Course objectives
- Apply differential calculus to analyze and optimize electronics and electrical engineering systems. 2. Use multiple integrals to solve problems in electromagnetics and wireless communication. 3. Apply matrix algebra to analyze electrical networks and communication systems. 4. Solve differential equations for electrical circuits, signals, and control systems. 5. Apply vector calculus to analyze electromagnetic fields and antenna systems.
Unit I
Differential Calculus: 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.
Unit II
Multiple Integrals : 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.
Unit III
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.