND HIGHER EDUCATION, BENGKULU UNIVERSITY

FACULTY OF TEACHER TRAINING AND EDUCATION, DEPARTMENT OF MATHEMATICS AND NATURAL SCIENCES

MATHEMATICS EDUCATION STUDY PROGRAM

Jl. WR. Supratman Lemonade Cage, Bengkulu 38371 A Phone : (0736) 21186, Facsimile : (0736) 21186

Page : www.fkip.unib.ac.id e-mail : dekanat.fkip@unib.ac.id

SEMESTER LESSON PLAN

Study Program/Department       : Mathematics Education/JPMIPA FKIP           

Course                                          : Real Analysis

Course Code                                 : MAT-                        

Weight of credits per semester   : 3 credits / 2

Prerequisite Courses                   : Basic Mathematics, Calculus

Effective Lecturer                        : Dr. Dra. Hanifah, M.Kom

A.                 Course Learning Outcomes

1.        Students are able to solve the problem of Algebra of Sets and Functions

2.        Students are able to use Mathematical Induction

3.        Students are able to explain the Real Number System, Algebraic Properties R and Sequence Properties in R

4.        Students are able to use Absolute Value, Completeness R Nature, and apply the Supremum Trait Application

5.        Students are able to determine Rows and Limits, Limit Theorems

6.        Students are able to define the Monotonous Lineup, Subline and Bolzano-Weiestrass Theorem  

7.        Students are able to determine the Cauchy Criteria, and Pure Divergent Rows

8.        Mid-term Exam

9.        Students are able to solve function limit problems

10.    Students are able to use the Limit Theorems

11.    Students are able to use the Expansion of the Limit Concept

12.    Students are able to solve questions about Continuous Functions

13.    Students are able to solve the problem of Combination of Continuous Functions

14.    Students are able to complete Continuous Functions at Intervals, and Uniform Continuity

15.    Students are able to solve questions about monotonous functions and inverse functions

16.    Final Semester Exam

 

B.                 Brief Description of Course

        The Real Analysis course is a compulsory course in the Mathematics Study Program. Real Analysis material is a core course that is able to build students’ critical thinking skills. To be able to master the Real Analysis material well, students must master well the basic mathematical materials such as Sets, Basic Logic, and Calculus. In general, the materials studied in Real Analysis are: Set Algebra, Functions, Mathematical Induction, Real Number System, Algebraic Properties of R and Sequence Properties in R, Absolute Values, Completeness Properties of R, and applying the Application of Supremum Traits, Rows and Limits, Limit Theorems, Monotonous Rows, Sublines and Bolzano-Weiestrass Theorems, Cauchy Criteria, and Pure Divergent Rows, Limit-limit Functions, Limit Theorems,  Extension of the Concept of Limits, Continuous Functions, Combinations of Continuous Functions, Continuous Functions at Intervals, and Uniform Continuity

C.            Study materials / Learning materials.

1.        Set and Function

2.        Real Number System

3.        Rows of Real Numbers

4.        Limit Function

5.        Continuity of Functions

D.            Reference Library

Main: Jafar (2012). Real Analysis.          Al Khwarizmi Unaaha Study Community

Supporters: Bartle, Robert G. 2000. Introductions to Real Analysis. Third Edition. New York : John Wiley & Sons, Inc.

                                                       : Source from the internet in the form of videos or articles

 

E.     Description of Each Meeting Material –

 

 

 

Valuation

 

Forms/Methods of Defense,

Student Assignments

 

Week To

Final ability of learning outcomes

Indicators

Criteria and Forms of Assessment

Learning Materials

Online

Offline

 

Assessment Weight (%)

(1)

(2)

(3)

(7)

(4)

(5)

 

(8)

1

Able to solve Set and Function problems

 

1.1 Accuracy of understanding  Sets and Functions

1.2 Accuracy  of presenting problems and  solving the material of Sets and Functions

 

Criterion:

Accuracy, mastery of Sets and Functions

Form of Assessment:

Observations and post test

Presentation of materials

Set and Function

 

 

 

Class Discussion

Class Discussion

5%

2

Able to use the Induction Method

2.1 Accuracy of using the Induction Method for formula proof.

2.2 Ketrepatan presents the problem of the Induction Method and its solution

Criterion:

Accuracy, mastery of induction methods

Form of Assessment:

Observations and post test

Presentation of materials

Induction Methods

Class Discussion

Class Discussion

5%

3

Able to explain about System real numbers. Algebraic Properties of R and Properties of Sequences in R

3.1. Accuracy and completeness of information about the real number system.

3.2. Accuracy presents the problems of the Real Number System as well as their solutions

Criterion:

Accuracy, mastery of the material of the real number system

Form of Assessment:

Observations and post test

Presentation of materials

System real numbers. Algebraic Properties of R and Properties of Sequences in R

 

Class Discussion

Class Discussion

5%

4

Able to use Absolute Value. Completeness Properties of  R, and applying the Application of Supremum Properties

4.1 Accuracy and completeness of information about Absolute Value, Real numbers, and supremum properties

4.2 Accuracy presents the problem and solution of Absolute Value, Real numbers, and supremum properties. 4.3

Criterion:

Accuracy, mastery of Absolute Value material, Real number, and supremum properties

