Mathematics 265 Introduction to Calculus I
Course Information
Introduction
Welcome to Mathematics 265: Introduction to Calculus I, the first of two three-credit courses in introductory-level university calculus.
There are no prerequisites for Mathematics 265; however, students are expected to have completed Mathematics 30, or an equivalent matriculation-level high-school mathematics course.
This Course Manual is designed to supply you with essential information about the course design, the course materials, and the procedures you should follow to complete the course successfully. It also contains information about the assignments you must complete to obtain credit in Mathematics 265. Before you begin your studies, please read this manual through carefully. If you have any questions about the course itself, or how to proceed with your studies, please contact your tutor or the course professor.
Note: These course materials have been designed for students who are taking the individualized-study version of this course. Students who are in a grouped-study environment should follow the course outline, study schedule, and learning activities provided by their instructor.
Learning Outcomes
Upon successful completion of this course, you will be able to
- demonstrate a foundational understanding of single variable calculus (I), with a focus on limits, differentiation, optimization, and anti-differentiation.
- use single variable calculus methods for applied problem solving in various areas, with a focus on sciences.
- apply background knowledge to pursue further learning in single variable calculus, including MATH 266 and other calculus-based courses.
- communicate mathematical ideas and analyses in a clear and organized manner.
Course Materials
Textbooks
Stewart, James. Readings from Stewart: Single Variable Calculus, Fifth Edition: Custom Edition for MATH 265 Introduction to Calculus, Athabasca University. Scarborough, ON: Thomson Nelson, 2006.
Note: This is a digital textbook (eTextbook). Access and download it through the link on the course home page. Because this course has transitioned from a print textbook to an eText, you may notice minor discrepancies between the textbook page numbers referred to in the course and the page numbers in the eText.
The commercial textbook for this course is a customized monograph prepared exclusively for Athabasca University’s Mathematics 265 from:
Stewart, James. Calculus: Single Variable, 5th ed. Belmont, CA: Brooks/Cole, 2003.
MATH 265: Student Solution Manual to Accompany Introduction to Calculus. Scarborough, ON: Thomson Nelson, 2006.
This manual contains solutions to all of the odd-numbered exercises in the textbook, and is based on:
Student Solutions Manual for Stewart’s Single Variable Calculus, 5th ed. Belmont, CA: Brooks/Cole, 2003.
Athabasca University Materials
Student Manual
The online Student Manual contains information you need to complete this course successfully, including information on the course contract, applying for examinations, library services, student services, student support, and the MyAU portal.
Course Information
The Course Information (the document you are reading) provides essential information specific to the course, the course materials, and the procedures you should follow to complete the course successfully. Please read it through carefully before beginning your studies.
Study Guide
The Study Guide is designed to guide your study of the content of this course. It takes the place of the classroom lectures you would receive in a traditional university. The Study Guide will refer you to the tutorials, which you can find linked on the course home page.
Each unit of the Study Guide includes a “Learning from Mistakes” section. To find hints and solutions for the problems in these sections, look under the Appendices heading on the course home page. There you will also find solutions to the exercises in the Study Guide and an index/glossary of concepts. Note that it is very important that you make a concerted effort to solve all problems independently before you consult the answers provided
Supplementary Materials
Supplementary materials prepared for Mathematics 265 include sample examinations and solutions to those sample examinations.
In addition, you have access to a website that accompanies the textbook:
https://www.stewartcalculus.com/media/5_home.php
This site includes additional examples and other helpful information, such as a review of algebra. You can consult the Homework Hints section of this site if you want additional practice exercises.
Note: Because this course does not cover all of the chapters in Stewart’s original textbook, not all of the examples given on this supplementary site apply to Mathematics 265.
If you need assistance with the supplementary materials, please contact your tutor.
How to Proceed
The Study Guide explains exactly what you are to do to complete the course. Each unit of the Study Guide contains the components listed below.
Objectives
The objectives describe what you should be able to do when you finish the unit.
Prerequisites
The prerequisites listed in each section identify the background any student will need to understand the mathematical concepts and examples presented in the section.
Examples and Exercises
The Study Guide provides examples and exercises to help you learn the mathematical concepts and skills needed to complete the course. Solutions to all exercises in the Study Guide are given in the Appendices, answers to odd numbered exercises from the textbook are in the Student Solutions Manual. If you require further assistance contact your tutor.
Remember, mathematics can only be learned by doing. It is not a passive activity. Also, remember that it is actually beneficial to be stumped at times, and to have to think hard about a problem. When this happens, you will remember the problem and its solution better. The solutions to exercises are provided so you can check your results, and to help you when you have no idea about how to proceed. It is very important that you do not look up the solutions before you have made a serious attempt to solve a problem on your own. When you do refer to the solutions, use them judiciously: read only to the point where you can continue independently, and then proceed on your own.
Learning from Mistakes
Each unit contains a section titled “Learning from Mistakes”—a short assignment in which you are asked to identify and correct some of the most common errors students tend to make when learning calculus. Hints are included in the appendix to the Study Guide.
