Mathematics for Economists
Ken Danger
Problem Set 1
1)
Use the definition of the derivative to determine the derivatives of the following
functions.
a)
b)
Mathematics for Economists
Ken Danger
Problem Set 2
1)
Use calculus techniques to establish the first and second derivatives of the following
functions and to graph the functions below by indicating 1
Mathematics for Economists
Ken Danger
Problem Set 8
1.
Partially differentiate the following equations with respect to x1 and x2. Note the
superscript stand for a power and the subscript stands for th
Mathematics for Economists
Ken Danger
Problem Set 9
1.
Partially differentiate the following with respect to x1 and x2:
2.
Find the total differential of the following functions:
3.
Find the total der
Mathematics for Economists
Ken Danger
Problem Set 6
1)
For the following system of equations,
a)
Find solutions to the values of x1, x2, and x3 using the matrix inversion technique.
b)
Find solutions
Mathematics for Economists
Ken Danger
Problem Set 3
1)
Solve the following equations for x:
2)
Solve the equation
3.
Differentiate the following functions:
hint: Factor out the term (x-1). Also, you
s
Basic Rules of Differentiation;
First and Second Order Conditions;
and Graphing
1
Derivative of a constant
(1a) f(x) k constant
(1b)
df(x)
0
dx
Example of a constant function
2
Power Rule
(2a)
(2b)
f(
Exponents and Logarithms
Review and Look Forward
So far we have studied polynomials such
as
y = x2 + 2x + 3
y = (x2+5)4
Many processes naturally have the
variable in the exponent such as
Y = 2x
2
Exam
Solving a System of Equations
through Matrix Inversion and
Cramers Rule
Solving a System Using Matrix
Inversion
1.
2.
3.
4.
5.
6.
Find the determinant
Find all minors and cofactors for the
coefficient
Solutions to Systems of Linear
Equations and
Matrix Algebra
System of Equations
A system of linear equations is given by
(1a)
(1b)
2x + 3y = 7
x
+y =1
A nonlinear system is given by
(2a)
x2 y = 0
(2b)
Integration
Review and Look Forward
Weve studied the derivatives of certain
types of functions
Integration (or anti derivatives) undo the
derivative to find the underlying function.
Power Rule
(1)
1
x
Single Variable Calculus:
Foundations
Any Two Points on a Straight Line
Gives You the Slope
For a degree one polynomial, any two points can be used to calculate
straight line.
(1)
y 2 - y1
m
x2 x1
Exa