Welcome to the MAST Basic Calculus Homepage. On this page you will find links to the lessons for this course, a listing of available papers submitted by students of this course, and a list of references that were useful in making this course.
Calculus is the mathematics that describes change. There are three parts of this story:
In this course we will cover all of these things.
I will assume that you have a knowledge of algebra, geometry, and trigonometry equivalent to the Precalculus Mathematics course offered by MAST. I will freely use examples and principles from this course with little or no explanation. I will also assume that you have become comfortable with the idea of proofs and logic, and so proving theorems and using logic to deduce formulas and principles will be a common theme.
Option 1: You are taking the course to learn the techniques of calculus to apply them in everyday scientific work. In this option you will be expected to perform all of the basic material, nothing else is required.
Option 2: You are planning on doing theoretical science work. It is vital that you understand the theoretical underpinnings of the subject and have a complete mastery of the techniques. You must do all basic material and all theory-track material.
Option 3: You are interested in pure mathematics. Here you will spend most of your time working out principles and proving theorems. You must do all basic material and all pure-track material.
In all options you must maintain a project notebook according to the standards found on the MAST Degrees Page. This will be worth 1 point by itself. You may choose more than one option if you wish.
Option 1: Develop the entire structure of each part of the course including stating all assumptions, axioms, definitions, conjectures, theorems, corollaries, and proofs. The goal is to develop the mathematical framework of calculus. This will be the equivalent of a narrow topical study. This will be worth 3 points per part.
Option 2: Develop each technique, step-by-step, of each part of calculus along with several examples of their use. This will be the equivalent of a narrow topical study. This will be worth 3 points per part.
Option 3: Collect/invent no less than 30 problems and their solutions for each part. This will be worth a point per part per 30 problems.
Option 4: Make a list of all important concepts. This is a topical overview. This will be worth a point per part.
Option 5: Write a proposal for a research project, complete the project, and then write a paper about your results. This will be worth 3 points
Option 6: One timed and written exam per part. This will be a one hour exam and will be worth a total of 1 point assuming you pass each exam.
Option 7: One timed oral exam per part. This will be a one hour exam and will be worth a total of 1 point assuming you pass each exam.
Option 8: One-week written take-home exam per part. This will result in a paper per part and will be worth a total of 10 points.
The lessons of this course will be written and administered using Mathematica. You will need either MathReader or a copy of Mathematica to read these lessons. MathReader is freely available and can be found here. If you are taking this course officially you can discuss the matter with your instructor who can get you a copy of Mathematica (free for six months, or the student version for $140 for as long as you are a MAST/SAS student with the ability to upgrade to the professional version for $350, at toal of $590 — a savings of over $600).
There are no student projects at this time.
Frank Ayres, Jr., Elliott Mendelson, (1999), Schaum's Outline of Calculus, 4th Ed. McGraw-Hill.
This book is a complete textbook of calculus, along with 1103 solved problems. It details the theory and applications of calculus. It is also very inexpensive. Normally it is around $16, SAS members can get it for 25% off the normal price (that means you pay only $12).
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