Discourse is the creation and organization of the segments of a language above as well as below the sentence

https://call-for-papers.sas.upenn.edu/node/39688

Discourse is 'language above the sentence or above the clause' (Stubbs 1983:1)

Discourse: 1. a serious speech or piece of writing about a particular subject; 2. serious conversation; 3. connected language in speech or writing; (Longman Dictionary of Contemporary English, 2nd edition, 1987)

https://en.wikipedia.org/wiki/Discourse_analysis

in linguistics, discourse refers to a unit of language longer than a single sentence.

Discourse studies, says Jan Renkema, refers to "the discipline devoted to the investigation of the relationship between form and function in verbal communication" (Introduction to Discourse Studies, 2004)

http://grammar.about.com/od/d/g/discourseterm.htm

"Discourse is the way in which language is used socially to convey broad historical meanings. It is language identified by the social conditions of its use, by who is using it and under what conditions. Language can never be 'neutral' because it bridges our personal and social worlds."

(Frances Henry and Carol Tator, Discourses of Domination. University of Toronto Press, 2002)

a careful study of something to learn about its parts, what they do, and how they are related to each other

an explanation of the nature and meaning of something

http://www.merriam-webster.com/dictionary/analysis

Analysis is the process of separating something into its constituent elements.

https://en.oxforddictionaries.com/definition/analysis

a separating or breaking up of any whole into its parts, esp. with an examination of these parts to find out their nature, proportion, function, interrelationship, etc.

a statement of the results of this process

http://www.yourdictionary.com/analysis

"[Discourse analysis] is not only about method; it is also a perspective on the nature of language and its relationship to the central issues of the social sciences. More specifically, we see discourse analysis as a related collection of approaches to discourse, approaches that entail not only practices of data collection and analysis, but also a set of metatheoretical and theoretical assumptions and a body of research claims and studies."(Linda Wood and Rolf Kroger, Doing Discourse Analysis. Sage, 2000)

(Discourse analysis is a vast area within linguistics, encompassing as it does the analysis of spoken and written language over and above concerns such as the structure of the clause or sentence (McCarthy 1991)

Discourse Analysis is concerned with the study of the relationship between language and the contexts in which it is used (McCarthy 1991)

Discourse analysis (DA), or discourse studies, is a general term for a number of approaches to analyze written, vocal, or sign language use, or any significant semiotic event.

https://en.wikipedia.org/wiki/Discourse_analysis

Discourse analysis is a broad term for the study of the ways in which language is used in texts and contexts. Also called discourse studies.

http://grammar.about.com/od/d/g/discanalysisterm.

Discourse analysis is concerned with language use as a social phenomenon and therefore necessarily goes beyond one speaker or one newspaper article to find features which have a more generalized relevance. This is a potentially confusing point because the publication of research findings is generally presented through examples and the analyst may choose a single example or case to exemplify the features to be discussed, but those features are only of interest as a social, not individual, phenomenon." (Stephanie Taylor, What is Discourse Analysis? Bloomsbury, 2013)

http://grammar.about.com/od/d/g/discanalysisterm.