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Vedic Mathematics, an ancient system derived from the Vedas, offers efficient and intuitive techniques for solving complex mathematical problems. This paper explores the integration of Vedic Mathematics with advanced calculus, particularly focusing on derivatives, integrals, and differential equations. By leveraging Vedic Sutras such as  Divaja Ghata ,  Calana-Kalanabhyam , and  Urdhva-Tiryagbhyam , we demonstrate how traditional calculus problems can be simplified and solved more effectively. Detailed examples are provided to illustrate the application of these Sutras in differential calculus, integration, and partial differential equations (PDEs).The study highlights the potential of Vedic Mathematics to enhance computational efficiency and conceptual clarity in advanced calculus.