Moduł oferowany także w ramach programów studiów:
Informacje ogólne:
Nazwa:
Mathematics In Geophysics
Tok studiów:
2013/2014
Kod:
BGF-2-107-AG-s
Wydział:
Geologii, Geofizyki i Ochrony Środowiska
Poziom studiów:
Studia II stopnia
Specjalność:
Applied geophysics
Kierunek:
Geofizyka
Semestr:
1
Profil kształcenia:
Ogólnoakademicki (A)
Język wykładowy:
Angielski
Forma i tryb studiów:
Stacjonarne
Osoba odpowiedzialna:
dr Czyżewska Katarzyna (kasia@agh.edu.pl)
Osoby prowadzące:
dr Czyżewska Katarzyna (kasia@agh.edu.pl)
dr hab. inż. Zych Marcin (zych@agh.edu.pl)
Krótka charakterystyka modułu

Opis efektów kształcenia dla modułu zajęć
Kod EKM Student, który zaliczył moduł zajęć wie/umie/potrafi Powiązania z EKK Sposób weryfikacji efektów kształcenia (forma zaliczeń)
Wiedza
M_W001 He/she will be familiar with and will understand the advanced phenomena of physics and various and diverse geophysical processes GF2A_U02, GF2A_W01, GF2A_K01, GF2A_U01, GF2A_K02, GF2A_K07, GF2A_U04 Egzamin,
Kolokwium
M_W002 He/she will know and understand those advanced methodologies used in the field of Mathematics which are vital in describing and explaining the complex problems in the field of Geophysics GF2A_W02, GF2A_U02, GF2A_U01, GF2A_K02, GF2A_K03, GF2A_U04, GF2A_K08 Aktywność na zajęciach,
Egzamin,
Kolokwium
M_W003 He/she will acquired a deep knowledge of the various methodologies used in Mathematics and their application in general and applied Geophysics GF2A_U18, GF2A_U01, GF2A_K02, GF2A_K07, GF2A_W04, GF2A_U09 Egzamin,
Kolokwium
Umiejętności
M_U001 he/she will acquired a deep knowledge of Mathematics that will enable him/her to properly analyse the parameters of Geophysics (used) in the context of the physical properties of rock formations and in the context of various geophysical processes GF2A_W02, GF2A_K05, GF2A_U02, GF2A_W05, GF2A_K07, GF2A_U04 Egzamin,
Kolokwium
M_U002 he/she will be familiar with those methodologies used in Mathematics which are also used to solve the problems in the field of Geophysics GF2A_W02, GF2A_W01, GF2A_K07, GF2A_W07, GF2A_U04, GF2A_U11 Aktywność na zajęciach,
Egzamin,
Kolokwium
M_U003 he/she will be familiar with the advanced methodologies of Mathematics and he/she will be able to apply them when analysing the experimental data GF2A_W02, GF2A_U03, GF2A_U02, GF2A_W05, GF2A_W01, GF2A_K02, GF2A_K07, GF2A_U04 Egzamin,
Kolokwium
M_U004 he/she will be able to carry out further independent research that will involve finding and reading literature in both Polish and English languages GF2A_W02, GF2A_K05, GF2A_K01, GF2A_U01, GF2A_K07, GF2A_U17, GF2A_U16 Aktywność na zajęciach,
Egzamin,
Kolokwium
Kompetencje społeczne
M_K001 he/she will be able to work in a group and find the solution to any given problem in the field of Engineering GF2A_W02, GF2A_U02, GF2A_K02, GF2A_K03, GF2A_K04, GF2A_U04 Aktywność na zajęciach,
Projekt,
Referat
Matryca efektów kształcenia w odniesieniu do form zajęć
Kod EKM Student, który zaliczył moduł zajęć wie/umie/potrafi Forma zajęć
Wykład
Ćwicz. aud
Ćwicz. lab
Ćw. proj.
Konw.
Zaj. sem.
Zaj. prakt
Inne
Zaj. terenowe
Zaj. warsztatowe
E-learning
Wiedza
M_W001 He/she will be familiar with and will understand the advanced phenomena of physics and various and diverse geophysical processes + - - - - - - - - - -
M_W002 He/she will know and understand those advanced methodologies used in the field of Mathematics which are vital in describing and explaining the complex problems in the field of Geophysics + - - + - - - - - - -
M_W003 He/she will acquired a deep knowledge of the various methodologies used in Mathematics and their application in general and applied Geophysics + - - + - - - - - - -
Umiejętności
M_U001 he/she will acquired a deep knowledge of Mathematics that will enable him/her to properly analyse the parameters of Geophysics (used) in the context of the physical properties of rock formations and in the context of various geophysical processes - - - + - - - - - - -
M_U002 he/she will be familiar with those methodologies used in Mathematics which are also used to solve the problems in the field of Geophysics + - - + - - - - - - -
M_U003 he/she will be familiar with the advanced methodologies of Mathematics and he/she will be able to apply them when analysing the experimental data - - - + - - - - - - -
M_U004 he/she will be able to carry out further independent research that will involve finding and reading literature in both Polish and English languages - - - + - - - - - - -
Kompetencje społeczne
M_K001 he/she will be able to work in a group and find the solution to any given problem in the field of Engineering - - - + - - - - - - -
Treść modułu zajęć (program wykładów i pozostałych zajęć)
Wykład:

