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Most engineering disciplines, including mechanical, require about 4 to 5 semesters of higer level math ( Calculus/ differential equations/ matrix algebra/ etc) to graduate. As an engineer, I rarely use any math higher than algebra as most of the formulae are provided for you. However, it is imperative that you understand the concepts and theory discuvered in the higher level math.
Math is critical to all aspects of Engineering. Math is required to demonstrate that your invention is feasible; both technically and to build a business case so that you can get funding, or sell it.