Math IV: The Physics of Motion and Foundations of Calculus

Description: Calculus was invented by Sir Isaac Newton in the 17th century in order to formulate his laws of motion, and in that context the concepts of calculus are actually very easy to understand. The physics presented in this class uses geometry to convey the fundamental ideas of calculus in order for the students to understand, not only the equations for motion, but also how they are derived. We will explore the relationship of distance, velocity, and acceleration for motion in one, two, and three dimensions. We will also introduce trigonometry and vectors in order to extrapolate motion from one-dimension to two and three dimensions.

  • Describing Motion
  • Linear Motion with Constant Velocity
  • Relative Motion
  • Average Speed
  • Linear Motion with Constant Acceleration
  • Slope and Area Under the Curve (Differentiation and Integration)
  • Zeno’s Paradoxes and the Concept of a Limit
  • Newton’s Laws of Motion
  • Vectors and Motion in Two Dimensions
  • Basic Trigonometry
  • Projectile Motion

Homework: Math is not a spectator sport. You never really know if you truly understand math until you solve problems. Practice is essential, hence twenty to thirty minutes of homework three times a week and a desire to improve will be the key to getting the most out of this course.

Prerequisites: Students should be advanced in mathematical reasoning beyond grade level and must be fluent with basic pre-algebra skills such as fractions, decimals, percents, and ratios. Students should also have some experience solving basic algebraic equations and working with roots and exponents.