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Numerical analysis is a general term for the theory, development, and use of numerical methods, techniques for approximating solutions of equations through the use of a lot of arithmetic. A book or course about numerical methods may indicate that by incorporating the phrase numerical analysis in the title.
The alternative to numerical methods are analytical methods, i.e., using equations by solving for the wanted value through algebraic manipulation, etc. If analytical methods only lead to equations or integrals for which no such solution is known, something numerically close to the wanted value can often be found through the use of a lot of arithmetic. What we term computers were essentially invented to carry out numerical methods, which already had been studied and developed for centuries, but were laborious to carry out. The invention of computers motivated further development of numerical methods, both because computers leveraged the capabilities of the methods, and because some long-used methods were tailored to human abilities.