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School: Duke
Final Exam - Math 139 Dec 16th Instructor Web page Mauro Maggioni www.math.duke.edu/ mauro/teaching.html You have 3 hours. You may not use books, internet, notes, calculators. The exam should be stapled, written legibly, with your name written at the top
School: Duke
Math 135, Fall 2011: HW 6 This homework is due at the beginning of class on Wednesday October 19th, 2011. You are free to talk with each other and get help. However, you should write up your own solutions and understand everything that you write. Problem
School: Duke
Math 135, Fall 2011: HW 2 This homework is due at the beginning of class on Wednesday September 7th, 2011. You are free to talk with each other and get help. However, you should write up your own solutions and understand everything that you write. Problem
School: Duke
Course: Ord & Prtl Diff Equations
1 Physics and Measurement CHAPTER OUTLINE 1.1 1.2 1.3 1.4 1.5 1.6 1.7 Standards of Length, Mass, and Time Matter and Model-Building Density and Atomic Mass Dimensional Analysis Conversion of Units Estimates and Order-ofMagnitude Calculations Significant F
School: Duke
6 A v 9P27P2j!u v X4qP2u5C Squ64d r v U 9Hdd7B5v$!#j9j 5$wgB14(!vAsqX954h6!mA1j Bq5 S5G! 3PH32U75qmqPjxP5#5FhCu2#CBPx95 UvC h pqs(G6e61 A6e6j15U(v(17& v X(Gs(G(a% o e '& ) ' % ) %
School: Duke
Course: Real Analysis
Lecture 8: Weak Law of Large Numbers 8-1 Lecture 8 : Weak Law of Large Numbers References: Durrett [Sections 1.4, 1.5] The Weak Law of Large Numbers is a statement about sums of independent random variables. Before we state the WLLN, it is necessary to de
School: Duke
Course: Real Analysis
Lecture 7 : Product Spaces 7.3 Product spaces and Fubinis Theorem i Denition 7.3.1 If (i , Fi ) are measurable spaces, i I (index set), form For simplicity, i = 1 . i i . i (write for this) is the space of all maps: I 1 . For i i , = (i : i I, i i ). is e
School: Duke
Course: Real Analysis
Lecture 6 : Distributions Theorem 6.0.1 (Hlders Inequality) If p, q [1, ] with 1/p + 1/q = 1 then o E(|XY |) |X |p |Y |q (6.1) Here |X |r = (E(|X |r )1/r for x [1, ); and |X | = inf cfw_M : P(|X | > M ) = 0. Proof: See the proof of (5.2) in the Appendix o
School: Duke
Course: Real Analysis
Lecture 5: Inequalities 5-1 Lecture 5 : Inequalities 5.7 Inequalities Let X, Y etc. be real r.v.s dened on (, F , P). Theorem 5.7.1 (Jensens Inequality) Let be convex, E(|X |) < , E(|(X )|) < . Then (E(X ) E(X ) (5.11) Proof Sketch: As is convex, is the s
School: Duke
Course: Real Analysis
Lecture 4: Expected Value 4-1 Lecture 4 : Expected Value References: Durrett [Section 1.3] 4.5 Expected Value Denote by (, F , P) a probability space. Denition 4.5.1 Let X : R be a F\B -measurable random variable. The expected value of X is dened by E(X )
School: Duke
Final Exam - Math 139 Dec 16th Instructor Web page Mauro Maggioni www.math.duke.edu/ mauro/teaching.html You have 3 hours. You may not use books, internet, notes, calculators. The exam should be stapled, written legibly, with your name written at the top
School: Duke
Math 135, Fall 2011: HW 6 This homework is due at the beginning of class on Wednesday October 19th, 2011. You are free to talk with each other and get help. However, you should write up your own solutions and understand everything that you write. Problem
School: Duke
Math 135, Fall 2011: HW 2 This homework is due at the beginning of class on Wednesday September 7th, 2011. You are free to talk with each other and get help. However, you should write up your own solutions and understand everything that you write. Problem
School: Duke
Course: Laboratory Calculus I
Tiffany Labon Michael Mclennon Osagie Obanor Bryce Pittard Varying Density Lab Report Part 1: 1. The mosquitoes in the park are most concentrated closest to the river and the least concentrated furthest from the river. This is clear from the function
School: Duke
Math 32L Professor Bookman Will Park Jeff Chen Ralph Nathan Air Pollution: Particulate Matter Lab Report Part 4 1.) M Volume Density 4 p g M 1012 cm3 1.5 3 3 2 cm M 2.5( ) p 3 1013 g 3 2.) Total Mass = Mass of particle * number of particles
School: Duke
Course: Single Variable Calculus
Fall 2013 Math 122L Syllabus (Friday Lab) Textbook: Calculus: Concepts & Contexts (4th ed), by James Stewart Day 1-1 Date 27-Aug Topic Review of AP AB Differentiation topics Lab: L'Hopital's Rule and Relative Rates of Growth Riemann Sums Lab: Riemann Sums
School: Duke
Course: Single Variable Calculus
Fall 2013 Math 122L Syllabus (Thursday Lab) Textbook: Calculus: Concepts & Contexts (4th ed), by James Stewart Day 1-1 Date 26-Aug Topic Review of AP AB Differentiation topics Lab: L'Hopital's Rule and Relative Rates of Growth Riemann Sums Lab: Riemann Su
School: Duke
Course: Calculus
Math 32 Section 6 Fall 2008 Instructor: Tim Stallmann Oce: 037 Physics, West Campus email: tmstallm@math.duke.edu Oce Hours: by appointment About this Course Math 32 is a second-semester calculus course which covers with rigor Riemann sums and the denitio
School: Duke
Course: Multivariable Calculus
Homework Homework problems are assigned for every lecture, and students should ideally complete each assignment on the day of the lecture. The assigned problems for each lesson will be listed on the syllabus. (Note, we might find ourselves behind or ahead
School: Duke
Course: Multivariable Calculus
Syllabus for Math 102, Spring 08-09, Clark Bray Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (Note: New homework problems will be added throughout semester; be sure you are looking at a current version!) Linear Algebr