Tahun Akademik:
Gasal 2023/2024
Kelas-Offr:
M-M
Deskripsi:
Fourier Series and Transforms: 1. Introduction, 2. Simple Harmonic Motion and Wave Motion; Periodic Functions, 3. Applications of Fourier Series, 4. Average Value of a Function, 5. Fourier Coefficients, 6. Dirichlet Conditions, 7. Complex Form of Fourier Series, 8. Other Intervals, 9. Even and Odd Functions, 10. An Application to Sound, 11. Parseval’s Theorem, 12. Fourier Transforms. Calculus of Variations: 1. Introduction, 2. The Euler Equation, 3. Using the Euler Equation, 4. The Brachistochrone Problem; Cycloids, 5. Several Dependent Variables; Lagrange’s Equations, 6. Isoperimetric Problems, 7. Variational Notation. Special Functions: 1. Introduction, 2. The Factorial Function, 3. Definition of the Gamma Function; Recursion Relation, 4. The Gamma Function of Negative Numbers, 5. Some Important Formulas Involving Gamma Functions, 6. Beta Functions, 7. Beta Functions in Terms of Gamma Functions, 8. TheSimple Pendulum, 9. The Error Function, 10. Asymptotic Series, 11. Stirling’s Formula, 12. Elliptic Integrals and Functions. Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions: 1. Introduction, 2. Legendre’s equation, Leibniz’ rule diffrentiating product, 4. Rodrigues’ formula, 5. Generating function for Legendre polynomials, 6. Complete sets of orthogonal functions, 7. 8Orthogonality of Legendre polynomials, 8. Normalizationof Legendre polynomials, 9. Legendre series, 10. The associated Legendre functions, 11. Generalized power series or the method of Fobenius, 12. Bessel’ equation, 13. The second solution of Bessel’s equations, 14. Tables, graphs, and zeros of Bessel function, 15. Recursion relations, 16. A general diffrential equantion having Bessel functions as solutions, 17. Other kinds of Bessel functions, 18. The lengthening pendulum, 19. Orthogonality of Bessel functions, 20. Aprroximate formulas for Bessel functions, 21. Some general comments abaout series solutions, 22. Hermite functions; Laguerre functionn;Lladder operators.
Capaian Pembelajaran
Gasal 2023/2024
Kelas-Offr:
M-M
Deskripsi:
Fourier Series and Transforms: 1. Introduction, 2. Simple Harmonic Motion and Wave Motion; Periodic Functions, 3. Applications of Fourier Series, 4. Average Value of a Function, 5. Fourier Coefficients, 6. Dirichlet Conditions, 7. Complex Form of Fourier Series, 8. Other Intervals, 9. Even and Odd Functions, 10. An Application to Sound, 11. Parseval’s Theorem, 12. Fourier Transforms. Calculus of Variations: 1. Introduction, 2. The Euler Equation, 3. Using the Euler Equation, 4. The Brachistochrone Problem; Cycloids, 5. Several Dependent Variables; Lagrange’s Equations, 6. Isoperimetric Problems, 7. Variational Notation. Special Functions: 1. Introduction, 2. The Factorial Function, 3. Definition of the Gamma Function; Recursion Relation, 4. The Gamma Function of Negative Numbers, 5. Some Important Formulas Involving Gamma Functions, 6. Beta Functions, 7. Beta Functions in Terms of Gamma Functions, 8. TheSimple Pendulum, 9. The Error Function, 10. Asymptotic Series, 11. Stirling’s Formula, 12. Elliptic Integrals and Functions. Series Solutions of Differential Equations; Legendre, Bessel, Hermite, and Laguerre Functions: 1. Introduction, 2. Legendre’s equation, Leibniz’ rule diffrentiating product, 4. Rodrigues’ formula, 5. Generating function for Legendre polynomials, 6. Complete sets of orthogonal functions, 7. 8Orthogonality of Legendre polynomials, 8. Normalizationof Legendre polynomials, 9. Legendre series, 10. The associated Legendre functions, 11. Generalized power series or the method of Fobenius, 12. Bessel’ equation, 13. The second solution of Bessel’s equations, 14. Tables, graphs, and zeros of Bessel function, 15. Recursion relations, 16. A general diffrential equantion having Bessel functions as solutions, 17. Other kinds of Bessel functions, 18. The lengthening pendulum, 19. Orthogonality of Bessel functions, 20. Aprroximate formulas for Bessel functions, 21. Some general comments abaout series solutions, 22. Hermite functions; Laguerre functionn;Lladder operators.
Capaian Pembelajaran
- Peserta menunjukkan penguasaan terhadap metode matematika Deret Fourier dan Transformasi Fourier, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Kalkulus Variasi, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Fungsi Khusus, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Peserta menunjukkan penguasaan terhadap metode matematika Penentuan Solusi Persamaan Diferensial dengan Deret: Fungsi Legendre, Bessel, Hermite, dan Laguerre, kemampuan menerapkannya untuk menghasilkan model matematis bagi suatu sistem fisis, dan kemampuan mengambil keputusan secara tepat berdasarkan solusi dari model yang dihasilkan untuk menjawab permasalahan dari sistem fisis tersebut.
- Mary L. Boas, 2006, Mathematical Methods In The Physical Sciences, 3th edition
- Edwin J Purcell, 2006, Caculus with Differential Equations, 9th edition, Pearson
- Teacher: Sulur S