Despite the key role mathematics plays in our technology-dependent society, the fact is that high schools may not be preparing students for Higher Mathematics. Did you know that throughout North America, the success rate for first-year Calculus is around 50%? (The success rate is calculated as the percentage of enrolling students who complete the standard two-semester Introductory Calculus sequence in one year.) At UPEI, and throughout Atlantic Canada, the success rate has been quite similar to the rest of North America.
If you want to be on the right side of this statistic, there are some things you can do to get ready for Calculus.
If you are planning on majoring in any of Biology, Chemistry, Physics, Computer Science, Engineering, or Mathematics, you are probably required to take this Calculus sequence, and possibly Calculus courses beyond the introductory level. Students in programs from outside the Faculty of Science (for example, Economics) are also often advised to take this Calculus sequence.
This page is designed to be an information repository for all things related to Math 151/152. The information has been broken into sections with the following headings:
What is Calculus all about?
Calculus is the study of change, or to be more precise, changing
quantities. Mathematical topics before Calculus, like Arithmetic,
Algebra, Geometry and Trigonometry, involve unchanging quantities.
In algebra, for example, any unknown quantities are usually fixed
real numbers that we wish to solve for.
Functions are the mathematical objects that link quantities (for
example: the area of a circle is a function of its radius and the
position of a falling object is a function of time), so much of
Calculus involves manipulating functions.
The two key areas of Calculus are Differential Calculus (covered in Math 151) and Integral Calculus (covered in Math 152).
In Differential Calculus the basic problem is finding the slope of the tangent line to a curve at a given point on the curve. This seemingly innocuous problem is the core of Differential Calculus, since this slope tells how fast the output variable of the function is changing with respect to the input variable. Solving this problem lets us find the instantaneous rate of change of y=f(x) with respect to x, which is the derivative.
In Integral Calculus is the basic problem is finding the area under a positive function on an interval. This leads to the definition of the definite integral and solving this problem lets us find the accumulation of a quantity over an interval.
To solve either of these problems, the mathematical concept of limit is required.
The big surprise is that these two seemingly unrelated problems are actually connected via the Fundamental Theorem of Calculus.
In science, one goal is to predict what will happen in the future. (i.e. Will this chemical reaction cause an explosion? Will this population reach a steady state? Will it rain tomorrow? Will our sun keep burning for the next one million years?) To do this we must determine how changes in certain quantities will affect future behavior of other quantities. This is what Calculus does best, and why it was actually invented (to help study astronomy). Introductory Calculus lays the foundation for understanding all sorts of scientific models.
Why do I have to take Calculus?
The short answer is that you do not have to take Calculus. Its a free country, and no one is forced to take Calculus. Many people function perfectly well throughout their lives without knowing the slightest bit of Calculus. But if you choose a career path that requires any level of mathematical sophistication (such as Engineering, Economics or any branch of Science), you will need Calculus.
Areas of study that require the most Math:
- Mathematics (of course)
- Physics
- Engineering
- Computer Science
- Chemistry
- Economics
- Biology
Of course, the amount of Math required also depends on which subdiscipline you choose. For example: Electrical Engineering probably requires the most mathematics of any Engineering discipline, and Civil Engineering probably requires the least. Some areas of Biology (i.e. population dynamics or genetics) require some very advanced mathematics.
The Departments who set the curriculum for programs in these areas have laid out a course of study that includes Calculus. If you are not good at mathematics, or have a negative attitude about mathematics, you might want to reconsider your career options.
Another reason why many UPEI programs require Calculus credits is as an early test of a student's academic ability. To succeed in Calculus (and Mathematics in general) you must be able to: solve problems, reason logically and understand abstract concepts. The ability to master these skills is a key indicators of success in future academic endeavors. It is in everyone's best interest to find out as soon as possible if a student is capable of completing the course of study they have embarked on.
For these (and other) reasons Introductory Calculus may be the most important course you take at university.
How can I prepare for the Calculus sequence?
The first thing is to take as much Mathematics as possible in High School. And try to understand the ideas and not just memorize formulas. You will need all of your High School mathematics when you get to university. Knowledge of Algebra, Trigonometry and Analytic Geometry, as well as the basic understanding of functions (including exponential and logarithmic functions) is key for Calculus. Some of this stuff will be reviewed (very quickly) during the first week of class, but you will be responsible for knowing all mathematics in the High School Curriculum.
