Advanced mathematics, physics and special physical or mathematical courses are taught in 3 departmental lecture halls, 10 training laboratories in mechanics, molecular physics, electricity and magnetism, optics and atomic physics.

The Department of Physical and Mathematical Sciences conducts research work within the framework of the state budget topic "Modern Methods of Complex Analysis and Mathematical Modeling in Oil and Gas Engineering".
Among the faculty members of the department are many talented scientists who work fruitfully in both classical areas of mathematics and applied fields. The following areas of research are developed by our scientists:
- Theory of functions (Assoc. Prof. Savchuk Y.I., Prof. Bandura A.I.);
- Differential equations (Assoc. Prof. Shehda L.M., Assoc. Prof. Tymkiv I.R.);
- Mathematical modeling in engineering (Prof. Moisyshyn V.M., Associate Professor Gural I.M., Associate Professor Smolovyk L.R., Associate Professor Kryshtopa L.I., Associate Professor Tyrlych V.V., Professor Chernova M.E., Professor Bandura A.I.);
- mathematical modeling in economics (Assoc. Prof. Vytvytska O. M., Prof. Bandura A. I.);
- creation of computer technologies for the study of stresses and deformations of structural elements (Assoc. Prof. Ripetskyi R.Y., );
- Pedagogy and Psychology (Prof. Moiseenko L.A., Associate Professor Gural I.M., Associate Professor Smolovyk L.R.). - Physics and Chemistry of Semiconductor Films (Prof. Galushchak M.O., Associate Professor Mazur M.P., Associate Professor Mazur T.M., Associate Professor Mateik G.D., Associate Professor Vakaliuk V.M.).
Among the most significant achievements of the department's scientists in recent years are the scientific discovery "Patterns of changes in the stress state of the rock massif, which is in an extremely stressed state when drilling deep wells" made by Prof. V.M. Moisyshyn together with his doctoral students, for which the authors were awarded silver medals named after P.L. Kapitsa. L. Kapitsa silver medals; six instructional documents and two monographs by Prof. V.M. Moisyshyn devoted to various issues of well drilling; monograph by Prof. L.A. Moiseenko "Psychology of Creative Mathematical Thinking" and two scientific and methodological manuals written by her in co-authorship with well-known Ukrainian psychologists.
The department maintains scientific relations with both Ukrainian and foreign scholars. In particular, Prof. L.A. Moiseienko collaborates with specialists from the Institute of Psychology of the National Academy of Sciences of Ukraine, and a galaxy of analysts, Associate Professor Y. Savchuk and Professor A. Bandura, have joint works with mathematicians from Lviv and Kharkiv Universities and Lviv Polytechnic. Thanks to the grant won, Prof. Bandura (at that time an associate professor) had the opportunity to train for three months in 2014 with Prof. S. Ivashkovych on geometric methods of multidimensional complex analysis (University of Lille 1, France).
Based on the results of our research, we annually publish 30 to 50 scientific articles and prepare 10-15 presentations at scientific conferences. You can find a list of scientific works of a particular teacher of the department on his or her page by contacting the department staff.
The department has a doctoral program, postgraduate studies, and a scientific seminar "Mathematical modeling in mining", which is headed by Prof. V.M. Moisyshyn.
Scientists of the department take an active part in the work of the Small Academy of Sciences (as supervisors and jury members), pay great attention to the scientific work of young people. Every year, students submit 7-10 reports on their research, conducted under the guidance of teachers, to student scientific and technical conferences. The best of them are sent to national competitions and have been repeatedly awarded with certificates and diplomas. In addition, teachers constantly work as jury members of the regional tournament of young mathematicians, young physicists, as well as regional competitions in these subjects.
 

The Department of Physics and Mathematics of IFNTUOG together with the Faculty of Mathematics and Informatics of the Precarpathian University named after V. Stefanyk and Ivano-Frankivsk center of the National Science and Technology School. It publishes the series Number of the professional journal Precarpathian Bulletin of the Schevchenko Scientific Society. Precarpathian University named after V. Stefanyk and Ivano-Frankivsk center of the National Science and Technology School publishes the series "Number" of the professional journal "Precarpathian Bulletin of the Schevchenko Scientific Society. Number".
 

