Sequences and Series of Real Numbers Sequence of real num- bers, convergence of sequences, bounded and monotone sequences, con- vergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms comparison test, ratio test, root test; Leibniz test for convergence of alternating series.
Functions of One Real Variable: Limit, continuity, intermediate value property, differentiation, Rolles Theorem, mean value theorem, L'Hospital rule, Taylor's theorem, maxima and minima.
Integral Calculus: Integration as the inverse process of differenti- ation, definite integrals and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculat- ing volumes using triple integrals.
Differential Equations: Ordinary differential equations of the first order of the form y'=f(x,y), Bernoullis equation, exact differential equa- tions, integrating factor, orthogonal trajectories, homogeneous differ- ential equations, variable separable equations, linear differential equa- tions of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.
Vector Calculus: Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theo- rems.
Linear Algebra: Finite dimensional vector spaces, linear indepen- dence of vectors, basis, dimension, linear transformations, matrix rep- resentation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equa- tions, consistency conditions, eigenvalues and eigenvectors for matrices, Cayley-Hamilton theorem.
Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylors series, radius and interval of conver- gence, term-wise differentiation and integration of power series.
Digital Design: Number Systems & Codes, Boolean Algebra and Minimization Techniques, Digital CMOS Logic, Combinatorial Circuits & Systems, Sequential Circuits & Systems, Finite State Machines.
Analog Electronics: Circuit Theorems and KCL/KVL, Op-amp, RC, RLC Circuits, Physics of transistors, Characteristics and biasing of BJT, Small signal (incremental) equivalent circuits, CE, CB and CC amplifiers, Difference Amplifier Design, Oscillators and Filters: Bode plots, Clipping, Clamping and other Non-Linear Op-Amp applications, Power supplies, DAC: Principles and Circuits, ADC: Principles and Circuits.
Signals and Systems: Linear time invariant (LTI) systems: Discrete and continuous, Fourier representation of periodic signals, Fourier Transform of aperiodic signals, Laplace and z-transform, Linear Feedback Systems.
Digital Signal Processing: Transform analysis of LTI systems, Structures for Discrete Time systems, FIR Filter Design Techniques, FFT, Multi-rate digital Signal Processing, Adaptive signal Processing, Stochastic signals, Wiener Filtering, LMS and RLS algorithms, spectral estimation.