Complex Residues. Let P(s)/Q(s) be a rational function with deg P < deg Q and suppose (s-?)2 + ?2 is a nonrepeated quadratic factor of Q. (That is, are complex conjugate zeros of Q.) Prove that the portion of the partial fraction expansion of P(s)/Q(s) corresponding to (s-?)2+?2 is where the complex residue ?B+i?A is given by the formula (Thus we can determine B and A by taking the real and imaginary parts of the limit and dividing them by ?.)

Carbohydrates: Monday, September 18, 2017 2:34 PM What are carbohydrates • Essential vs. Non-essential- they're not essential • Organic vs. Non-organic- It is organic nutrient because it contains carbon. • Still necessary for optimal health • Composed of C, H, and O. Ratio is same as water 2:1 • Glucose: C6H12O6 "hexose sugar" • Glucose comes from photosynthesis (plants store in starch: long linked glucose) Monosaccharides: • Glucose is an example • Mono- one • Saccharide- sugar • Fructose, Galactose, Glucose • Glucose: blood sugar -significant to nutrition -in fruits and veggies • Fructose: -Fruit sugar, honey, soda, high-fructose corn syrup -sweeter than glucose -5-side