Mathematics-I
The complete RGPV syllabus for Mathematics-I (BT102), the first-semester course common to all B.Tech branches under the AICTE Flexible Curricula — calculus, sequences and series, Fourier series, vector spaces and matrices (linear algebra).
Engineering Mathematics-I
by Dr. D.C. Agarwal · ₹490 — covers this full RGPV syllabus.
Course contents — unit by unit
Unit 1 · Calculus
Rolle's theorem, mean-value theorems, expansion of functions by Maclaurin's and Taylor's series (one variable); Taylor's theorem for functions of two variables, partial differentiation, maxima and minima (two and three variables), method of Lagrange multipliers.
Unit 2 · Calculus (Integral)
Definite integral as a limit of a sum and its application to summation of series; Beta and Gamma functions and their properties; applications of definite integrals to surface areas and volumes of revolution. Multiple integrals, change of order of integration, and their applications to area and volume.
Unit 3 · Sequences & Series
Convergence of sequences and series, tests for convergence; power series, Taylor's series, series for exponential, trigonometric and logarithmic functions; Fourier series — half-range sine and cosine series, Parseval's theorem.
Unit 4 · Vector Spaces
Vector space, vector subspace, linear combination of vectors, linear dependence and independence, basis of a vector space, linear transformations.
Unit 5 · Matrices
Rank of a matrix, solution of simultaneous linear equations by elementary transformation, consistency of equations, eigenvalues and eigenvectors, diagonalization of matrices, Cayley-Hamilton theorem and its application to finding the inverse.