Worksheets

Notes

Each of these worksheets could be tailored to a particular class.

Teaching them the pattern - you learn an abstract concept, you're confronted with a problem, you apply your new concept (together with everything you know up to this point)

Teach them the name of the game in engineering - it's not how closely you follow the rules, it's the creativity and and outside-the-box thinking you bring to the problem

The greater your diversity of tools, the more prepared you are to come up with ideas (increase raw material)

Engineering design process and engineering design thinking should be weaved into each worksheet.

Calculus Topics

Archimedes: Don't Disturb My Circles

• area, volume, surface area
• sphere and cylinder shapes
• geometric thinking

Simpson's Rule

• numerical integration
• approximating the area under a curve
• spreadsheet formulas

Centroids

• Civil engineering application of Simpson's Rule to centroids
• Building a highway going through a town
• Design of highway: top X rectangle is asphalt, bottom X rectangle plus cut-out half-circle is concrete, coord system has split down middle
• Curve design is a piecewise curve. Given a set of formulas.
• Use Simpson's Rule to compute the x and y centroids of the highway shape (Figure). Assume density of materials is same and is 2400 kg/m3.
• Use the arc length formula to find the total length of the road ft.
• Highway standards require a minimum lane width of 15 feet, 10 feet for side shoulder, 5 feet for inner shoulder, 3 lanes both directions
• Use Simpson's Rule to find the total volume of asphalt, volume of concrete required (use Pappus' Theorem to obtain the volume via V = A * length traveled)

Euler's Method

• electrical circuit
• Solving a differential equation
• Different right-hand sides, different time steps

Topics

Ideas for topics for worksheets:

Rockets

Motors, motor currents, motor control

insect populations - logistic equation, chemical treatment, population dynamics equations

insect motion and dynamics, work, force, energy - insect drones, batteries

droplets, slow motion, aerosols, force balances

piston cylinder systems, integrating ideal gas law

solid mechanics, rotational forces, warped CD drive, slow motion

arc length calculation

root-finding using midpoint method

studying convergence of series sum_{1}^{infty} 1/n^2 = pi^2/6

Insect drones: mass, power, force, work, distance, batteries

Feedback and control systems (1D control problems?)

Rocket propellant, P dV, casing and curing and consistency and chemistry

Apple power supply teardowns, plus high voltage, power transmission, etc.