\( \newcommand{\abs}[1]{\left| \, {#1} \, \right| } \) \( \newcommand{\cm}{\mathrm{cm} } \) \( \newcommand{\sec}{ \, \mathrm{sec} \, } \) \( \newcommand{\vhat}[1]{\,\hat{#1}} \) \( \newcommand{\vhati}{\,\hat{i}} \) \( \newcommand{\vhatj}{\,\hat{j}} \) \( \newcommand{\vhatk}{\,\hat{k}} \) \( \newcommand{\vect}[1]{\boldsymbol{\vec{#1}}} \) \( \newcommand{\norm}[1]{\|{#1}\|} \) \( \newcommand{\arccot}{ \, \mathrm{arccot} \, } \) \( \newcommand{\arcsec}{ \, \mathrm{arcsec} \, } \) \( \newcommand{\arccsc}{ \, \mathrm{arccsc} \, } \) \( \newcommand{\sech}{ \, \mathrm{sech} \, } \) \( \newcommand{\csch}{ \, \mathrm{csch} \, } \) \( \newcommand{\arcsinh}{ \, \mathrm{arcsinh} \, } \) \( \newcommand{\arccosh}{ \, \mathrm{arccosh} \, } \) \( \newcommand{\arctanh}{ \, \mathrm{arctanh} \, } \) \( \newcommand{\arccoth}{ \, \mathrm{arccoth} \, } \) \( \newcommand{\arcsech}{ \, \mathrm{arcsech} \, } \) \( \newcommand{\arccsch}{ \, \mathrm{arccsch} \, } \)

17Calculus - How To Save on Bags and Supplies Including Calculators

SV Calculus

MV Calculus

Differential Equations

Precalculus

Practice

Calculus 1 Practice

Calculus 2 Practice

Practice Exams

Tools

Calculus Tools

Additional Tools

Articles

SV Calculus

MV Calculus

Practice

Calculus 1 Practice

Calculus 2 Practice

Practice Exams

Tools

Calculus Tools

Additional Tools

Articles

On this page, we will give you suggestions and links on how to find and choose the best bags, calculators and supplies that will save you money.

backpack

 

messenger bag

 

calculators

Backpack

For most people, a backpack is the best way to regularly carry your supplies with you. This is particularly true if you leave your dorm or apartment for the entire day and you need to carry everything with you. Here are some suggestions on how to get the right backpack for you.
1. Padding - - Get one with padded straps and a padded back (the part that sits against your back). If you opt for a large one, it will help to have the part that sits on your hips to also be padded. For larger backpacks especially, find one that has straps that come around your chest and stomach for extra support.
2. Material - - Get a backpack made of a tough fabric used for hiking. Your books are heavy and can easily tear a cheaper bag.
3. Pockets - - Get a backpack with plenty of pockets, both internal and external. You will need to carry money and id inside the bag and a bottle of water in an outside pocket. Think carefully about everything you need to carry including makeup, wallet or billfold, facial tissues, lip gloss and any medications.
4. Wearing - - Always wear your backpack on both shoulders. This will prevent back, shoulder and neck problems.
5. Buying - - Investing in a good bag is important but does not need to be expensive. My personal favorite place to buy bags of any kind is eBags.com. They allow returns and the prices have always been very good. I have purchased maybe 10 bags from them and returned a couple more. The descriptions and pictures are very accurate, so read them carefully and ask questions before buying. I have also purchased from Amazon and have liked what I got. Here are some links to get you started.

Messenger Bag

In addition to a good backpack, we suggest a messenger bag just big enough for a notebook or two, some writing utensils and a small book. This type of bag is good for days when you just have one or two classes and you won't be gone long from home. Do not carry a lot of heavy books in this type of bag, since carrying heavy loads across your body can cause back, shoulder and neck problems.
To make the transition between backpack and messenger bag easy, it would be good to invest in a small pencil box or small bag that holds your notetaking supplies. This bag can be easily thrown from one to the other bag quickly before you head off to class.
Both eBags and Amazon have good selections of messenger bags.

