Page 274 - Buku Panduan Program Sarjana Muda APIUM 20262027-reduce

Kursus Elektif Program / Programme Core Courses

SIF1001 Kaedah Matematik I / Mathematical Methods I

Kredit / Credit : 3
Prasyarat Kursus / Course : Tiada / None
Pre-requisite(s)
Bahasa Pengantar / Medium : Bahasa Inggeris / English Language
of Instruction

Hasil Pembelajaran Kursus / Learning Outcomes
Pada akhir kursus ini, pelajar dapat: atau setelah menamatkan kursus ini, pelajar berupaya untuk:
At the end of the course, students are able to:

1 Kumpulan, siri dan had, nombor kompleks
Groups, series and limits, complex numbers
2 Pembezaan dan penyepaduan separa
Partial differentiation and integration
3 Algebra vektor, kalkulus vektor, matriks, ode
Vector algebra, vector calculus, matrices, odes

Sinopsis Kandungan Kursus / Synopsis of Course Content
Matriks dan penyelesaian untuk set persamaan linear: matriks dan pengurangan baris; vektor and
notasi; operasi matrik; gabungan linear, fungsi linear, operator linear; operator matriks, transformasi
linear; nilai eigen dan vektor eigen; matriks khas. Pembezaan separa: siri kuasa dalam dua
pembolehubah; jumlah pembeza; petua rantai; pembezaan tersirat; aplikasi pembezaan separa
untuk masalah maksimum dan minimum termasuk kekangan; Pengganda Lagrange, masalah titik
akhir dan titik sempadan; perubahan pembolehubah; pembezaan kamiran, petua Leibniz. Kamiran
berganda: kamiran bersepadu; aplikasi kamiran; kamiran tunggal dan berganda; pertukaran
pembolehubah dalam kamiran; Jacoban; kamiran permukaan. Analisis vektor: aplikasi vektor
pendaraban; produk hasil darab ganda tiga; medan; terbitan berarah, kecerunan; ungkapan lain yang
melibatkan pembezaan capahan; kamiran garisan; Teorem Green dalam satah; kecapahan dan
teorem kecapahan; Ikal dan Teorem Stoke. Persaman pembezaan biasa: persamaan terpisahkan;
persamaan linear tertib pertama; persamaan linear tertib kedua.

Matrices and solutions for sets of linear equations: matrix and row reduction; vectors and their
notation; matrix operations; linear combinations, linear functions, linear operators; matrix operators,
linear transformations; eigenvalues and eigenvectors; special matrices. Partial differentiation: power
series in two variables; total differentials; chain rule; implicit differentiation; application of partial
differentiation to maximum and minimum problems including constraints; Lagrange multipliers,
endpoint and boundary point problems; change of variables; differentiation of integrals, Leibniz rule.
Multiple integrals: integrated integrals; applications of Integrations; single and multiple integrals;
change of variables in integrals; Jacobian; surface integrals. Vector analysis: applications of vector
multiplication; triple products; fields; directional derivative, gradient; some other expressions involving
divergence; line integrals; Greenʼs Theorem in a plane; divergence and divergence theorem; Curl
and Stokeʼs Theorem. Ordinary differential equations: separable equations; linear first- order
equations; second-order linear equations.

Kaedah Pentaksiran / Assessment Methods
Pentaksiran Berterusan / Continuous : 40%
Assessment
Peperiksaan Akhir / Final Examination : 60%

248