The Department's scientific achievements in the field of physics are facilitated by close cooperation with scientists from the institutes of the National Academy of Sciences of Ukraine: Institute of Physics, Institute of Semiconductor Physics, Institute of Metallophysics, as well as with renowned scientists from Precarpathian and Lviv National Universities, Lviv and Kyiv Polytechnics, and Sumy State University.
 

In particular, in 2010 and 2013, Prof. Halushchak (then Head of the Department of General and Applied Physics) won a tender among the research projects announced by the Ministry of Education and Science of Ukraine. Since January 1, 2010, the department has been implementing the state budget fundamental theme "Research of new methods of converting solar and thermal energy into electricity." One Doctor of Science, 6 Candidates of Science, 2 postgraduate students, and 2 students participated in theoretical and experimental research. The project was designed for 3 years. The result of the research work is the development of a new method for converting solar and thermal energy into electricity and a prototype of a technical device for implementing the developed method.
 

In 2014, a tender was won for a two-year state budget applied topic "Technology of semiconductor structures and thermoelectric energy converters for special purposes".
 

Today, the department's staff conducts research related to the development of new ways to produce the latest thermoelectric materials and the creation of renewable energy sources.

The department provides teaching of the following disciplines:
- Advanced Mathematics;
- Operations Research;
- Mathematical Methods for Public Administration;
- Business Mathematics;
- Probability Theory and Mathematical Statistics; 
- Physics.

-General physics;

-Fundamentals of physics;
- Physics.
- An e-course in physics for applicants.

The educational and methodological work at the department is aimed at studying and mastering the basic concepts and theoretical results of mathematical disciplines by students in order to use them in the study of special disciplines. It also involves mathematical modeling of processes and structures related to the general activities of specialists. At the same time, the development of cognitive abilities and creative thinking of students, the formation of their readiness for independent study of the achievements of science and technology and their active use in their professional activities are carried out.
The work programs and calendar plans, based on the credit-module system, set out the required amount of educational material and establish the most appropriate sequence of its study. A clear interrelation between lectures, practical, and laboratory classes and students' independent study of the necessary material has been developed.
The disciplines of the department are fully provided with textbooks and methodological developments. Almost all sections of higher mathematics are provided with lecture notes written by the department's teachers. Over the past 20 years, the department has prepared and published more than 100 educational and methodological publications in Ukrainian. The main ones include:

1. Практикум з вищої математики Частина 1: Навчальний посібник / В.М. Мойсишин, Я.І. Савчук, А.І. Бандура та ін.; За ред. В.М. Мойсишина, Я.І. Савчука. – Івано-Франківськ: ІФНТУНГ, 2022. – 623с. ISBN 978-966-694-410-1 
2. Практикум з вищої математики. Частина 2: Навчальний посібник / В.М. Мойсишин, Я.І. Савчук, А.І. Бандура та ін.; За ред. В.М. Мойсишина, Я.І. Савчука. – Івано-Франківськ: ІФНТУНГ, 2022. – 658с. ISBN 978-966-694-411-8 

3. Тестові завдання з вищої математики : навч. посіб. / Гургула С.І., Мойсишин В.М., ред. - Івано-Франківськ : ІФНТУНГ Факел, 2008. - 737 с.

   Збірник містить 200 теоретичних питань та 3350 тестових завдань, що охоплюють весь нормативний курс вищої математики для ВНЗ і призначені для тестового контролю знань та умінь студентів.

   Розпочати читання частини 1 (c.1-600, до завдання 9.2.23).

   Розпочати читання частини 2 (c. 601-737, від завдання 9.2.24).

4. Збірник завдань для розрахункових робіт з вищої математики : навч. посіб. / С. І. Гургула, В. М. Мойсишин, С. С. Гулька, І. М. Гураль. - Івано-Франківськ : ІФНТУНГ, 2010. - 451 с.

   Збірник завдань адресовано студентам технічних та економічних спеціальностей внз, навчальні плани яких передбачають виконання розрахункових робіт. 

   Розпочати читання.