Calculators

Using a calculator while learning math is a double-edged sword. Most math teachers require a calculator, but watch out for teachers who rely too heavily on the calculator, not allowing you to learn math. For advanced math, like calculus, we recommend using the calculator only for graphing. An HP is best for engineers, while a TI-89 will work for most everyone else.
For algebra, a TI-84 will work. Here are some links to get you started.
Note - - Although you might be tempted to save a few bucks and buy a used calculator, that is not a good idea. You don't know if it has been dropped and calculators can be easily damaged. Spend a few bucks more and get a new one. It will be worth it.

You CAN Ace Calculus

Trig Formulas

The Unit Circle

The Unit Circle [wikipedia]

Basic Trig Identities

Set 1 - basic identities

\(\displaystyle{ \tan(t) = \frac{\sin(t)}{\cos(t)} }\)

\(\displaystyle{ \cot(t) = \frac{\cos(t)}{\sin(t)} }\)

\(\displaystyle{ \sec(t) = \frac{1}{\cos(t)} }\)

\(\displaystyle{ \csc(t) = \frac{1}{\sin(t)} }\)

Set 2 - squared identities

\( \sin^2t + \cos^2t = 1\)

\( 1 + \tan^2t = \sec^2t\)

\( 1 + \cot^2t = \csc^2t\)

Set 3 - double-angle formulas

\( \sin(2t) = 2\sin(t)\cos(t)\)

\(\displaystyle{ \cos(2t) = \cos^2(t) - \sin^2(t) }\)

Set 4 - half-angle formulas

\(\displaystyle{ \sin^2(t) = \frac{1-\cos(2t)}{2} }\)

\(\displaystyle{ \cos^2(t) = \frac{1+\cos(2t)}{2} }\)

Trig Derivatives

\(\displaystyle{ \frac{d[\sin(t)]}{dt} = \cos(t) }\)

 

\(\displaystyle{ \frac{d[\cos(t)]}{dt} = -\sin(t) }\)

\(\displaystyle{ \frac{d[\tan(t)]}{dt} = \sec^2(t) }\)

 

\(\displaystyle{ \frac{d[\cot(t)]}{dt} = -\csc^2(t) }\)

\(\displaystyle{ \frac{d[\sec(t)]}{dt} = \sec(t)\tan(t) }\)

 

\(\displaystyle{ \frac{d[\csc(t)]}{dt} = -\csc(t)\cot(t) }\)

Inverse Trig Derivatives

\(\displaystyle{ \frac{d[\arcsin(t)]}{dt} = \frac{1}{\sqrt{1-t^2}} }\)

 

\(\displaystyle{ \frac{d[\arccos(t)]}{dt} = -\frac{1}{\sqrt{1-t^2}} }\)

\(\displaystyle{ \frac{d[\arctan(t)]}{dt} = \frac{1}{1+t^2} }\)

 

\(\displaystyle{ \frac{d[\arccot(t)]}{dt} = -\frac{1}{1+t^2} }\)

\(\displaystyle{ \frac{d[\arcsec(t)]}{dt} = \frac{1}{\abs{t}\sqrt{t^2 -1}} }\)

 

\(\displaystyle{ \frac{d[\arccsc(t)]}{dt} = -\frac{1}{\abs{t}\sqrt{t^2 -1}} }\)

Trig Integrals

\(\int{\sin(x)~dx} = -\cos(x)+C\)

 

\(\int{\cos(x)~dx} = \sin(x)+C\)

\(\int{\tan(x)~dx} = -\ln\abs{\cos(x)}+C\)

 

\(\int{\cot(x)~dx} = \ln\abs{\sin(x)}+C\)

\(\int{\sec(x)~dx} = \) \( \ln\abs{\sec(x)+\tan(x)}+C\)

 

\(\int{\csc(x)~dx} = \) \( -\ln\abs{\csc(x)+\cot(x)}+C\)

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