Differentiation of functions, Limited developments and Integration

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This manual is addressed to university-first-year students who want to study some more advanced topic in calculus such as differentiation, limited development and integration. It does not intend to make the subject easy, but it helps the readers to review some basic ideas in mathematical analysis and understand new notions. This manual aims to enhance mathematical intuition and problem-solving skills. It's a step forward for those who aspire to excel in higher mathematics.