Week 4

In Calculus I, the students do the following:

• Rates of Change: Rectilinear Motion (average and instantaneous rates of change, displacement, velocity, acceleration) Section 2.4
• Chain Rule (definition pg. 121) Section 2.5
• Implicit Differentiation, Related Rates Sections 2.6-2.7
• Newton-Raphson Method for finding roots of nonlinear equations Section 2.9
• Generalized Derivative Formulas
• Tangent Line Approximation (linearization of a function - pg. 145, incremental approximation formula- pg. 147) Section 2.8
• Differentials (differential rules) Section 2.8

In Physics I, the students do the following:

• Work, Kinetic Energy Ch. 6 Sections 1-3
• Energy, Power,
  
• Gravitational Potential Energy Ch. 6, Sections 4-5;Ch. 7, Sections 1-2
• Conservation of Energy
• Elastic Potential Energy (springs) Ch. 7, Sections 3-4

Links:

1. Immediate Connections:
   • Page 114 Ex. 3 in Calculus (An Application to Physics)
   • Page 116 Ex. 4 in Calculus (Falling Body Problem, height of an object)
   • power - the derivative of work
   • collisions, velocity, rates of change
2. Long Range Connections:
   • Work as an integral
   • Gyroscope problem - Ch. 10, Section 7
   • gravitational potential energy for motion along a curved path - concavity