AMATYC 2013Applications of
Engineering and Science in the Calculus Sequence
Omar Adawi
Parkland College
Calculus I
Velocity and Acceleration in One Dimension – Physics I
Free Fall – Physics I
Simple Harmonic Motion – Physics I, III
Average Value of a Function – Time Average Over a Cycle – Physics II, III
Separable Differential Equations – Radioactive Decay – Chemistry II, Physics III
Newton’s Law of Cooling – Physics II
Malthusian Population Model – Biology
Van Bertanlanffy Growth Model – Biology
Calculus II
Trigonometric Integrals – Fourier Series – Electrical Engineering
Integrals of Rational Functions – Logistic Population Model - Biology
Improper Integrals – Physics II
Taylor Series – Physics I, II, III
Conic Sections – Parabolas – Parabolic Trajectories – Physics I
Orbits of Planets and Comets - Astronomy
Calculus III
Unit Vectors – Statics
Dot Product –Bond Angles – Chemistry I
Work – Physics I, II
Direction Cosines – Statics
Vector Cross Product – Torque – Physics I, II, Statics
Vector-Valued Functions – Helix – Charged Particle in a Magnetic Field – Physics II
Projectile Motion – Physics I, Dynamics
Curvature and Normal and Tangential Components of
Acceleration – Dynamics
Functions of Several Variables – Level Curves – Ideal Gas Law – Chemistry I, Physics II
Level Surfaces – Equipotential Surfaces of a Point
Charge – Physics II
Directional Derivatives – Gradients – Physics II, III
Double and Triple Integrals – Center of Mass, Centroid – Physics I, Statics
Moments of Inertia – Physics I, Statics
Probability Distributions:
Maxwell-Boltzmann Velocity Distribution – Physics II,
Chemistry I
Hydrogen Atom Wavefunctions – Chemistry I, Physics III
Theorem of Pappus – Statics
Vector Fields – Electric Field due to a Point Charge – Physics II
Divergence and Curl – Physics II (Maxwell’s Equations)
Line Integrals – Electric Potential – Physics II
Path Independence:
Conservation of Energy and Conservative Vector Force Fields – Physics
I, II
Thermodynamic State Functions – Chemistry I, II
Differential Equations
Separable Equations - Radioactive Decay – Chemistry II, Physics III
Newton’s Law of Cooling – Physics II
Malthusian Population Model – Biology
Van Bertanlanffy Growth Model – Biology
Logistic Population Model – Biology
Chemical Rate Laws – Chemistry II
Linear First-Order Equations – Compartmental Analysis – Chemical Engineering
RC - Circuit – Physics II
RL - Circuit – Physics II
Velocity and Acceleration with Air Resistance -
Dynamics
Second-Order Linear Equations – Mass-Spring System – Physics I, Dynamics
RLC – Circuit – Physics II
Simple Pendulum – Physics I, Dynamics
Laplace Transforms – Electrical and Mechanical Engineering
Heaviside Function – Electrical Engineering
Linear First-Order Systems – Compartmental Analysis – Chemical Engineering
Selected References
- Bedford, A. and W. Fowler, Dynamics. 3rd Ed. Upper Saddle River, N.J.: Prentice Hall, 2002.
- Bedford, A. and W. Fowler, Statics. 3rd Ed. Upper Saddle River, N.J.: Prentice Hall, 2002.
- Finney, Ross L. and George B. Thomas, Jr., Calculus. 2nd Ed. Reading, MA: Addison-Wesley, 1994.
- Schey, Harry M., Div, Grad and Curl and All That. New York: Norton, 1975.
- Swokowski, Earl W. Calculus. 5th Ed. Belmont, CA:Brooks/Cole, 1991.
- Tipler, Paul A. Physics: For Scientists and Engineers. 4th Ed. New York: Freeman/Worth, 1999.