Welcome to AP Calculus BC with 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 BC with 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 BC with 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 Exams Some of your test problems throughout the year come from AP exams: Both multiple choice and free response. more...

The Exams These 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 BC with 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 BC with 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.’

Participation When 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, 7 th 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 M athematica ; 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 ! e x dx e  i =-1

Lab Rules You 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 Rules We are often listening to each other’s suggestions for solving problems. When you are listening, you aren’t talking, ing, 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 go Prime Time!

AP Calculus BC with Mathematica: Where you’ll learn a lot more than Math!