coarser / courser are similar-sounding terms with different meanings (referred to as homophones). To better understand the differences, see below for definitions, pronunciation guides, and example sentences using each term. 👇
coarser: (adjective) of textures that are rough to the touch or substances consisting of relatively large particles. (adjective) lacking refinement or cultivation or taste. (adjective) of low or inferior quality or value; - Shakespeare.
courser: (noun) a huntsman who hunts small animals with fast dogs that use sight rather than scent to follow their prey. (noun) a dog trained for coursing. (noun) swift-footed terrestrial plover-like bird of southern Asia and Africa; related to the pratincoles.
coarser: k·AO·r·s·er
courser: k·AO·r·s·er
(Examples are Wikipedia snippets under the CC ShareAlike 3.0 license. Definitions drawn from WordNet.)