MA102: SINGLE-VARIABLE CALCULUS II

This course is the second installment of Single-Variable Calculus. In Part I (MA101), we studied limits, derivatives, and basic integrals as a means to understand the behavior of functions. In this course (Part II), we will extend our differentiation and integration abilities and apply the techniques we have learned.

Additional integration techniques, in particular, are a major part of the course. In Part I, we learned how to integrate by various formulas and by reversing the chain rule through the technique of substitution. In Part II, we will learn some clever uses of substitution, how to reverse the product rule for differentiation through a technique called integration by parts, and how to rewrite trigonometric and rational integrands that look impossible into simpler forms. Series, while a major topic in their own right, also serve to extend our integration reach: they culminate in an application that lets you integrate almost any function you’d like.

Integration allows us to calculate physical quantities for complicated objects: the length of a squiggly line, the volume of clay used to make a decorative vase, or the center of mass of a tray with variable thickness. The techniques and applications in this course also set the stage for more complicated physics concepts related to flow, whether of liquid or energy, addressed in Multivariable Calculus (MA103).

Part I covered several applications of differentiation, including related rates. In Part II, we introduce differential equations, wherein various rates of change have a relationship to each other given by an equation. Unlike with related rates, the rates of change in a differential equation are various-degree derivatives of a function, including the function itself. For example, acceleration is the derivative of velocity, but the effect of air resistance on acceleration is a function of velocity: the faster you move, the more the air pushes back to slow you down. That relationship is a differential equation.

Course Designer: Clare Wickman

Primary Resources: This course is comprised of a range of different free, online materials. However, the course makes primary use of the following materials:

• University of Michigan: Scholarly Monograph Series: Wilfred Kaplan and Donald J. Lewis’s Calculus and Linear Algebra Vol. 1
• University of Wisconsin: H. Jerome Keisler’s Elementary Calculus
• Whitman College: Professor David Guichard’s Calculus
• University of Houston: Dr. Selwyn Hollis’s “Video Calculus”
• MIT: Professor Jerison’s Single Variable Calculus
• Temple University: Gerardo Mendoza and Dan Reich’s Calculus on the Web
• Clinton Community College: Elizabeth Wood’s “Supplemental Notes for Calculus II”

Requirements for Completion: In order to complete this course, you will need to work through each unit and all of its assigned materials.  You will also need to complete:

• Unit 1 Assessments
• Unit 2 Assessments
• Unit 3 Assessments
• Unit 4 Assessments
• Unit 5 Assessments
• Unit 6 Assessments
• The Final Exam

Note that you will only receive an official grade on your Final Exam. However, in order to adequately prepare for this exam, you will need to work through all of the resources and assessments in each unit.

In order to “pass” this course, you will need to earn a 70% or higher on the Final Exam.  Your score on the exam will be tabulated as soon as you complete it. If you do not pass the exam, you may take it again.

Time Commitment: This course should take you approximately 125 hours to complete. At the beginning of each unit, there is a detailed list of time advisories for each subunit. These estimates factor in the time required to watch each lecture, work through each reading thoughtfully, and complete each assessment. However, these should be seen as guidelines, not goals; each learner is different, and you may find that your pace changes throughout the course. Mastery of the material, rather than strict adherence to the time estimates, is the measure of success in this course. It may be useful to take a look at these time advisories, to determine how much time you have over the next few weeks to complete each unit, and then to set goals for yourself. For example, Unit 1 should take approximately 20.25 hours. Perhaps you can sit down with your calendar and decide to complete sub-subunit 1.1.1 (a total of 2 hours) on Monday night; sub-subunits 1.1.2 and 1.1.3 (a total of 3.5 hours) on Tuesday night; sub-subunit 1.1.4 (a total of 4 hours) on Wednesday night; etc.

Tips/Suggestions: If a lecture stops making sense to you, pause it – this is a luxury you only have in a course of this nature! – and return to the readings to get up-to-speed on the material. Remember to note down the time at which you paused the lecture, in case your browser times out. As noted in the “Course Requirements,” Single-variable Calculus Part I (MA101) is a pre-requisite for this course. If you are struggling with the mathematics as you progress through this course, consider taking a break to revisit MA101.

As you study the resources in each unit, take careful notes on a separate sheet of paper. Mark down any important equations, formulas, and definitions that stand out to you. These notes will serve as a useful review as you study for your Final Exam.