MA101: Single-Variable Calculus I

• 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.

Suggested Prerequisites

In order to take this course, you should:

• have read the Saylor Student Handbook.