Calculus III
Syllabus.
Solutions distributed in class.
The course so far
The Greek Alphabet.
Topics to review from Calc I and Calc II.
Dot products and angles.
Cauchy-Schwarz and Triangle Inequalities.
Determinants and the Laplace expansion.
The cross product.
Speed and arclength.
Curvature and acceleration.
Comparing Calc I and Calc III limit laws.
The derivative of a function of two variables.
The Chain Rule in higher dimensions.
Comparing Calc I and Calc III max/min rules.
Proof of Clairaut's Theorem.
The "chart method" for certain integrals.
The center of mass of a lamina.
The area of surface z=f(x,y).