INTEGRASI ALJABAR LINEAR DAN KALKULUS II MELALUI APLIKASI DIAGONALISASI MATRIKS PADA DERET PANGKAT
DOI: https://doi.org/10.30605/2htk4v90
Deret Pangkat, Diagonalisasi Matriks, Fungsi Matriks, Pembelajaran Terintegrasi, Sintesis Literatur.
Abstract
Pembelajaran matematika di perguruan tinggi pada umumnya disajikan secara terpisah antar mata kuliah seperti Aljabar Linear dan Kalkulus II. Hal ini cenderung menyebabkan mahasiswa mengalami kesulitan dalam memahami keterhubungan antarkonsep, khususnya ketika mempelajari fungsi matriks yang direpresentasikan melalui deret pangkat. Dalam Aljabar Linear, konsep diagonalisasi matriks secara teoritis mampu menyederhanakan perhitungan deret pangkat matriks yang banyak dibahas dalam Kalkulus II. Namun demikian, pemanfaatan diagonalisasi matriks sebagai jembatan integrasi kedua mata kuliah tersebut masih jarang dibahas secara sistematis dalam literatur pembelajaran matematika. Penelitian ini bertujuan menganalisis integrasi konseptual kedua materi tersebut melalui metode Systematic Literature Review (SLR) berstandar PRISMA terhadap 21 artikel terpilih. Hasil penelitian menunjukkan bahwa letak masalah utamanya bukan pada materi masing-masing, melainkan pada pemisahan kurikulum dan tingginya beban kognitif mahasiswa sewaktu berpindah topik. Sebagai solusinya, dirumuskan skema integrasi empat langkah: menyusun matriks, menyederhanakan bentuknya, menerapkan fungsi deret, kemudian menginterpretasikan hasilnya. Seluruh proses ini dihubungkan oleh satu rumus utama, Ak = PDkP-1. Selain terbukti jauh lebih cepat dan akurat daripada hitungan manual, temuan ini juga menggeser fungsi diagonalisasi dari sekadar alat hitung menjadi jembatan kurikuler yang menghasilkan model sintesis konseptual sebagai rujukan penyusunan materi terintegrasi tanpa menambah beban SKS.
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