Lecture 1 - Lecture 1 Math Review & Special Topics The...

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Dr. Steven Waters Econ 380 Page 1 of 10 Lecture 1 Math Review & Special Topics The hardest arithmetic to master is that which enables us to count our blessings. Eric Hoffer, Reflections On The Human Condition This is both a math review and a set of math topics that we will be covering over the course of the semester. The review is found on pp. 1-4 of this lecture and covers the basics of logs, exponents, derivatives, and optimization. We will be using these concepts early and often in the class. The topics on pp. 5-10 of this lecture will be introduced throughout the semester – refer back to this lecture as necessary. The Economics Outline 1. Review Syllabus The Mathematics Outline 1. Calculus / Math Review 1.1. Logs & Exponents 1.2. Derivatives 1.3. Partial Derivatives 2. Univariate Optimization Rules 3. Multivariate Optimization 4. New Concepts using Existing Skills 4.1. Young’s Theorem 4.2. Total Differentials 4.3. Implicit Functions 4.4. The Envelope Theorem Log Rules Rule Example 1) ) ln( ) ln( ) ln( y x xy + = ) 3 ln( ) 5 ln( ) 3 5 ln( + = 2) ) ln( ) ln( ) ln( y x y x = ) 3 ln( ) 5 ln( ) 3 5 ln( = 3) ) ln( ) ln( x A x A = ) 3 ln( 5 ) 3 ln( 5 =
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L1: Math Review & Special Topics Dr. Steven Waters Econ 380 Page 2 of 10 Exponent Rules Rule Example 1) b a b a x x x + = 8 3 5 x x x = 2) ab b a x x = ) ( 15 3 5 ) ( x x = 3) b a b a x x x = 2 3 5 x x x = Derivative Rules Type Function Derivative Power Function n Ax y = 1 = n nAx dx dy Example 3 5 x y = 2 15 x dx dy = Log Function ) ln( x A y = x A dx dy = Example ) ln( 7 x y = x dx dy 7 = Product Rule ) ( ) ( x g x f y = ) ( ' ) ( ) ( ' ) ( x f x g x g x f dx dy + = Example ) 4 ( 3 + = x x y 2 / 1 3 2 2 1 ) 4 ( ) 3 ( + + = x x x x dx dy Note: ) 4 ( ) ( , ) ( 3 + = = x x g x x f
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L1: Math Review & Special Topics Dr. Steven Waters Econ 380 Page 3 of 10 Quotient Rule ) ( ) ( x g x f y = 2 ) ( ) ( ' ) ( ) ( ' ) ( x g x g x f x f x g dx dy = Example ) 4 ( 3 + = x x y 2 3 2 2 / 1 3 ) 4 ( ) 3 ( 2 1 ) 4 ( + + = x x x x x dx dy Chain Rule: ( ) ) ( x g f y = ) ( ' ) ( ' x g g f dx dg dg df dx dy = = Example ) 2 ln( 7 x y = x x x dx dy 7 14 2 1 6 7 = = Note: 7 2 ) ( , ) ln( ) ( x x g g g f = = Exponent Rule: x a y = a a dx dy x ln = ) ( x f a y = a x f a dx dy x f ln ) ( ' ) ( = Special Case ) ( x f e y = ) ( ' ln ) ( ' ) ( ) ( x f e e x f e dx dy x
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This note was uploaded on 11/30/2011 for the course STAT 380 taught by Professor Stevens during the Spring '11 term at Brigham Young University, Hawaii.

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Lecture 1 - Lecture 1 Math Review & Special Topics The...

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