\chapter*{Preface}


\section*{Introduction to the Kentucky Text:}
This text is a minor adaptation of Professor Neal Koblitz's notes from his
University of Washington Math 125 course and material from two chapters of
 a book by
Professor J. H. Wells.  Professors \index{Koblitz} Koblitz and Wells 
have generously permitted their use in this extension to Kentucky of 
Koblitz's idea of a complete
calculus text for which students pay only the reproduction costs. 

Errors which have been introduced into the text during the adaptation process
are the responsibility of the Affordable Text Project of the University of
Kentucky.  


This project has been supported by the National Science Foundation
(\index{NSF} NSF) {\bf Calculus} and {\bf Advanced Technical Education}
(\index{ATE} ATE) programs. 



\section*{Advice for Students}

 
The overwhelming emphasis in this course is on applications --- story
problems.  To master story problems one needs a tremendous amount of
practice --- doing homework, worksheet, and practice exam problems.
For this reason, this course will require much more of your time than
would a high school or community college calculus course that does not have
such a focus on word problems.

Here are some pointers for doing story problems:

\begin{enumerate}

\item%(1) 
Carefully read each problem twice before writing anything.

\item%(2) 
Assign letters to quantities that are described only in words;
draw a diagram if appropriate.

\item%(3) 
Decide which letters are constants and which are variables.  A letter
stands for a constant if its value remains the same throughout the problem.

\item%(4) 
Using math notation, write down what you know and then write down
what you want to find.

\item%(5) 
Decide what category of problem it is (this might be obvious if the
problem comes at the end of a particular chapter, but will not necessarily
be so obvious if it comes on an exam covering several chapters).

\item%(6) 
Double check each step as you go along; don't wait until the end to
check your work.

\item%(7) 
Use common sense; if an answer is out of the range of practical
possibilities, then check your work to see where you went wrong.

\end{enumerate}

\bigskip
\centerline{\bf Suggestions for Using These Notes}
%\subsection{\bf Suggestions for Using These Notes}

\medskip

\begin{enumerate}
\item%(1) 
Read the example problems carefully, filling in any steps that are
left out (ask someone if you can't follow the solution to a worked
example).

\item%(2) 
Later use the worked examples to study by covering the solutions,
and seeing if you can solve the problems on your own.

\item%(3) 
Give yourself the practice midterms and finals in an exam situation
(without access to material other than a single sheet of notes, and with
the same time limit as on the exam).

\item%(4) 
The answers to homework and practice exam problems that are in the back
of the notes should be used only as a final
check on your work, not as a crutch.  Keep in mind that sometimes an
answer could be expressed in various ways that are algebraically
equivalent, so don't assume that your answer is wrong just because it
doesn't have exactly the same form as the answer in the back.
\end{enumerate}
 
\newpage

\thispagestyle{empty}

\centerline{\bf \index{Formulas} Formulas Used in This Course }


\begin{align*}
\intertext{\bf Algebra}
&\text{Completing the square: }
    X^2+bX+c=(X+\frac{b}{ 2})^2~-\frac{b^2}{ 4}+c\,. \\
&\text{Quadratic formula: roots of $aX^2+bX+c$ are } 
      \frac{-b\pm\sqrt{b^2-4ac}}{ 2a}\,. \\
&\text{Exponents: } 
a^b\cdot a^c=a^{b+c}; \quad
\frac{a^b}{a^c}=a^{b-c}; \quad
(a^b)^c=a^{bc}; \quad
a^{1/b}={\root b \of a}\,.
\\
%
&\\
\intertext{\bf Geometry}
&\text{Circle: } 
   \text{circumference}=2\pi r;   \;
   \text{area}=\pi r^2\,. 
 \\
&\text{Sphere: }
 \text{vol}=\frac{4}{ 3}\pi r^3;  \; 
 \text{surface area}=4\pi r^2\,. 
 \\
&\text{Cylinder: } 
 \text{vol} =\pi r^2h;   \;
 \text{lateral area}= 2\pi rh;   \;
 \text{total surface area} =2\pi rh+2\pi r^2. 
 \\
&\text{Cone: }
 \text{vol}=\frac{1}{ 3}\pi r^2h;  \;
 \text{lateral area}=\pi r\sqrt{r^2+h^2};  \; 
 \text{total surface area}= \pi r\sqrt{r^2+h^2}+\pi r^2.
\\
%
&\\
\intertext{\bf Analytic geometry}
&\text{Point-slope formula for straight line: } y=y_0+m(x-x_0). \\
&\text{Circle centered at $(h,k)$: }    (x-h)^2+(y-k)^2=r^2. \\
&\text{Ellipse with semimajor axis along $x$-axis and semiminor axis
along $y$-axis: } 
    \frac{x^2}{ a^2}+\frac{y^2}{ b^2}=1.
\\
%
&\\
\intertext{\bf Trigonometry}
&\sin= \frac{\text{opposite}}{\text{hypotenuse}}; \;
\cos= \frac{\text{adjacent}}{\text{hypotenuse}};  \;
\tan= \frac{\text{opposite}}{\text{adjacent}};  
\\
%
&\sec= \frac{1}{\cos};  \;
\csc= \frac{1}{\sin};  \;
\cot= \frac{1}{\tan};  \;
\tan= \frac{\sin}{\cos};  \;  
\cot= \frac{\cos}{\sin};  
\\
&
\sin x=\cos\left(\frac{\pi}{2}-x\right) ;    \;
\cos x=\sin\left(\frac{\pi}{2}-x\right) ;  \; 
\\
%                        
&
\sin(x+\pi)=-\sin x;  \;
\cos (x+\pi)=-\cos x.
\\ 
&\text{Law of cosines: }
a^2=b^2+c^2-2bc\cos A.
\\
&\text{Law of sines: }
    \frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}.
\\
&\text{Sine of sum of angles: }
\sin(x+y)=\sin x\cos y+\cos x\sin y.
\\
&\text{$\sin^2$ and $\cos^2$ formulas: }
 \sin^2+ \cos^2=1; \;     
 \sin^2x=\frac{1-\cos(2x)}{ 2}; \;
 \cos^2x=\frac{1+\cos(2x)}{ 2}.
\end{align*}






