Module 1: Calculus (Polar Curves): Polar coordinates, angle between radius vector and tangent, angle between curves, pedal equations, curvature, and radius of curvature.
Module 2: Series Expansion: Taylor’s and Maclaurin’s series expansion for functions of one variable, indeterminate forms.
Module 3: Ordinary Differential Equations (ODE) of First Order: Linear and Bernoulli’s, exact, and reducible to exact differential equations, orthogonal trajectories.
Module 4: Partial Differentiation & Integral Calculus: Partial derivatives, Euler’s theorem, total derivatives, Jacobians. Multiple integrals (double/triple), change of order, area, and volume.
Module 5: Linear Algebra: Rank of a matrix, Consistency and Solution of system of linear equations (Gauss-elimination, Gauss-Jordan, Gauss-Seidel), Eigenvalues, and Eigenvectors using Rayleigh’s power method.