Week 3

In Calculus II, the students do the following:

• Area Between Curves (pg. 311) (area by vertical strips and horizontal strips) Section 4.7
• Exponential Functions (bracketing theorem for exponents, graph of an exponential function, properties of exponential functions, natural exponential base (e), exp notation) Section 5.1
• Inverse Functions (pg. 334) (criteria for the existence of an inverse function, graph of an inverse function, derivative of an inverse function) Section 5.2
• Logarithmic Function (pg. 338) (basic properties of logarithmic functions, limits, natural logarithm, change-of -base theorem, properties of natural logarithm) Section 5.2
• Derivatives involving e^x and ln x (derivative of natural log arithmic function and exponential function, logarithmic differentiation) Section 5.3
• Applications involving derivatives of e^x and ln x (evaluating limits using logarithms and L'Hopital's Rule) Section 5.4
• Integrals involving e^x and ln x (power rule - pg. 359, integration of tan x and cot x) Section 5.5

In Physics II, the students do the following:

• Capacitors amd Calculating Capacitance Ch. 25, Sections 1-2
• Capacitors in series and in parallel (equivalent capacitance) Ch. 25, Section 3
• Electric-Field Energy (energy density, potential energy of a charged capacitor)
• Current (current density, drift velocity) Ch. 26, Section 1
• Resistivity and Resistance (Ohm's Law) Ch. 26, Section 3
• Electromotive Force and Circuits (internal resistance, terminal voltage) Ch. 26, Section 4
• Energy and Power in Electric Circuits (pure resistance, power output and input of a source) Ch. 25, Section 5
• Theory of Metallic Conduction (microscopic mechanisms of conductivity) Ch. 26, Section 6

Links:

1. Immediate Connections:
   • an integral involving ln(x) (pg. 721 - University Physics
2. Long Range Connections:
   • Work as an integral (pg. 695 - University Physics)
   • Current as a derivative (pg. 715 - University Physics)
   • Power as the derivative of work (pg. 727 - University Physics)