Welcome to AP Calculus BCwith Mathematica

You may be wondering:

• What will I learn?• How will I be graded?

• How much work will I have to do?

• What are the rules in here?

But let’s start with a question or two:

Do you:

• enjoy doing math?• realize that math can be

an experimental science?• enjoy figuring things out for yourself?

If you are intrigued by these questions,

then AP Calculus BC

with Mathematica

is just the place for you!

AP Calculus BCwith Mathematica:

What we learn• Calculus: “The algebra of

change.”

• Analysis: All about the right triangle; the trig functions and their inverses; complex numbers.

• Math you will use: vectors, power series and other fun stuff.

Calculus Topics• Limits• Derivatives: what they are,

how to find ‘em• Uses for derivatives:

so much more than mere slopes and tangents!

• Differential equations

More Calculus Topics

• The ntegral: more than just the area under a curve

• um integration techniques• Mean values • Areas and volumes• More differential equations• Power series

Analysis Topics• Vectors and vector operations• The Unit Circle and polar

coordinates• Properties of trig functions

and their inverses• Complex numbers

More Topics• Parametric equations• Arc length and area of polar and

parametric curves• Strange and interesting

behaviors of periodic functions

Physics Topics• Vector dot and

cross products• Particle motion• Use of parametric

equations• Work and

potential energy• Center of mass,

moment of inertia

Topics from other subjects

• Biology: population growth

• Chemistry: reaction rate, radioactive decay, thermodynamics

Topics from other subjects

• Business and economics

• Manufacturing• Modeling the real

world with differential equations

AP Calculus BCwith Mathematica: How much work?

• Labs: Primarily self-paced; designed to be done in class.

• Homework: Regular practice develops skills.

• Projects: Once you have met the expectations given, how far you go is up to you.

• Quizzes and tests: Be ready!

Grading

• Labs and homework problems (30%): you will turn something in at least once a week.

• Quizzes (20%): short, but frequent

• Tests (25%): two or three a quarter, but they may be double period

more...

Grading, cont’d

• Projects (15%): ‘open-ended investigations,’ more substantial than labs.

• Class Participation (10%): pay attention to due dates, do your work diligently, help others, do your Calculus work.

How much memorization?

Some things you will just have to know:• Values of trig functions around the unit

circle;• Domains and ranges

of their inverses;• Basic derivatives and integrals;• Certain power series expansions

and convergence tests.

Math 3: The ExamsSome of your test problems

throughout the year come from AP exams:

Both multiple choice and free response.

more...

The ExamsThese exams will give you lots of

practice for the Calc ‘BC’ AP exam you will take in May.

Note: We will not have a final exam; however there will be a substantial

final project due after the AP exam on Tuesday, May 3, 2005.

AP Calculus BCwith Mathematica: So much more than the AP

The level of work expected in this class is

far above that which gives you an opportunity

to earn a 4 or 5 on the AP exam.

AP Calculus BCwith Mathematica: So much more . . .

“The goal of the AP program is not just getting you college credit for a

course you take in high school.

The AP program is designed to equip you for success in the

courses you take in college.”

Do not be lulled into apathy by the mystique of the ‘AP curve.’

ParticipationWhen you finish your own work, see if you can help someone else: We learn from each other!

Ask lots of questions:but don’t be shocked when you have to go look for answers!

Textbook: a powerful reference

tool• Larson, Calculus, 7th edition • D&S AP Calculus BC Prep book• SAT 2 Prep book

Just what is Mathematica?

• A math programming language: if you can write it, you can evaluate it and better still, plot it.

• Don’t fight the syntax. Learn the language.

• Getting help starts by looking in the ‘Help Browser’.

Mathematica?

You will be required to learn some of the basics: plotting, evaluating, solving, etc.

What about a calculator?

• Some parts of the class will use Mathematica;

• Some will use your graphing calculator (TI-83 or 89).

• Some things you will do by hand.

Bring your calculator to class every day!

1/n

dy/dx

ex dx

e i=-1

Lab RulesYou will be informed each day if

you will spend the period working

on the computer, or if it’s time to

look at what’s on the board or

shown on the screen. more...

Lab RulesWe are often listening to each other’s suggestions for solving

problems.

When you are listening, you aren’t talking, emailing,

listening to music, browsing or typing:

That’s a big part of your participation grade!

Q140 is a classroom

If you find the computer lab too

much of a distraction, we can

help you find a math class better

suited to your learning style.

But we really want you to stick with

us:You might be surprised how far you’ll go in just one year!

So, get ready to goPrime Time!

AP Calculus BCwith Mathematica: Where you’ll learn

a lot more than Math!