Mathematics-III
The complete RGPV syllabus for Mathematics-III (BT301), the third-semester course common to all B.Tech branches under the AICTE Flexible Curricula — numerical methods, transform calculus (Laplace and Fourier), and probability distributions.
Engineering Mathematics-III
by Dr. D.C. Agarwal · ₹400 — covers this full RGPV syllabus.
Course contents — unit by unit
Unit 1 · Numerical Methods – I
Solution of polynomial and transcendental equations — bisection, Newton-Raphson and Regula-Falsi methods. Finite differences, relation between operators, interpolation using Newton's forward and backward difference formulae; interpolation with unequal intervals — Newton's divided-difference and Lagrange's formulae.
Unit 2 · Numerical Methods – II
Numerical differentiation; numerical integration — trapezoidal rule and Simpson's 1/3 and 3/8 rules. Solution of simultaneous linear algebraic equations by Gauss elimination, Gauss-Jordan, Crout's, Jacobi, Gauss-Seidel and relaxation methods.
Unit 3 · Numerical Methods – III
Ordinary differential equations — Taylor's series, Euler and modified Euler's methods, fourth-order Runge-Kutta, Milne's and Adam's predictor-corrector methods. Partial differential equations — finite-difference solution of Laplace and Poisson equations; heat equation (Bender-Schmidt, Crank-Nicholson); wave equation (explicit method).
Unit 4 · Transform Calculus
Laplace transform and its properties, Laplace transform of periodic functions, inverse Laplace transform, convolution theorem, evaluation of integrals and solving ODEs by Laplace transform; Fourier transforms.
Unit 5 · Concept of Probability
Probability mass function, probability density function; discrete distributions (binomial, Poisson); continuous distributions (normal, exponential).