Form of Assessment:

Embedding and post test

Presentation of materials

Absolute value. Completeness Properties of  R, and applying the Application of Supremum Properties

 

Class Discussion

Class Discussion

5%

5

Able to determine the Rows and Limits, Limit Theorems

5.1 Clarity and completeness of information about Rows and Limits and their theorems.

5.2 5.2 Accuracy presents the problems of Rows and Limits and their theorems. and solutions

 

Criterion:

Accuracy, mastery of Rows and Limits, Limit Theorems

Form of Assessment:

Observations and post test

 

Presentation of materials

Rows and Limits, Limit Theorems

 

Class Discussion

Class Discussion

5%

6

Able to determine monotonous Rows, Sublines and Bolzano-Weiestrass Theorems  

6.1 Clarity and completeness of monotonous lineup information, etc.

6.2 Accuracy of presenting monotonous Row problems, etc. and solutions

 

Criterion:

Precision, mastery of monotonous Rows, Sublines and the Bolzano-Weiestrass Theorem  

Form of Assessment:

Observations and post test

 

Presentation of materials

Monotonous Sequences, Sublines and the Bolzano-Weiestrass Theorem  

 

Class Discussion

Class Discussion

5%

7

Able to determine the cauchy criteria, and pure divergent rows

7.1 Clarity and completeness of cauchy criteria information, and lineup

7.2 Accuracy of presenting the Cauchy Criterion problem, and rows and solutions

 

Criterion:

Accuracy, mastery of the Cauchy Criterion, and Purely Divergent Ranks  

Form of Assessment:

Observations and post test

Material Presentation

Cauchy Criteria, and Purely Divergent Rows

 

 

5%

8

Mid-term exam

 

Essay questions

 

 

UTS In The Classroom

5%

9

Able to solve function limit problems

9.1 Clarity and completeness of information about Function Limits

9.2 Accuracy of presenting the Function Limit problem

and

 

Accuracy, mastery of the Cauchy Criterion, and Purely Divergent Ranks 

 Form of Assessment:

Observations and post test

Presentation of materials

Function Limits

 

Class Discussion

Class Discussion

5%

10

Able to use  Limit Theorems

10.1 Clarity and completeness of information about the Limit Theorem

10.2 Accuracy of presenting the problem of the Limit Theorem and solutions

Accuracy, mastery of the Limit Theorem

Form of Assessment:

Observations and post test

 

Presentation of materials

Limit theorems

 

Class Discussion

Class Discussion

5%

11

Able to uses Expansion of the Limit Concept

11.1 Clarity and completeness of information on the Expansion of the Limit Concept.

11.2 Accuracy of presenting the problem of Expansion of the Concept of Limit and solution

 

Accuracy, mastery of the Expansion of the Limit Concept

Form of Assessment:

Observations and post test

Presentation of materials

Expansion of the Limit Concept

 

Class Discussion

Class Discussion

5%

12

Able to  solve problems about Continuous Functions

12.1 Clarity and completeness of information Continuous functions.

12.2 Accuracy of presenting the problem of Continuous Functions and solutions

Accuracy, mastery of continuous functions.

Form of Assessment:

Observations and post test

Presentation of materials

Continuous Functions

 

Class Discussion

Class Discussion

5%

13

Able to solve problems of Combinations of Continuous Functions

13.1 Clarity and completeness of information Combination of Continuous functions.

13.2 Accuracy of presenting problems Combination of Continuous Functions and solutions

Accuracy, mastery of the Combination of Continuous Functions of the Form of Assessment:

Observations and post test

Presentation of materials

Combinations of Continuous Functions

 

Class Discussion

Class Discussion

5%

14

Able to complete Continuous Functions at Intervals, and Uniform Continuity

14.1 Clarity and completeness of information Continuous functions at intervals, and uniform continuity

1 4.2 Accuracy presents the problem Continuous functions at intervals, and uniform continuity and solution

 

 

Accuracy, mastery of Continuous Functions at Intervals, and Uniform Continuity

Form of Assessment:

Observations and post test

Presentation of materials

Continuous Functions at Intervals, and Uniform Continuity

 

Class Discussion

Class Discussion

5%

15

Able to solve problems about Monotonous Functions and Inverse Functions

15.1 Clarity and completeness of information of Monotonous Functions and Inverse Functions

13.2 Accuracy presents the problem of Monotonous Functions and Inver Functions as well as solutions

 

 

Accuracy, mastery of monotonous functions and inverse functions of assessment forms:

Observations and post test

Presentation of materials

Monotonous Function and Inverse Function

 

Class Discussion

Class Discussion

5%

16

Final Semester Exam (UAS)

 

Essay Questions

 

 

 

30%

 

 

Final Value Assignment

Final Grade (NA) = Total value of subcompetence

Information

The criteria for determining the value of subcompetence are as follows.

                                                     Component

Weight

Report

20%

Presentation

50%

Attitudes/Attendance

00 %

Post Test

30%

                                  

Knowing                                                                                                            Bengkulu,            September  2022

Head of Study Program,                                                                                Ybs Lecturer,                                                                                                                                                                                                                                                                            

(………………………………………………. )                                                          Dr. Dra. Hanifah, M.Kom          Dr. Hari Sumardi, M.Si