Differential Calculus and Linear Algebra

Introduction of Limits, continuity and differentiability for function of two variables, Partial derivatives, Composite functions, Total derivative, Euler’s Theorem for homogeneous functions, Taylor’s and Maclaurin’s expansion for function of two variables, Jacobians, properties of Jacobian (without proof), Maxima & Minima for a function of up to two variables. Applications: Signal strength analysis, Communication system optimization, Frequency response analysis, Amplifier gain optimization, Antenna parameter optimization.

Evaluation of double and triple integrals, change of order of integration, Change of variable (double -integral), Beta and Gamma functions, Properties of Beta and Gamma function. Dirichlet’s Integral. Application of double integrals and Triple Integral to find area and volume. Applications: Electromagnetism, Wireless Communication, Antenna Theory.

Matrix Algebra: Introduction to Matrices, Elementary Transformation, Inverse by E- transformation, Rank of a Matrix by Echelon Form, Solution of system of linear Equations by direct method (Gauss Elimination Method), and Iterative method (Gauss Seidel Method), Eigen Values & Eigen Vectors, Diagonalization. Applications: Error detection and correction codes, Loop Current Analysis.

Vector spaces (over the field of real numbers), Subspaces, Spanning set, Linear independence, Basis and Dimension. Linear transformations, Range and Null space, Rank- Nullity theorem, Matrix of a linear transformation. Applications : Digital signal processing (DSP), wireless communication, antenna array processing, image.

Scalar point function, Vector point function, Gradient of a scalar field, Directional derivatives, Divergence and curl of a vector function and their application to solenoidal and irrotational vectors respectively. Integration of Vectors, Stokes Theorem and Gauss Divergence Theorem(Without Proof). Applications: Electromagnetism, Wireless Communication, Antenna Theory.