5
Mathematics of Finance
5.1
Simple and Compound Interest
Buying a car usually requires both some savings for a down
5.2
Future Value of an Annuity
payment and a loan for the balance. An exercise in Section 2
5.3
Present Value of an Annuity;Amortization
C
Lecture 10: Applications of
Differential Equations
By
Assoc.Prof. Mai Duc
Thanh
A Predator-Prey Model
by Lotka-Volterra
Let x=f(t) denote the population of the
predator, and y=g(t) denote the population
of the prey at time t
Assume that if there were no p
Determinants
Lecture 2
3. Properties of Determinants
4. Cramers Rule
By
Dr. Mai Duc Thanh
3. Properties of Determinants
n
Thm: (Determinant of a matrix product)
det (AB) = det (A) det (B)
Notes:
(1)
(2)
det( A B ) det( A) det( B )
a11
a22 b22
a31
a12
a22
Chapter 4: Linear Systems of Equati
ons
Lecture: Matrices in Echelon Form
By
and Gauss Elimination method
Assoc.Prof. Mai Duc Thanh
Ho Chi Minh City
International University
Example: An animal breeder bu
ying three types of food for pigs
Each case of Bran
Lecture: Matrix Operations
By
Assoc.Prof. Mai Duc Thanh
Ho Chi Minh City
International University
The Algebra of Matrices; Four Descriptio
ns of the Products
A matrix is a rectangular array of numbers
Column
a
11 a12
a
21 a22
A=
M
M
a
m1 am 2
L a1n
L a2
Eigenvalues and Eigenvect
ors
By
Dr. Mai Duc Thanh
EigenvaluesandEigenvectors
LetA bean n n matrix.Supposethatxisanonzero
vectorand is a number suchthat
Ax = x
(1)
ThenxiscalledaneigenvectorofA,and iscalledan
eigenvalueofA.
Wesaythat is the eigenvalue ass
Determinants
Lecture:
1 The Determinant of a Matrix
2 Evaluation of a Determinant using Elementary
Operations
By
Dr. Mai Duc Thanh
1. The Determinant of a Matrix
The determinant of a 2 2 matrix:
a11 a12
A
a21 a22
det( A) | A | a11a22
n
Note:
a11 a12
CopperChemistry
h i
Cu:1s
Cu : 1s22s22p63s23p63d104s1
F.A.Cotton,G.Wilkinson,C.A.Murillo,M.Bochman,AdvancedInorganicChemistry,6th ed.,JohnWiley,NewYork,pp.855864.
Cu has a single s electron in its fourth shell. One may be inclined to think, based
on its e
CALCULUS II (BA)
ASSIGNMENT 2
Assoc. Prof. DrSc. Nguyen Dinh
Department of mathematics
INTERNATIONAL UNIVERSITY, VNU-HCM
December 30, 2014
Assoc. Prof. DrSc. Nguyen Dinh
CALCULUS II (BA) ASSIGNMENT 2
Asignment 2 - Chapters 4 & 5
Instruction
1. Marks: Mark
CALCULUS 2 FOR BA
Assoc. Prof. Nguyen Dinh
International University
Ngy 25 thng 12 nm 2013
Assoc. Prof. Nguyen Dinh
CALCULUS 2 FOR BA
Chapter 5. EIGENVECTORS AND EIGENVALUES
Contents
1. Determinants of square matrices
2. Cramers rule
3. Matrix inverses
4.
Chapter1:MathematicsofFinance
Lecture 6: Double Integrals
by
Assoc.Prof. Mai Duc
Thanh
Motivations
How can we find the volume of a bottle
with curved sides?
Given a function f(x,y) we can take integral
with respect to x and y separately:
b
d
a
c
f
f
( x,
Calculus 2-BA
By: Assoc.Prof. Mai Duc
Thanh
Lecture 8: Linear firstorder differential
equations
Basic Concepts
A differential equation may involve derivatives of
higher-order, such as f, f, f, etc
The order of a differential equation is that of
the highes
Chapter1:MathematicsofFinance
Lecture 3: Annuities
By
Assoc.Prof. Mai Duc
Thanh
Agenda
Compound Interest
Compound interest and compound amount (p.
93-96)
Effective Rate and Present Value (p. 121-123)
Continuous Money Flow (sec. 8.3, page
476-484)
Total Mo
Chapter 2: Multivariable
Calculus
Lecture 2: Partial Derivatives
by
Assoc.Prof. Mai Duc
Thanh
Partial Derivatives
Rate of change of a function f(x,y)
depends on the direction
Begin by measuring the rate of change if
we move parallel to the x or y axes
The
Chapter 2: Multivariable
Calculus
Lecture 3: Maxima and Minima
by
Assoc.Prof. Mai Duc
Thanh
Relative Maxima and Minima
Let (a,b) be the center of a circular region G
contained in the xy-plane. Then, for a function
z=f(x,y) defined on G:
f(a,b) is a relati
Chapter 2: Multivariable
Calculus
Lecture 4: Lagrange Multipliers
by
Assoc.Prof. Mai Duc
Thanh
Example
The profit from the sale of x units of
radiators for automobiles and y units of
radiators for generators is given by
P(x,y)= -x2 y2 + 4x + 8y
Find value
Chapter 2: Multivariable
Calculus
Lecture 1: Functions of Several Variables
By
Assoc.Prof.MaiDuc
Thanh
Motivations: Functions of Two
Variables
1.
How are the amounts of labor and capital
needed to produce a certain number of
items related?
2.
The volume V
Chapter 2: Multivariable
Calculus
Lecture 5: Total Differentials
andby
Approximations
Assoc.Prof. Mai Duc
Thanh
Motivation
How do errors in measuring the length and
radius of a blood vessel affect the
calculation of its volume?
Total Differential for two
Lecture 9: Eulers method
By
Assoc.Prof. Mai Duc
Thanh
Motivations
Many differential equations cannot be solved by
analytic methods: Exact solutions cannot be
found explicitly
Eulers method gives approximate solutions to
initial value problem for different
Lecture 7: Solutions of
elementary and separable
differential equations
By
Assoc.Prof. Mai Duc Thanh
Differential Equations: Example
Sales (in thousands) of a certain product
are increasing at a rate proportional to the
amount of sales, with a growth cons
Chapter1:MathematicsofFinance
Lecture 1: Compound Interests
By
Assoc.Prof. Mai Duc
Thanh
Course Information
Lecturer: Associate Professor Mai Duc
Thanh
E-mail: mdthanh@hcmiu.edu.vn
Mobile phone: 090 888 1652
Textbooks:
1.
2.
Calculus with Applications, Li