Tutor profile: Bart V.

What is the fundamental idea of integrals and differentiation? HInt: think about the meaning of the integral symbol.

An important idea in calculus is that the sum of infinitely many parts can equal a finite value, if those parts are infinitely small. This is exploited when integrating functions, but infinitesimal parts are also used to differentiate functions, i.e. define their slope. The relation between the integration and differentiation operations is expressed by the Fundamental Theory of Calculus, which can be proven using limit theory.

Name two important drivers of aerospace vehicle design. Think about accomplishing the mission objectives safely and efficiently.

Weight (or mass in space) and redundancy are drivers in most aerospace projects. From rockets to aircraft, the structural weight, propellant fraction, and fuel efficiency are each correct answers to what drives design. They can be further broken down into material strength and fatigue properties, engine efficiency, aerodynamic efficiency, and so on. Redundancy is a way to make systems more robust, but with the penalty of adding mass. Examples in aircraft are vehicle actuation systems, and duplicat flight sensors in spacecraft. Other correct answers include the project cost, time to completion, technology readiness, ground safety and risk, human rated flight systems, etc.

Professionally, some physicists prioritize theory while others prioritize experiments. Thinking in a more philosophical way, is one more important than the other in physics?

No. Physics is an empirical science, which means that the value of a theory is judged by how accurately it predicts real world events. Theories are also valued more if they make numerous new predictions to test. Experiments and theory are inseperable in the field of physics.