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Mathematics (analysis) Description

Key Elements

Code

MATH 171

Formation

BS Earth and life sciences

Semester

1

Credits

6

Number of Teaching Hours

24

Number of Tutoring Sessions

36

Number of Laboratory Sessions

0

Content

Objective

At the end of this course, students will be able to: 1. Specify the characteristics of the motion of a point mass. 2. Apply Newton's laws. 3. Apply and verify the conservation laws of energy, and of linear momentum in collisions. 4. Describe the state of equilibrium of a solid. 5. Apply the fundamental principle of hydrostatics. 6. Distinguish a real fluid from an ideal fluid. 7. Study the motion of a ball through a viscous fluid. 8. Study the cyclic transformations of a thermodynamical system. 9. Compare the performance of a heat engine to that of Carnot’s engine.

Content

Kinematics: position vector, velocity vector and acceleration vector of a point mass. Study is restricted to Cartesian and polar coordinates. Dynamics: Types of forces, Newton's three laws of motion. Applications: motion on an inclined plane, free fall, satellites, central forces. Rotation: Moment of a force, moment of inertia, angular momentum. Energy: work of a constant force, work of the weight of a body, work of a frictional force and of the tension force in a spring. Theorem of kinetic energy. Conservation laws: conservation and non-conservation of mechanical energy, conservation of linear momentum and angular momentum. A solid in equilibrium: Conditions of equilibrium. Hydrostatic: fundamental principle and hydrostatics. The buoyant force. Fluid dynamics: Bernoulli's theorem, viscosity, Poiseuille's law, the motion of a spherical body in a viscous medium. First law of thermodynamics: Enthalpy, energetic treatment of thermal cyclic - processes. Concept of work. Second law of thermodynamics: Performance of a heat engine, Carnot's theorem. Entropy. References: 1. Lumbroso (mechanics and thermodynamics) 2. Resnick and Holliday, Serway. 3. General Physics (Schaum series, Spiegel). 4. Dunod physique Tome 1 mécanique. Controlling knowledge: 1. Partial exam of 60 min (25% of the final grade) 2. Final written test 120 min (75% of the final grade).