Mathematics 266 Introduction to Calculus II

Course Orientation

Introduction

Welcome to Mathematics 266: Introduction to Calculus II, the second of two three-credit courses in introductory-level university calculus.

The five units of Mathematics 266 are listed below.

Unit 1  Inverse Functions: Exponential, Logarithmic and Hyperbolic Functions
Unit 2  Inverse Trigonometric and Hyperbolic Functions; L’Hopital’s Rule
Unit 3  Techniques of Integration
Unit 4  Applications of Integration
Unit 5  Differential Equations
Unit 6  Infinite Sequences and Series

To register in Mathematics 266, you must have completed Athabasca University’s Mathematics 265, or an equivalent course from another university.

Learning Outcomes

Upon successful completion of this course, you will be able to

• demonstrate a foundational understanding of single variable calculus (II), with a focus on integration, differential equations, sequences and infinite series, and applications.
• use single variable calculus methods for applied problem solving in various areas, with a focus on sciences.
• apply knowledge gained in course to pursue further learning in multivariable calculus, including MATH 365 and other calculus-based courses.
• communicate mathematical ideas and analyses in a clear and organized manner.

Course Materials

Textbook

The course Study Guide is the main document to guide you through the course. In addition, this course using the following eBook:

The Study Guide will direct you to the Lyryx labs and quizzes at the appropriate times in the course. The Lyryx exercises open in your Athabasca University course browser. Once you are in the Lyryx system, locate the lab or quiz for the section of the Study Guide you just completed, and then follow the online instructions.

Athabasca University Materials

The forms you need to request examinations or inform the University of a change in your status as a student are available through your myAU home page or for download from the Office of the Registrar’s Online Services (OROS) website.

What to Do If Something Is Missing

If any of the above items are missing from your course package, please contact Course Materials at Athabasca University as soon as possible, by sending an email to cmat@athabascau.ca.

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. 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 an eighteen-week period. This time frame is more closely in line with those of traditional institutions and 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.

Study Schedule

Student Evaluation

Your final grade in Mathematics 266 is a composite of the grades you achieve on 8 quizzes, four assignments, a midterm examination, and a final examination.

To pass this course, you must submit all quizzes, the four course assignments and complete them to the satisfaction of your tutor. You must also achieve a grade of at least 50 percent on each examination, and a course composite grade of at least 50 percent. Students who do not achieve a minimum passing grade of 50 percent on an examination will be allowed to write a supplemental examination. For further information, see the section of the online Student Manual titled “Procedures for Applying for and Writing Examinations.”

Use the Assignment Drop Boxes on the course home page to submit all assignments. Do not submit your assignments by email. If you are unable to use the drop boxes for any reason, contact your tutor.

The table below provides information about the due date and weighting of each assessment component.

Applying for and Writing Examinations

Both exams follow the same format:

• You will have 3 hours to complete the exam.
• The exam is a closed-book examination. 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 the exam.
• You must securely destroy all used paper upon exam completion. Failure to destroy any used paper and/or sharing exam content can result in a charge of academic misconduct.
• You are allowed to use a simple scientific calculator; however, graphing calculators, programmable calculators, and handheld 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 examination.
• The examination comprises 20 questions and is 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 change your answers as many times as you like before you click Submit Assignment to submit the entire exam. Only the final response for each question will be marked.
• Read each question carefully. Some questions specify the format in which the response must be entered so that they can be auto-marked correctly (e.g., as a fraction, to specific decimal places). Be sure to enter your responses in the format specified.
• In each response box, enter only your answer and no additional text.
• Double check your work and calculations before submitting your responses.
• Click the Preview button, when available, to check your responses before submitting them.

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 you will need to understand the mathematical concepts and examples presented in the section.

Examples and Exercises

The Study Guide developed by Athabasca University 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 Appendix, answers to some exercises from the textbook are in the Selected Exercises Answers section of the textbook. If you require further assistance, contact your tutor.

Remember, mathematics can only be learned by doing. It is not a passive activity. The exercises in the videos presented are intended as guided exercises. To benefit from these exercises, you must follow them with pencil and paper at hand. Math is learned by doing, not by watching. 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, then proceed on your own.

Test Yourself

Each unit contains Test Yourself questions designed to help you test your command of the materials presented in the unit. We encourage you to complete the Test Yourself questions within the time limit specified, and to mark them using the solutions provided in “Appendix D” of the Study Guide.

Examination Hints

You must write two examinations to complete Mathematics 266. The first examination covers the material presented in Units 1–4; the final covers Units 5 and 6. You are allowed three hours for each examination.

You will be assessed and assigned a grade based on how well you have learned the material, not through 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 examinations are comprehensive: they do not emphasize one topic over others.

Both examinations are closed-book; however, you are permitted to consult your own personal notes contained on one and only one 8.5 × 11 double-sided page. This page, which must include your name and student ID number, is to be handed in together with the examination.

Simple calculators—not graphic or programmable calculators—are allowed in each examination. Please note that you will not be allowed to bring a smart phone or other digital device into the examination room, nor will you be allowed to consult with anyone while writing the examination.

We strongly recommend that you begin the examination by glancing over all of the questions, and answering those you feel most confident about first. Leave to the end those questions that present special difficulty for you.

Examinations consist of 10–12 questions, so you should give yourself about 10–15 minutes per question. When preparing for an examination, time yourself and make sure you can do 12 questions in about three hours. Both examinations have “bonus” questions. There is no penalty for choosing not to attempt these questions, or for answering them incorrectly, but you obtain extra points if you do them correctly.

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; instead, read the question carefully and 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.