Advanced Engineering Math: Understanding Eigenvalues, Determinant Method, Matrix Inverses, and Cramer's Rules in Solving Systems of Linear Equations

MOOC MOOC Fakultas Ilmu Terapan (FIT)

Advanced Engineering Math: Understanding Eigenvalues, Determinant Method, Matrix Inverses, and Cramer’s Rules in Solving Systems of Linear Equations

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Telkom University

Last Update:

July 9, 2024

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About Course

Source : onlinelearning.telkomuniversity.ac.id

Hi Engineering Kids!

Welcome to Engineering Math 1

Course Identity

Technical Mathematics 1 (VKI1F2) in the D3 Computer Technology Study Program, Faculty of Applied Sciences, which is found in semester 1 of the 2020 Curriculum and is one of the compulsory courses at the first level. This course is one of the courses that repeats the basic understanding of mathematics that has actually been obtained in secondary school (matrices and SPL), as well as understanding new material, namely complex numbers and graph theory. This course will teach the concept of Matrix which includes matrix operation, determinant, inverse, and eigen value; solving Linear Equation System (SPL) using inverse method and Cramer’s Rules; and graph theory and its application which includes graph coloring, shortest path and huffman code. While Complex Numbers does not use this LMS.

Course Profile and History

This Technical Mathematics 1 course provides knowledge of basic mathematical concepts regarding matrices, solving SPL and graph theory. This course is a development course from the previous course, namely technical mathematics and emerged during the formulation of the 2020 curriculum. This is because for the Computer Technology Study Program it is deemed insufficient only in discrete mathematics, but requires an understanding of other mathematics, so it is split into 2, namely Engineering Mathematics 1 and Engineering Mathematics 2. The content of this course is 2 credits which is part of the compulsory course for D3 Computer Technology students at the first level.

Course Relevance (Urgency)

The urgency of the Engineering Mathematics 1 course is that this course is a compulsory course for all D3 Computer Technology students at the first level. By taking this course, students will gain a basic understanding of mathematics that will be needed as a basis in other courses.

Links to other courses

Engineering Mathematics is a type of course that must be taken by all D3 Computer Technology students. This course is held in the first semester, and has no prerequisite courses. Meanwhile, the material will be applied in several courses in the current semester or the next semester, such as the Electric Circuit course.

Learning Outcomes (LO)

The Learning Outcomes of this course are that students are expected to be able to:

Able to work on problems related to matrix operations.
Able to work on problems related to determinants.
Able to work on problems related to inverses.
Able to work on problems related to eigenvalues
Able to work on problems related to solving SPL using inverse matrix.
Able to work on problems related to solving SPL using Cramer’s Rules.

Subject matter

This course will be conducted for 32 meetings in 16 weeks of lectures with the topics for each week as follows:

Week 1: Introduction to Matrices and Matrix Operations
Week 2: Determinants
Week 3: Inverse Matrix
Week 4: Eigenvalues
Week 5 : Solving SPL using matrix inverse
Week 6 : Solve SPL using Cramer’s Rules
Week 7 : Assessment I
Week 8: Repetition of the concept of trigonometric values
Week 9: Complex Number Operations
Week 10: Converting Complex Numbers
Week 11: Assessment II
Week 12: Graph Theory
Week 13: Graph Applications: Graph Coloring and Shortest Path
Week 14: Graph Applications: Huffman Code
Week 15: Assessment III
Week 16: Remedial

e-Learning Based Course Learning Plan

E-learning based learning from this course is only available for week 1 to week 6. That is matrix and SPL material with 6 subject matters.

Best Practice (Tips and Trick)

To master this course easily, what can be done include:

Learn and understand the basic concepts well and correctly.
Follow and comply well with the agreed lecture rules.
Do lots of question exercises.
Increase discussion with friends in working on problem exercises.

Certification

There are no certifications associated with this course.

Course Reference

Danang Mursita. Matematika untuk Perguruan Tinggi. 2011. Bandung : Rekayasa Sains.
Encu Sutarman. Matematika Teknik. 2013. Yogyakarta : Andi.
Markoni. Pengantar Dasar Matematika Rekayasa. 2014. Yogyakarta : Graha Ilmu.
Heru Nugroho, S.Si., M.T.. Matematika Diskrit dan Implementasinya Dalam Dunia Teknologi Informasi (Bagian 1). 2002. Yogyakarta : Deepublish.

Course lecturer

Name : Lisda Meisaroh
Lecturer’s Code : LSD
Email : lisda@tass.telkomuniversity.ac.id

Course Content

Nilai Eigen
Hai Anak Teknik!Ketemu lagi dengan Matematika.Pada pokok bahasan kali ini, kita akan mempelajari nilai eigen. Dimana nilai eigen ini sangat erat kaitannya dengan matriks.CAPAIAN PEMBELAJARAN Mampu mengerjakan soal yang berkaitan dengan nilai eigenMATERI PEMBELAJARAN 1. Pengenalan nilai eigen suatu matriks. 2. Mencari nilai eigen suatu matriks.

Menyelesaikan SPL dengan Metode Determinan dan Invers Matriks
Hai Anak Teknik!Ketemu lagi dengan Matematika.Pada pokok bahasan kali ini, kita akan membahas mengenai penyelesaian Sistem Persamaan Linear (SPL) dengan menggunakan metode determinan dan invers matriks.CAPAIAN PEMBELAJARAN Mampu mengerjakan soal yang berkaitan dengan penyelesaian Sistem Persamaan Linear (SPL) dengan menggunakan metode invers matriksMATERI PEMBELAJARAN Pengenalan Sistem Persamaan Linear (SPL). Menyelesaikan SPL 3 varibel dengan menggunakan metode invers matriks.

Menyelesaikan SPL dengan Cramer’s Rules
Hai Anak Teknik!Ketemu lagi dengan Matematika.Pada pokok bahasan kali ini, kita akan membahas mengenai penyelesaian Sistem Persamaan Linear (SPL) dengan menggunakan Cramer's Rules.CAPAIAN PEMBELAJARAN Mampu mengerjakan soal yang berkaitan dengan penyelesaian Sistem Persamaan Linear (SPL) dengan menggunakan Cramer's RulesMATERI PEMBELAJARAN Pengenalan Cramer's Rules Menyelesaikan SPL 3 variabel dengan menggunakan Cramer's Rules

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