Calculus I

<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>