Foundations of Calculus-Based Mechanics

Apply integration techniques to solve kinematics problems with non-uniform acceleration.

Formulate and solve differential equations of motion for systems with velocity-dependent forces, such as air resistance.

Derive the work-energy theorem from Newton's second law for a variable force.

Apply the principles of impulse and momentum to analyze collisions and variable mass systems like rockets.

Solve constraint motion problems involving pulleys, strings, and inclined planes using Newtonian dynamics.

Derive equations of motion in non-inertial (accelerating) reference frames, including pseudo-forces.

Analyze the motion of a center of mass for a system of particles.

Solve high-level problems in Newtonian dynamics, incorporating engineering applications.