Differential Calculus and Linear Algebra

Course objectives
1. 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.

Course content
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. 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. 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: 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. Vector Calculus: 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. Course Outcomes CO Course Outcome Statement KL CO1 Apply differential calculus to solve and optimize engineering K3 problems. CO2 Use multiple integrals to analyze engineering systems and K3 field applications. CO3 Apply matrix algebra to solve linear systems and circuit K3 problems. CO4 Solve differential equations for modeling electrical and K4 electronic systems. CO5 Apply vector calculus to analyze electromagnetic fields and K4 communication systems.