5. Bandura A. I. Operational calculus: lectures / A. I. Bandura, I. Ye. Ovchar, O. M. Vytvytska, IFNTUOG.  -- Ivano-Frankivs'k: IFNTUOG, 2015. -- 105 p. Посилання на читальню.
6. Bandura A. I. Theory of probability and mathematical statistics: lectures / A. I. Bandura, L. I. Kryshtopa, I. Ye. Ovchar, IFNTUOG. -- Ivano-Frankivs'k: IFNTUOG, 2015. -- 169 p. Посилання на читальню.
7.  Bandura A. I. Theory of probability and mathematical statistics: practices / Bandura A. I., Kryshtopa L. I., Ovchar I. Ye.  // Ivano-Frankivs'k: IFNTUOG, 2016. -- 163 p. Посилання на читальню.
8. Bandura A. I. Higher Mathematics (Differention and Integration of Several Variables Functions): lectures / Bandura A. I., Kryshtopa L. I.  // Ivano-Frankivsk : IFNTUOG, 2017.  -- 228 p. Посилання на читальню.
9. Bandura A.  Partial differential equations: lectures / Bandura A., Ovchar I., Tymkiv I. -- Ivano-Frankivs'k: IFNTUOG, 2018. -- 138 p. 
10. Bandura A.  Partial differential equations: practices / Bandura A., Ovchar I., Tymkiv I. -- Ivano-Frankivs'k: IFNTUOG, 2019. - 112 p. 
11. Bandura A. I., Ovchar I. Ye., Tyrlych V. V. Operational calculus: practices. - Ivano-Frankivs'k:  IFNTUOG, 2020. - 69 p.
12. Bandura, A. I. Advanced Mathematics (Theory of the complex variable function) [Текст] = Вища математика : lectures / A. I. Bandura, L. І. Kryshtopa. -- Ivano-Frankivsk: IFNTUOG, 2023. -- 89 р.
13. Higher Mathematics (Differention of several variables functions): lectures / Y.I.Savchuk, L.M.Shegda, L.I.Kryshtopa, N.O.Shkolna. - Івано-Франківськ: ІФНТУНГ, 2011. - 95 c.
14. Kryshtopa L. I., Shkolna N. O. Higher mathematics (series): lectures. -- Ivano-Frankivs'k, IFNTUOG. -- 2012. -- 115 p.
15. Tyrlych V. V. Higher mathematics (Differential Equations): lectures / V. V. Tyrlych, L. I. Kryshtopa. Ivano-Frankivs'k: IFNTUOG, 2014. -- 114 p.

16. Kryshtopa L.  Higher Mathematics (Differention and Integration of One Variable Functions): lectures.  Kryshtopa L. , Gural I. M. Ivano-Frankivs’k: IFNTUOG, 2017.
     

