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This textbook is meant for first-year undergraduates majoring in mathematics or disciplines where formal mathematics is important. It will help students to make a smooth transition from high school to undergraduate differential calculus. Beginning with limits and continuity, the book proceeds to discuss derivatives, tangents and normals, maxima and minima, and mean value theorems. It also discusses indeterminate forms, functions of several variables, and partial differentiation. The book ends with a coverage of curvature, asymptotes, singular points, and curve tracing. Concepts are first presented and explained in an informal, intuitive, and conceptual style. They are then covered in the form of a conventional definition, theorem, or proof. Each concept concludes with at least one solved example. Additional solved examples are also provided under the section "More Solved Examples". Practice numerical exercises are included in the chapters so that students can apply the concepts learnt and sharpen their problem-solving skills.