MATHEMATICS & STATISTICS FOR FINANCIAL
ENGINEERING
LECTURE #2
CALCULUS: PART I
Logs and e
The basics: very quick review
Multivariable calculus
Partial derivatives
Gradients
Hessians
Taylor's theorem
Leibnitz rule for differentiating integrals
LOGS &
Mini-Quizzes
Lecture #3
Do Not Open!
(dont worry, this will not be graded)
Mathematics & Statistics for Financial Engineering
Mini-Quiz #1
1) Find the solution to the following differential equation.
1
= and (0) =
2
1
=
1
=
1
ln() + 1 = 2 + 2
2
1 2
ln(
Solving a partial differential equation using
separation of variables
Problem
Given a function of two variables, f(x, t) where
=
Equation 1
and x and t are independent variables (x is not a function of t, and t is not a function of x). Find the genera
MATHEMATICS & STATISTICS FOR FINANCIAL
ENGINEERING
LECTURE #4
STATISTICS
Random variables
Expectations
Standard deviation and variance
Parametric distributions
Linear regressions, hypothesis testing
RANDOM VARIABLES
Random variable
More than one pos
MATHEMATICS & STATISTICS FOR FINANCIAL
ENGINEERING
LECTURE #1
OUTLINE
Class #1: Linear algebra
Class #2: Calculus
Class #3: Calculus
Class #4: Statistics
OVERVIEW
Purpose of this lecture series
Additional resources
Online: www.sosmath.com
Mathematic
Mini-Quizzes
Lecture #4
Do Not Open!
(dont worry, this will not be graded)
Mathematics & Statistics for Financial Engineering
Mini-Quiz #1
1) Assume the weather and change in the S&P 500 are independent random variables. The probability of
rain tomorrow i
Mini-Quizzes
Lecture #2
Do Not Open!
(dont worry, this will not be graded)
Mathematics & Statistics for Financial Engineering
Mini-Quiz #1
1) Express z as a linear combination of ln(x) and ln(y).
= ln ( 5 )
= ln() ln( 5 ) = ln() 5ln()
2) Find the extrem