Matematika untuk Kimia

Tahun Akademik:
Gasal 2024/2025
Kelas-Offr:
I-I
Deskripsi:
(1) Fungsi dan Grafik: Sistem Koordinat, Representasi Grafik Fungsi, Keluarga Fungsi Penting dalam Kimia, (2) Kalkulus Diferensial: Diferensial Fungsi Variabel Tunggal, Diferensial Fungsi Beberapa Variabel (Turunan Parsial), Diferensial Total, Turunan sebagai Rasio Perubahan Kecil Tak Terhingga, Maksima, Minima, Titik Belok, (3) Kalkulus Integral: Integral sebagai Antiturunan, Metode Integrasi Umum, Metode Integrasi Khusus, Integral sebagai Penjumlahan Unsur Kecil Tak Terhingga, Integral Garis, Integral Ganda dan Integral Rangkap Tiga, (4) Persamaan Diferensial: Persamaan Diferensial Orde Pertama, Persamaan Diferensial Orde Kedua dengan Koefisien Konstan, Metode Solusi Deret Umum, Solusi Polinomial Khusus Untuk Persamaan Diferensial, (5) Deret Tak Hingga: Uji Konvergensi dan Divergensi, Deret Pangkat, Deret Maclaurin dan Deret Taylor, Deret Fourier dan Transformasi Fourier, (6) Skalar dan Vektor: Skalar, Vektor dan Penjumlahannya, Perkalian Vektor, (7) Matriks dan Determinan: Matriks Bujungsangkar dan Determinan, Aljabar Matriks, Solusi Sistem Persamaan Linear, Persamaan Karakteristik Matriks, (8) Operator: Operator Vektor, Persamaan Nilai Eigen, Operator Hermitian, Operator Rotasi, Transformasi Operator Del Square ke Koordinat Bidang Polar. (1) Functions and Graphs: Coordinate Systems, Graphical Representation of Functions, Important Family of Functions in Chemistry, (2) Differential Calculus: Differential of Functions of Single Variables, Differential of Functions of Several Variables (Partial Derivatives), Total Differential, Derivative as a Ratio Of Infinitesimally Small Changes, Maxima, Minima, Inflection Points, (3) Integral Calculus: Integral as an Antiderivative, General Methods of Integration, Special Methods of Integration, The Integral as a Summation of Infinitesimally Small Elements, Line Integrals, Double and Triple Integrals, (4) Differential Equations: First Order Differential Equations, Second Order Differential Equations with Coefficient Constant, General Series Method of Solution, Special Polynomial Solutions To Differential Equations, (5) Infinite Series: Test for Convergence and Divergence, Power Series, Maclaurin and Taylor Series, Fourier Series and Fourier Transforms, (6) Scalars and Vectors: Scalars, Vectors and Their Addition, Multiplication of Vectors, (7) Matrices and Determinants: Square Matrices and Determinants, Matrix Algebra, Solutions of Systems of Linear Equations, Characteristic Equation of a Matrix, (8) Operators: Vector Operators, Eigenvalue Equations, Hermitian Operators, Rotational Operators, Transformation of Del Square Operator to Plane Polar Coordinates.
Capaian Pembelajaran

• Peserta memahami “Fungsi, Tabel, dan Grafik” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami “Kalkulus Diferensial” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami konsep “Kalkulus Integral” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami konsep “Persamaan Diferensial” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami konsep “Vektor” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami konsep “Aljabar Matrik” dan mampu mengaplikasikannya dalam kimia.
• Peserta memahami konsep “Operator” dan mampu mengaplikasikannya dalam kimia.

Daftar Pustaka:

• Kishor Arora, Poonam Sinha, 2012. Applications of Mathematics In Chemistry, MJP Publisher, New Delhi.
• Paul Monk, Lindsey J. Munro, 2021. Maths for Chemistry: A chemist's toolkit of calculations, Oxford University Press, Oxford.
• Fiona Dickinson, Andrew McKinley, 2020. Introduction to Contextual Maths in Chemistry- Royal Society of Chemistry (RSC).
• Mohammad Asadzadeh, Reimond Emanuelsson, 2024. Handbook of Mathematical Concepts and Formulas for Students in Science and Engineering
• Prerna Bansal, 2024. Maths in Chemistry, Numerical Methods for Physical and Analytical Chemistry, 2nd Edition-De Gruyter.
• Robert G. Mortimer, S.M. Blinder, 2023. Mathematics for Physical Chemistry, 5th edition, Elsevier.
• James R. Barrante, 2003. Applied Mathematics for Physical Chemistry, 3rd edition, Prentice Hall
• Paul C. Yates, 2023. Chemical Calculations Mathematics for Chemistry, Third Edition-CRC Press.
• J.E. Parker, 2013. Introductory Maths for Chemists.
• Martin Cockett, Graham Doggett, 2012. Maths for Chemists, Royal Society of Chemistry.