1. Mathematics: Calculus, differential equations (applied in all engineering courses)
2. Physics: Mechanics, thermodynamics (applied in Mechanical, Electrical, Civil, and Aerospace Engineering)
3. Chemistry: Materials science, chemical reactions (applied in Chemical, Petroleum, and Materials Engineering)
4. Materials Science: Properties of materials, material selection (applied in Mechanical, Civil, Aerospace, and Materials Engineering)
5. Engineering Mechanics: Statics, dynamics (applied in Mechanical, Civil, Aerospace, and Mechatronics Engineering)

1. Mechanical Engineering: Mechanics, thermodynamics, materials science
2. Electrical Engineering: Mathematics, physics, electronics
3. Civil Engineering: Physics, materials science, engineering mechanics
4. Aerospace Engineering: Physics, materials science, engineering mechanics
5. Chemical Engineering: Chemistry, materials science, mathematics
6. Petroleum Engineering: Chemistry, materials science, mathematics
7. Materials Engineering: Materials science, chemistry, physics
8. Mechatronics Engineering: Engineering mechanics, mathematics, electronics
9. Computer Science and Engineering: Mathematics, algorithms, computer systems
10. Artificial Intelligence and Machine Learning Engineering: Mathematics, computer science, statistics

These fundamental principles form the foundation of various engineering courses, and students learn to apply them to solve real-world problems.