Basic Mathematics, Calculus
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 –
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Valuation |
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Forms/Methods of Defense, Student Assignments |
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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
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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
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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) |
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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