Dierential Calculus
Integral Calculus
Day 3
Review of Basic Calculus
Sivaram
sivaambi@stanford.edu
Institute of Computational and Mathematical Engineering
Stanford University
September 21, 2011
Multi-Variable Calculus
Dierential Calculus
Integral Calculus
Probability and Statistics
Part 1. Probability Concepts and Limit Theorems
Chang-han Rhee
Stanford University
Sep 19, 2011 / CME001
1
Outline
Probability Concepts
Probability Space
Random Variables
Expectation
Conditional Probability and Expectation
Limit
Motivation
Introduction
Second Order ODEs
Ordinary Dierential Equations
Milinda Lakkam
Institute for Computational and Mathematical Engineering
Stanford University
September 21, 2011
Miscellaneous
Motivation
Introduction
Second Order ODEs
What is an ODE?
ICME Refresher Course
Lecture #1
Milinda Lakkam
Institute for Computational and Mathematical Engineering
September 19, 2011
Milinda Lakkam
ICME Refresher Course
1 / 20
Scalars, and Vectors, and Matrices.
scalar: single quantity or measurement. (Greek) ,
Review Problems 4
iCME and MS&E Refresher Course
Thursday, 16 September, 2010
The problems in this problem set concern a mouse randomly walking around a maze with n rooms. At
every room in the maze, the mouse chooses one of the doors in the room uniformly
Review Problems 3
iCME and MS&E Refresher Course
Wednesday, 15 September, 2010
1. Markov Matrices: Suppose that each year 10% of the people outside
California move in and 20% of the people inside California move out. We
start with y0 people outside and z0
Review Problems 2
ICME and MS&E Refresher Course
September 20, 2011
Linear Algebra
1. Let S = cfw_(4, 18, 6)T , (8, 0, 12)T , (22, 9, 2)T , (4, 9, 6)T . Show that the vectors in S are linearly dependent.
Solution: Observe that there are four vectors in R3
Review Problems 1
ICME and MS&E Refresher Course
September 19, 2011
Warm-up problems
1. For the following matrices
1
A=
2
1
2
1
2
1
2
B=
1
0
0 1
2
1
2
1
2
1
2
1
C = AB =
nd all powers A2 , A3 ,(which is A2 times A),. . . and B 2 , B 3 , . . . and C 2 , C
Probability and Statistics
Part 2. More Probability, Statistics and their Application
Chang-han Rhee
Stanford University
Sep 20, 2011 / CME001
1
Outline
Statistics
Estimation Concepts
Estimation Strategies
More Probability
Expectation and Conditional Expe