System Modeling Techniques - I (ICT-107), formerly known as Applied Mathematics 1 (BS-111), covers multivariable differential calculus, first-order and higher-order ODEs, power series, special functions (Bessel, Legendre, Gamma, Beta), linear algebra, matrices, eigenvalues, and vector differential and integral calculus.
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Open notes, one-shot revision, mindmaps, PYQs, or expand topics from one place.
Differential calculus of functions of several variables, partial derivatives, chain rule, implicit functions, exact differentials, Jacobians, Taylor series, maxima/minima, Lagrange multipliers, Leibniz integral rule, and first-order ODEs with applications.
Higher-order linear ODEs with constant coefficients, differential operators, Euler-Cauchy, Wronskian, variation of parameters, mass-spring oscillations, power series solutions, Bessel and Legendre equations/polynomials, recurrence relations, and Gamma/Beta functions.
Matrices, determinants, Gauss and Gauss-Jordan elimination, rank, linear independence, vector spaces, existence and uniqueness of solutions, Cramer's rule, eigenvalues and eigenvectors, symmetric/orthogonal matrices, diagonalization, quadratic forms, Gram-Schmidt, Cayley-Hamilton, and LU/Cholesky factorizations.
Vector and scalar fields, space curves, arc length, curvature, gradient, directional derivatives, divergence, curl, line integrals, path independence, double/triple integrals, surface integrals, Green's, Gauss divergence, and Stokes' theorems with engineering applications.