If you are not confident that your background in Algebra, Trigonometry, Analytic Geometry and Functions is strong, we recommend that you spend some time during the last month before coming to UPEI in September, to brush up on your Mathematics. You might want to get a book on High School Mathematics from your local library and review. There are also some other resources available to you:
The APICS (Atlantic Universities Inter-university Council on the Sciences) Mathematics Committee has prepared a small booklet called: Preparing for University Calculus. It is available for download from the APICS website or a hardcopy is available free from the UPEI Department of Mathematics and Statistics.
A site called EMR ( Exercises for Mathematical Readiness ) at University of Saskatchewan has a review of High School Math Topics that are most useful for Calculus.
Also, Eric Schecter at Vanderbilt has developed a webpage titled Common Errors in College Math which might be useful for the mathematically unwary to peruse.
If you have concerns that you need a major review of High School math topics (perhaps you've been out of school for awhile) you might want to consider taking Math 001:Precalculus which is offered in the Fall semester, as well as during summer session if there is enough interest. This is a non-credit course which covers all of the background material needed for Math 151/152.
What's this I hear about an Assessment Test?
Beginning in September 2000, the Department of Mathematics and Statistics at UPEI instituted a policy that requires every student enrolling in Math 151 to pass an Assessment Test which tests the basic skills of Arithmetic, Algebra, Trigonometry, Analytic Geometry and functions. The test is of 60 minutes duration and is written in the highshools and during a special session in the first week of classes. Students should check with the departmental office for details.
A number of universities throughout North America have instituted similar policies in response to a high failure and withdrawal rate for Calculus courses. Poor knowledge of the background material required to succeed in Calculus has been identified as a major cause for the low success rate and the Assessment Test is a response to this problem.
The Assessment test covers only material covered in the standard High School Mathematics Curriculum. In particular, no knowledge of Calculus is required.
Students who do not pass this Assessment Test are encouraged to take Math 001. If they pass this course, they are accepted into Math 151 in the Winter Semester and can take Math 152 in the summer session and be back on track with their Academic program.
The Assessment Test is a multiple choice test and no calculators are allowed. We encourage students to prepare for this test by reviewing High School Mathematics material.
Here is a previous year's Assessment Test in different formats (dvi, ps, pdf). You can test yourself by trying the Assessment Test during a sixty minute period and then checking your answers here.
What can I expect during the course?
The standard first-year Calculus course for Science students varies only slightly throughout Canada. We will be using the text Calculus - Concepts and Contexts , by James Stewart, whose Calculus books are the best-sellers in North America.
On the first day of classes a course outline will be distributed with more details concerning the course structure.
You can expect a much faster pace in University courses in general than you are used to from High School. In each of Math 151 and Math 152, there are 13 weeks of classes, with three 50 minute lectures per week in a semester and during this time approximately 36 sections are covered. Your instructor will not have time to go into the details of every aspect of the course material. His job will be to communicate the main ideas, and you will expected to do enough work on your own time to make sure you understand the details.
There are weekly tutorials where you can work on problems and get help from your instructor.
It is recommended that you spend at least 3 hours study and review, for each hour of class time.
Unlike High School, no one is going to check up on you to see if you are keeping up. In university you will be treated like adults, and it will be assumed that you have the discipline and organizational ability to manage your time wisely.
Another aspect of the course that will be new to you is the use of computer software to help solve problems. Gradually throughout Math 151 and Math 152, MAPLE ( a mathematical software package) will be incorporated into the course. MAPLE is one of the most popular general purpose mathematical software packages in use at Universities and Industry today. For more information on what MAPLE can do for you, visit MAPLE's Student Center . You can also experiment with MAPLE by entering some of the commands found here (this file has been converted from MAPLE to html).
This may sound a bit intimidating, but if you have the background and keep up with the work you will be successful.
What can I do to maximize my chances for success?
Top five
- Understand, don't memorize.
- Ask why, not how.
- See every problem as a challenge.
- Learn techniques, not results.
- Make sure you understand each topic before going on to the next.
Where can I find other Calculus resources on the web?
The aforementioned APICS website has some words of wisdom regarding preparing for University Calculus.
The best starting point for more general topics related to the teaching and learning of mathematics is The Math Forum . The website S.O.S. Mathematics also has useful material.
You might want to check out Zona Land for some interesting and fun stuff related to math and physics.
There are literally thousands of Math sites on the web. Any search using keywords like: algebra, trigonometry and calculus will give you more than you can handle. Of course, no one has verified the accuracy of many of these sites so be skeptical.
Department of Mathematics and Statistics