Suggested Study Schedule
Students who work through the course in a systematic and organized fashion are more likely to be successful in their studies than those who do not do so. Therefore, we strongly advise you to set up a study schedule to ensure that you finish within six months of active registration. In the schedule below, we have indicated the approximate amount of time that you should spend on each activity. You have six months from your contracted start date to complete this three-credit course, but you will note that the schedule provided below is based on a seventeen-week period. This time frame is more closely in line with those of traditional institutions, and also allows you some leeway in case any unforeseen circumstance interferes with your study.
If you find yourself falling behind, contact your tutor to discuss the situation. The course is challenging, but you should have no difficulty in meeting your deadlines if you set aside a study period and a lab period each week, and do not procrastinate.
Students registered in a grouped-study version of the course, or those receiving financial assistance, may face more rigorous time constraints. Please check your course registration for any restrictions on the length of registration, and be prepared to adjust your schedule.
Study Schedule
| Week | Activity |
|---|---|
| 1-2 | Read the Student Manual carefully, and look over the other course materials. |
| Contact your tutor, if he or she has not already contacted you. | |
| Set up your Study Plan. | |
| Read the section of the Study Guide titled “Introduction.” | |
| Complete Unit 1. | |
| Complete Assignment 1, and submit it to your tutor for grading. | |
| 3-4 | Complete Unit 2. |
| 5-7 | Complete Unit 3. |
| Complete Assignment 2, and submit it to your tutor for grading. | |
| Request the first examination, to be written on completion of Unit 4. See Requesting, Accessing and Navigating Your Möbius Exam for more information. | |
| 8-9 | Complete Unit 4. |
| Complete Assignment 3, and submit it to your tutor for grading. | |
| Study for and write the first examination. | |
| 10-11 | Complete Unit 5. |
| 12-13 | Complete Unit 6. |
| Request the final examination, to be written on completion of Unit 7. See Requesting, Accessing and Navigating Your Möbius Exam for more information. | |
| 14-15 | Complete Unit 7. |
| 16 | Complete Assignment 4, and submit it to your tutor for grading. |
| Study for the final examination. | |
| 17 | Review the feedback on your assignments. |
| Study for and write the final examination. | |
| Congratulations on completing the course! |
Student Evaluation
Your final grade in Mathematics 265 is a composite of the grades you achieve on four tutor-marked assignments, a midterm examination and a final examination. The four assignments are included in the section of this manual titled “Assignments for Credit.”
To pass this course, you must submit all the course assignments and complete them to the satisfaction of your tutor. You must also achieve a grade of at least 50 per cent on each examination, and a course composite grade of at least 50 per cent. Students who do not achieve a minimum passing grade of 50 per cent on an examination will be allowed to write a supplemental examination. For further information, see the section of this manual titled “Applying for and Writing Examinations.”
| Course Activity | Due Date | Weighting | ||
|---|---|---|---|---|
| Assignment 1 | After Unit 1 | 5% | ||
| Assignment 2 | After Unit 3 | 10% | ||
| Assignment 3 | After Unit 4 | 10% | ||
| Midterm examination | After Unit 4 | 25% | ||
| Assignment 4 | After Unit 7 | 10% | ||
| Final Examination | After Unit 7 | 40% | ||
| Total | 100% |
Applying for and Writing Examinations
Important
The graded exams in this course are to be completed in the Möbius platform. Be sure to request each exam well in advance of the date you intend to write it. Take the time to review the process for Requesting, Accessing and Navigating Your Möbius Exam.
Do not click an exam link on the course home page unless you have both (a) booked your exam with ProctorU; and (b) requested your exam through the Office of the Registrar. Note that ProctorU is the only invigilator available for the MATH 265 Möbius exams.
Both examinations are comprehensive; that is, they do not emphasize one topic over others. The first examination covers Units 1 to 4, and the second covers Units 3 to 7.
Note: You will be assessed and assigned a grade on the basis of how well you have learned the material, not on the basis of a comparison of your performance with that of others. Your grade in each examination will be based on your performance and achievement in that particular examination. Since the examinations are designed to match the objectives, you should have a clear idea in advance of the areas your examination will cover.
Both exams follow the same format:
- You will have 3 hours to complete each exam.
- The exams are closed-book examinations. You are allowed to consult your own personal notes, contained on one and only one 8.5 × 11-inch single page (both sides).
- You may bring scrap paper to each exam.
- Your personal notes page and scrap paper must be torn up/destroyed in front of the ProctorU invigilator at the end of each exam. Therefore, you will need to create separate, personal notes for each exam.
- You are allowed to use a simple scientific calculator; however, graphing calculators, programmable calculators, and hand-held computers are not allowed.
- You are not allowed to use tapes, cell phones, iPods, a BlackBerry, or other electronic or digital devices, or to consult with other people during the examinations.
- The examinations each comprise 20 questions and are each out of a total of 20 points. Each question is worth 1 point.
- Partial scores are possible when a question comprises multiple parts. In these cases, each part of the question is equally weighted for a total of 1 point for the whole question.
You may be familiar with some of the questions in the examinations, but be prepared for unfamiliar questions as well. Do not panic when confronted with an unexpected or unfamiliar question; read the question carefully, make sure you understand what is required. These questions are not necessarily difficult; they are designed to test your understanding of concepts, and how well you can put them to use when solving problems.
Although you do not need permission to apply for an examination, we recommend that you consult your tutor about your readiness to write, and about examination writing strategies. Your tutor can also provide information about the examination format and about study strategies.