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Calculus & Physics: Fluid Dynamics
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Module 1
Advanced Mathematical Tools for Physics
1
Vector Fields and Line Integrals
Define a vector field and compute the line integral of a vector field along a specified path.
2
Mass and Center of Mass of 2D Laminas
Set up and evaluate double integrals in Cartesian and polar coordinates to find the mass and center of mass of 2D laminas.
Mass and Center of Mass with Triple Integrals
Set up and evaluate triple integrals in Cartesian, cylindrical, and spherical coordinates to find the mass and center of mass of 3D solids.
4
Moment of Inertia: The General Integral Expression
Formulate the general integral expression for the moment of inertia of a continuous body about an axis.
5
Parallel and Perpendicular Axis Theorems
Apply the parallel and perpendicular axis theorems to simplify moment of inertia calculations.
Polar Coordinates: Velocity and Acceleration
Derive the expressions for velocity and acceleration vectors in polar coordinates.
7
Central Force Motion & Angular Momentum
Formulate Newton's second law for a central force in polar coordinates and derive the conservation of angular momentum.
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Advanced Applications in Mechanics