Week 2

In Calculus II, the students do the following:

• The Fundamental Theorem of Calculus (pg. 277) (integration formulas - pg. 280) Section 4.3
• Integration by substitution (pg. 280) Section 4.3
• Substitution with the Definite Integral (pg. 295) Section 4.3
• Mean Value Theorem for Integrals (pg. 295) Section 4.5
• Average Value of a Function (pg. 297) Section 4.5
• Second Fundamental Theorem of Calculus (pg. 299) (Leibniz's Rule - pg. 300) Section 4.5
• Numerical Integration (approximation by rectangles, trapezoid rule (pg. 304), Simpson's Rule (pg. 305)) Section 4.6

In Physics II, the students do the following:

• Electric Dipoles (electric dipole moment) Ch. 22, Section 8
• Electric Flux (surface integral) Ch. 23, Section 1
• Gauss's Law Ch. 23, Section 2
• Applications of Gauss's Law Ch. 23, Section 3
• Charges on Conductors (Faraday's icepail experiment) Ch. 23, Sectioni 4
• Electric Potential Energy (total potential energy - pg. 661) Ch. 24, Section 1
• Potential (calculations) Ch. 24, Sections 2-3
• Equipotential Surfaces (conducting surface) Ch. 23, Section 4
• Potential Gradient

Links:

1. Immediate Connections:
   • The work done on a dipole can be expressed as an integral. (pg. 692 - University Physics)
   • the surface integral; Gauss's Law (pg. 709 - University Physics)
   • Potential can be expressed as an integral. (pg. 731 - University Physics)
   • integration by tables (pg. 746 - University Physics)
   • The components of an electric field are related to the corresponding derivatives of the potential differences.
   • Note: The integrals in the definitions in the Physics book are first simplified symbolically for the students