    It is worth noting the highly professional and coordinated work of the department's teaching and support staff: leading engineer Bohdan Demkiv and engineer of the first category Liubomyra Dyakiv, who performed computer typing, editing, layout and layout of most of the above publications. In addition, thanks to the work of our engineers on a voluntary basis, twenty volumes of the "Carpathian Bulletin of the National Technical School" for 2009-2013 were published.
    The department is working on the introduction of mathematical special courses for senior students of various specialties into the educational process, and relevant lecture notes and textbooks have been published or are being prepared for publication:
    - Theory of fuzzy sets (Candidate of Physical and Mathematical Sciences, Associate Professor Savchuk Y.I., for the specialty "Automated control of technological processes");
    - Statistical analysis of data with STATISTICA package (Candidate of Physical and Mathematical Sciences, Associate Professor M.M. Osipchuk, for the specialty "Business Economics");
    - General Algebra (Candidate of Physical and Mathematical Sciences, Associate Professor Gurgula S.I., for the specialty "Automated Systems Software");
    - Operations Research (Candidate of Technical Sciences, Associate Professor Smolovyk L.R., for the specialty "Accounting and Auditing");
    - Spherical and Differential Geometry (Candidate of Pedagogical Sciences, Associate Professor Grigorchuk L.I., for the specialty "Geodesy, Cartography and Land Management");
    - Modeling of the drill string operation (Doctor of Technical Sciences, Prof. Moisyshyn V.M., for the students of the Institute of Postgraduate Education).
    The above-mentioned special courses are provided with the following manuals and lecture notes.
    1. Savchuk Y.I. Theory of fuzzy sets: Methodical manual. - Ivano-Frankivsk: Fakel, 2004. - 201 p.
    2. Statistical analysis of data with the STATISTICA package: Study guide / T.I. Manchych, A.Y. Openko, M.M. Osipchuk, V.G. Shportyuk - Drohobych: Renaissance, 2006. 208 p.
    3. Gurgula S.I. Selected issues of general algebra: Study guide. - Ivano-Frankivsk: Fakel, 2006. - 99 p.
    4. Research of operations: Lecture notes / L.R. Smolovyk, O.M. Vytvytska, K.V. Gresko and others - Ivano-Frankivsk: IFNTUOG, 2009. 140 p.
    5. Grigorchuk L.I., Grigorchuk G.V. Special sections of higher mathematics. Part 1. Spherical trigonometry: Lecture notes. - Ivano-Frankivsk: IFNTUOG, 2010. - 89 p.
    6. Grigorchuk L.I., Grigorchuk G.V. Special sections of higher mathematics. Part 2. Differential geometry: Lecture notes - Ivano-Frankivsk: IFNTUOG, 2010. 54 p.
    7. Vekeryk V.I., Moisyshyn V.M. Equation of equilibrium of sections of a drill string in a well oriented arbitrarily in space: Monograph. 2nd edition, revised - Ivano-Frankivsk: Fakel, 2007. 138 p.
    We also care about future students. More than a dozen educational and methodical publications have been prepared for the applicants preparing for the entrance exams in mathematics at the higher educational institutions of Ukraine and IFNTUOG in particular, including two collections of tasks with the stamp of the Ministry of Education and Science of Ukraine, which have been reprinted several times:
    1. Collection of competitive tasks in mathematics: Study guide. Second edition, supplemented / V.M. Moisyshyn, S.I. Gurgula, V.I. Gorgula, M.M. Osipchuk, B.S. Sikora; Edited by V.M. Moisyshyn and S.I. Gurgula - Ivano-Frankivsk: Fakel, 2010. - 625 p. Stamp of the Ministry of Education and Science of Ukraine (letter No. 1/11-5773 of 29.06.2010).
    2. Mathematics: Collection of test tasks for entrants. Seventh edition, supplemented / V.M. Moisyshyn, S.I. Gurgula, M.M. Osypchuk, Y.I. Savchuk, V.V. Tyrlych; Under the general editorship of V.M. Moisyshyn - Ivano-Frankivsk: DKD, 2010. 482 p. Stamp of the Ministry of Education and Science of Ukraine (letter No. 1/11-5694 of 24.06.2010).
    Along with this, the teachers of the department systematically organize competitions among university students, take an active part in the work of the jury of the regional mathematics competition among schoolchildren, the tournament of young mathematicians, work in visiting commissions for the recruitment of freshmen and at entrance exams in Ivano-Frankivsk.
     

    Gurgula S. I. (until his death on March 26, 2016) and Savchuk Y. I. work fruitfully with talented university students, holding weekly classes of the mathematics club and preparing them for the All-Ukrainian Student Mathematics Olympiads among technical universities. Thanks to this thorough preparation, the university students often win prizes at these competitions. Their many years of work have culminated in the publication of a book that collects olympiad-type problems over a long period of time in various areas of higher mathematics.
    1. Gurgula S. I., Savchuk Y. I. Collection of problems of student mathematical competitions // Ivano-Frankivsk: IFNTUOG, 2014. -- 357 с.
     

    The Department of General and Applied Physics once had the following special courses:
    1) Building physics
    2) Additional course of physics
    3) Special course of physics "Nuclear Physics" for masters
    4) Electronic special course "Nuclear Physics" for masters
    5) Physics of liquids, gases and solids
    6) Physics of solids

    1.Чернова, М. Є. Як розв'язувати задачі з фізики [Текст] = How to resolve problems in physics : навч. посіб. (українсько-англійський) у 2-х частинах. Ч. 1 / М. Є. Чернова. – Івано-Франківськ : ІФНТУНГ, 2020. – 312 с. https://search.library.nung.edu.ua/DocDescription?doc_id=463130
    2. Чернова, М. Є. Як розв’язувати задачі з фізики (How to resolve problems in physics) [Текст] : навч. посібник (українсько-англійський) у 2-х частинах. Ч. 2 / М. Є. Чернова. – Івано-Франківськ : ІФНТУНГ, 2021. – 205 с.  https://search.library.nung.edu.ua/DocDescription?doc_id=473511