"Mathematics For B.Sc. Students: Real Analysis-Ii, Linear Algebra & Hydrostatics, Partial Differential Equations & Calculus Of Variations (Nep 2020 Ranchi)"

This text is tailored for B.Sc. Fifth Semester Mathematics students, aligning with the Common Minimum Syllabus of Ranchi University and other institutions under the National Education Policy 2020 in Jharkhand. It's divided into three sections, delving into fundamental and advanced mathematical concepts. Real Analysis-II explores the Rigor of Limits, continuity, differentiability, Riemann and improper integrals, and special functions like Beta and Gamma, enhancing students' analytical skills. Linear Algebra & Hydrostatics provides a solid framework of vector spaces, linear transformations, eigenvalues and eigenvectors, and applies these to fluid statics, thrusts, and fluid pressures, connecting abstract mathematics to practical applications. Partial Differential Equations & Calculus of Variations investigates first and second-order PDEs with constant and variable coefficients, canonical forms, and variational methods, preparing students for complex mathematical modeling and real-world problem-solving.