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Lecture1-MathRev4ps

Lecture1-MathRev4ps - Lecture 1 Math Review Lecture 1 Math...

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Lecture 1 - Math Review. Topics from Calculus you should know: How to define a derivative How to interpret f 0 ( x ) = 2. What does that mean? How to calculate the derivative of: 1 polynomials, ex.: u ( x ) = 3 x 4 - 5 x 2 + 6 2 exponential functions, ex.: u ( x ) = e x 2 + 2 3 logrithmic functions, ex.: u ( x ) = x ln ( 3 x + 6 ) Know the product rule, quotient rule, and chain rule Implicit differentiation ECG 700 Lecture 1 - Math Review 1/ 18 Lecture 1 - Math Review. Topics from Calculus you should know (cont.): The first derivative test. The second derivative test. Partial derivatives Total differentiation Topics you probably don’t know but will learn: Legrange multipliers Envelope Theorem ECG 700 Lecture 1 - Math Review 2/ 18 Differentiation - a quick review Definition The derivative of a function at a: d dx f ( a ) = f 0 ( a ) = lim x a f ( x ) - f ( a ) x - a or equivalently: f 0 ( a ) = lim h 0 f ( a + h ) - f ( a ) h ECG 700 Lecture 1 - Math Review 3/ 18 Differentiation - a quick review What does the derivative represent? The slope of the tangent line at point a. The “instantaneous” rate of change For our purposes, marginal = derivative . The marginal utility of good x is the change in utility resulting from a change to the quantity of good x .

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