IV. Integral Calculus
Area Under the Curve and Riemann Sums: Definite Integrals
As we have seen before, the derivative of a function can be rewritten as the differential:
At a given point x=x0, this representation can be understood as the value of the fun
CHEM 45/5515 App Math fo P-Chem I, Spring 2016
HOMEWORK 1 (20 pts)
Due: Monday, Feb. 15, 10 am
Please show all work as neatly as possible to receive credit! Do NOT use a computer program
UNLESS instructed to do so! Do not return this paper with answers on
CHEM 45/5515 App Math fo P-Chem I, Spring 2016
HOMEWORK 4
Due: Monday, March 28, 10 am
Please show all work as neatly as possible to receive credit! Do NOT use a computer program
UNLESS instructed to do so! Do not return this paper with answers on it! Whe
CHEM 45/5515 App Math fo P-Chem I, Spring 2016
HOMEWORK 5
Due: Monday, April 10, 10 am
Please show all work as neatly as possible to receive credit! Do NOT use a computer program
UNLESS instructed to do so! Do not return this paper with answers on it! Whe
When using the while-type do-loop, there is no way to break out of the loop without
stopping the program if the size of the matrix is exceeded.
In the following programs, assume the raw data is given as a row matrix Y consisting
of numbers that can range
CHEM 45/5515 App Math fo P-
Chem I, Spring 2014
HOMEWORK 2
1. (6 pts)
Answer Key
Show that:
d
1
log a ( x ) =
dx
x ln a
a.
using relationships between logarithms with different base
b.
using the rule for differentiation of inverse fun
CHEM 45/5515 App Math fo P-
Chem I, Spring 2014
HOMEWORK 1
ANSWER KEY
1. (5 pt)
Reduce the following rational function to a form
P( x)
f ( x) = R( x) +
Q( x)
where degP(x) < degQ(x):
x6 + 2x4 4x2 + 2
x 2 3x + 4
x 4 + 3x 3 + 7 x 2 + 9
I. Basic algebra, numbers, units.
1. Physical quantities
In physical chemistry (and all chemistry) we deal with quantities, which describe physical properties.
Physical quantity = numerical value + unit
E=
13.6
eV
(energy)
(number) (unit: electronvolts)
II. Functions
Basic Definition and Properties
Function is a rule (prescription, recipe) which assigns to each number x another number y:
y = f (x)
In other words for a number (x) you get another number (y). This may sound stupid, but is
actually important
III. Differential Calculus
Derivative
The derivative of a function, F(x), is the instantaneous change of the function with respect to the
instantaneous change in the variable(s). Another way of saying this is that the derivative is the
slope of a tangent
V. Complex numbers
Imaginary numbers
Multiples of = i
Properties of i:
1.
2.
3.
ii = i2 = 1
i i = i/i = +1
Complex numbers
These are composed of a real number (R) and an imaginary number. For complex number, z, we
can write:
z = x + iy,
where x and y are
CHEM 45/5515 App Math fo P-Chem I, Spring 2016
HOMEWORK 7
Due: Friday, May 13, 11 am
Please show all work as neatly as possible to receive credit! Do NOT use a computer program
UNLESS instructed to do so! Do not return this paper with answers on it! When