Take Calculus I online at your own pace

  • ACE Credit®-recommended for 4.0 semester credits

Course description

Sophia’s Calculus I course helps you build mastery of the fundamental concepts of calculus. In this course, you will start by reviewing precalculus topics and then gain experience with limits and continuity, interpretations and applications of derivatives, and techniques of integration. You will also have the opportunity to demonstrate the application of these calculus topics with real-world situations.

Assessments and grading

This is a pass/fail course. You must complete 21 Challenges (formative assessments) and 6 Milestones (summative assessments) with an overall score of 70% or better.

Learning outcomes

<p>At the end of the course, you'll be able to:<br></p> <ul><li>Write equations of lines and circles.</li><li>Identify, evaluate, and utilize function notation in various situations including the difference quotient.</li><li>Analyze and graph combinations of functions by using basic functions.</li><li>Express average and instantaneous rates of change by using the difference quotient.</li><li>Use graphs, tables, and properties of limits to evaluate limit values or determine if a limit does not exist.</li><li>Determine where a function is continuous using the limit concept.</li><li>Demonstrate the formal definition of a limit.</li><li>Evaluate the derivative of a function using graphs, limits, and basic derivative rules.</li><li>Calculate first and higher-order derivatives using rules and properties of differentiation.</li><li>Differentiate composite, exponential, and logarithmic functions using the chain rule.<br></li><li>Approximate function values and errors in calculations by using differentials.</li><li>Use implicit differentiation to calculate the derivative.</li><li>Locate extreme values of functions using derivatives and critical values.</li><li>Apply Rolle's theorem and the mean value theorem where appropriate.</li><li>Apply the first and second derivatives to graph a function and apply to optimization problems.</li><li>Evaluate limits involving infinity and connect these limits with asymptotes.</li><li>Apply L'Hopital's rule to evaluate limits of indeterminate forms.</li><li>Approximate area using geometric formulas and Riemann sums.</li><li>Compute definite integrals using Riemann sums, areas, and properties.</li><li>Calculate indefinite integrals of various functions.</li><li>Apply the fundamental theorem of calculus to evaluate definite integrals in various application settings.</li></ul>

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