Complex function: complex derivative, Cauchy-Riemann equations, holomorfic function, harmonic function, conformal mapping, singular points of complex function, Taylor and Laurent series, complex integral, Cauchy theorem, residuum theorem with applications, Gamma and Beta functions
Integral transforms: Fourier and Laplace transform with applications
Special ordinary differential equations: Fuchs class equations, Frobenius method, Lagrange, Bessel, confluent, Legendre equations, Sturm-Liouville problem, orthogonal polynomials, generating function, Rodriguez formula
Mathematical physics equations: initial and boundary conditions, Laplace, heat and wave equations, separation of variables for partial differential equation, boundary value problems in various symmetries: rectangular, cylindrical and spherical

Ćwiczenia projektowe:

Complex function: complex derivative, Cauchy-Riemann equations, holomorfic function, harmonic function, conformal mapping, singular points of complex function, Taylor and Laurent series, complex integral, Cauchy theorem, residuum theorem with applications, Gamma and Beta functions
Integral transforms: Fourier and Laplace transform with applications
Special ordinary differential equations: Fuchs class equations, Frobenius method, Lagrange, Bessel, confluent, Legendre equations, Sturm-Liouville problem, orthogonal polynomials, generating function, Rodriguez formula
Mathematical physics equations: initial and boundary conditions, Laplace, heat and wave equations, separation of variables for partial differential equation, boundary value problems in various symmetries: rectangular, cylindrical and spherical

Nakład pracy studenta (bilans punktów ECTS)
Forma aktywności studenta Obciążenie studenta
Sumaryczne obciążenie pracą studenta 177 godz
Punkty ECTS za moduł 6 ECTS
Egzamin lub kolokwium zaliczeniowe 12 godz
Udział w wykładach 30 godz
Udział w ćwiczeniach audytoryjnych 30 godz
Przygotowanie do zajęć 30 godz
Samodzielne studiowanie tematyki zajęć 75 godz
Pozostałe informacje
Sposób obliczania oceny końcowej:

Evaluation: 50% seminars and 50% final exam

Wymagania wstępne i dodatkowe:

the student should obtain a ‘pass’ grade in the course in Mathematics (3 terms) and the course in Physics (2 terms)

Zalecana literatura i pomoce naukowe:

1. Arfken, G.; Mathematical Methods for Physicists, New York andLondon, Academic Press 1985
2. Conway, J.B.: Functions of One Complex Variable, Springer-Verlag Berlin and Heidelberg, Co. 2001
3. Hildebrand, F.B.: Advanced Calculus for Applications, Englewood Cliffs and New Jersey, Prentice-Hall, Inc. 1964
4. Boyce, DiPrima: Elementary Differential Equations and Boundary Value Problems, John Wiley and Sons, Inc. 2009
5. Titchmarsch, E.C.: Eigenfunction Expansions Associated with Second Order Differential Equations, London, Oxford University Press 1962
6. Farrel, O.J., Ross, B.: Solved Problems: Gamma and Beta Functions, Legendre Polynomials, Bessel Functions, New Yorn, The Macmillan Co. 1963
7. Watson, G.N.: A Treatise on the Theory of Bessel Fuctions, Cambridge, Cambridge University Press 1952

Publikacje naukowe osób prowadzących zajęcia związane z tematyką modułu:

Nie podano dodatkowych publikacji

Informacje dodatkowe:

Brak