Welcome to MA101: Single-Variable Calculus I. General information about this course and its requirements can be found below.
Course Designer: Clare Wickman
Requirements for Completion: You will only receive an official grade on your final exam. However, in order to adequately prepare for this exam, we recommend that you work through the materials 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 following a 7-day waiting period.
To earn credit from Excelsior College for this course, you will need to take the UExcel Calculus examination. Visit the UExcel website, and click on "MAT150 Calculus” for details about the UExcel Calculus examination. In order to adequately prepare for this exam, you will need to work through all of the resources in this course, the activities listed above, and Saylor's final exam. For more information about earning credit through Saylor Academy's partnership with Excelsior College, please go here. If you wish, you may take the Saylor Academy final exam as practice for the UExcel Calculus exam.
Time Commitment: While learning styles can vary considerably and any particular student will take more or less time to learn or read, we estimate that the "average" student will take 100 hours to complete this course. Each resource and activity within the course is similarly tagged with an estimated time advisory. We recommend that you work through the course at a pace that is comfortable for you and allows you to make regular (daily, or at least weekly) progress. It's a good idea to also schedule your study time in advance and try as best as you can to stick to that schedule.
It may be useful to take a look at these time advisories and to determine how much time you have over the next few weeks to complete each unit, and then to set a schedule for yourself. For example, Unit 1 should take you 9.5 hours. Perhaps you can sit down with your calendar and decide to complete subunits 1.1 and 1.2 (a total of 4.5 hours) on Monday night; subunit 1.3 (a total of 3 hours) on Tuesday night; etc.
Tips/Suggestions: Learning new material can be challenging, so below we've compiled a few suggested study strategies to help you succeed.
Take notes on the various terms, practices, and theories as you read. This can help you differentiate and contextualize concepts and later provide you with a refresher as you study.
As you progress through the materials, take time to test yourself on what you have retained and how well you understand the concepts. The process of reflection is important for creating a memory of the materials you learn; it will increase the probability that you ultimately retain the information.
If a video 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 make a note of the time at which you paused the video lecture in case your browser times out. Try to take notes on there sources, writing down any formulas or other information you need to know. These notes will be useful as you prepare and study for your final exam.
Pay special attention to Unit 1, as it will lay the groundwork for understanding the more advanced, explanatory material presented in the latter units.
Upon successful completion of this course, you will be able to:
- define and identify functions;
- define and identify the domain, range, and graph of a function;
- define and identify one-to-one, onto, and linear functions;
- analyze and graph transformations of functions, such as shifts, dilations, and compositions of functions;
- characterize, compute, and graph inverse functions;
- graph and describe exponential and logarithmic functions;
- define and calculate limits and one-sided limits;
- identify vertical asymptotes;
- define continuity and determine whether a function is continuous;
- state and apply the Intermediate Value Theorem;
- state the Squeeze Theorem, and use it to calculate limits;
- calculate limits at infinity, and identify horizontal asymptotes;
- calculate limits of rational and radical functions;
- state the epsilon-delta definition of a limit, and use it in simple situations to show a limit exists;
- draw a diagram to explain the tangent-line problem;
- state several different versions of the limit definition of the derivative, and use multiple notations for the derivative;
- describe the derivative as a rate of change, and give some examples of its application, such as velocity;
- calculate simple derivatives using the limit definition;
- use the power, product, quotient, and chain rules to calculate derivatives;
- use implicit differentiation to find derivatives;
- find derivatives of inverse functions;
- find derivatives of trigonometric, exponential, logarithmic, and inverse trigonometric functions;
- solve problems involving rectilinear motion using derivatives;
- solve problems involving related rates;
- define local and absolute extrema;
- use critical points to find local extrema;
- use the first and second derivative tests to find intervals of increase and decrease and to find information about concavity and inflection points;
- sketch functions using information from the first and second derivative tests;
- use the first and second derivative tests to solve optimization (maximum/minimum value) problems;
- state and apply Rolle's Theorem and the Mean Value Theorem;
- explain the meaning of linear approximations and differentials with a sketch;
- use linear approximation to solve problems in applications;
- state and apply L'Hopital's Rule for indeterminate forms;
- explain Newton's method using an illustration;
- execute several steps of Newton's method and use it to approximate solutions to a root-finding problem;
- define antiderivatives and the indefinite integral;
- state the properties of the indefinite integral;
- relate the definite integral to the initial value problem and the area problem;
- set up and calculate a Riemann sum;
- estimate the area under a curve numerically by using the Midpoint Rule;
- state the Fundamental Theorem of Calculus, and use it to calculate definite integrals;
- state and apply basic properties of the definite integral;
- use substitution to compute definite integrals;
- integrate transcendental, logarithmic, and hyperbolic functions;
- find the area between two curves;
- find the volumes of solids by using ideas from geometry;
- find the volumes of solids of revolution by using disks and washers;
- find the volumes of solids of revolution by using shells;
- write and interpret a parameterization for a curve;
- find the length of a curve;
- find the surface area of a solid of revolution;
- compute the average value of a function;
- use integrals to compute the displacement and the total distance traveled;
- use integrals to compute moments and centers of mass; and
- use integrals to compute work.
Throughout this course, you'll also see related learning outcomes identified in each unit. You can use the learning outcomes to help organize your learning and gauge your progress.
In order to take this course, you should:
- have read the Saylor Student Handbook.