Tahun Akademik:
Gasal 2021/2022
Kelas-Offr:
AB-AB
Deskripsi:
Fourier Series and Transforms: Periodic Functions, Average Value of a Function, Fourier Series (sine –cosine form), Fourier Series (complex form), Dirichlet Conditions, Even and Odd Functions and their Fourier series, Application Fourier series, Parseval’s Theorem, Fourier Transforms. Calculus of Variations: The Euler Equation, Using the Euler Equation, The Brachistochrone Problem; Cycloids, Several Dependent Variables; Lagrange’s Equations, Isoperimetric Problems, Variational Notation. Special Functions: The Factorial Function, Gamma Function (Recursion Relation, The Gamma Function of Negative Numbers, Some Important Formulas Involving Gamma Functions), Beta Functions (Beta Functions in Terms of Gamma Functions, The Simple Pendulum), The Error Function, Asymptotic Series, Stirling’s Formula, Elliptic Integrals and Functions. Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions: Series solution of differential equations, Legendre’s equation (Leibniz’ rule diffrentiating product, Rodrigues’ formula, Generating function for Legendre polynomials), Legendre’s equation (Complete sets of orthogonal functions, Orthogonality of Legendre polynomials, Normalizationof Legendre polynomials, Legendre series), The associated Legendre functions, Generalized power series or the method of Fobenius, Bessel’ equation (The second solution of Bessel’s equations, Tables, graphs, and zeros of Bessel function, Recursion relations), Bessel’ equation (A general diffrential equantion having Bessel functions as solutions, Other kinds of Bessel functions, The lengthening pendulum, Orthogonality of Bessel functions, Aprroximate formulas for Bessel functions), Some general comments abaout series solutions, Hermite functions; Laguerre functionn;Lladder operators.
Capaian Pembelajaran
  • Menguasai konsep esensial transfoemasi dan deret Fourier, kalkulus variasi, fungsi khusus, penyelesaian secara deret persamaan diferensial dan menerapkannya untuk menyelesaikan permasalahan matematika atau fisika yang terkait secara tepat, sistematis, mandiri, bertanggungjawab, dan memanfaatkan perkembangan ipteks.
Daftar Pustaka:
  • Mary L. Boas, 2006, Mathematical Methods In The Physical Sciences, 3th edition
  • Edwin J Purcell, 2006, Caculus with Differential Equations, 9th edition, Pearson