GATE EE Online Coaching in Kerala

Linear Algebra

• Systems Of Linear Equations
• Matrix Algebra
• Eigenvalues And EigenVectors

Calculus:

• Evaluation Of Definite And Indefinite Integrals, Application Of Definite Integral To Obtain Area And Volume
• Limit, Continuity, And Differentiability
• Gradient, Divergence And Curl, Vector Identities
• Taylor Series
• Functions Of Single Variable
• Mean Value Theorems, Local Maxima And Minima
• Partial Derivatives
• Total Derivative
• Line, Surface And Volume Integrals
• Directional Derivatives

Ordinary Differential Equation (ODE): 

• Initial And Boundary Value Problems
• Euler-cauchy Equations
• Higher Order Linear Equations With Constant Coefficients

• First Order (Linear And Nonlinear) Equations

Partial Differential Equation (PDE): 

• First And Second Order One-dimensional Wave Equation And Two Dimensional Laplace Equation
• Fourier Series
• Separation Of Variables
• Solutions Of One-Dimensional Diffusion Equation

Probability and Statistics: 

• Linear Regression
• Sampling Theorems
• Descriptive statistics – Mean, median, mode, and standard deviation
• Random Variables – Discrete and Continuous, Poisson and Normal Distribution
• Conditional Probability

Numerical Methods: 

• Single And Multi-step Methods For First Order Differential Equations
• Newton’s And Lagrange Polynomials
• Numerical Solutions Of Linear And Non-linear Algebraic Equation
• Error Analysis
• Integration By Trapezoidal And Simpson’s Rule
• Numerical Differentiation

Network elements 

• Dependent Sources, R, L, C, M Elements
• Ideal Voltage And Current Sources
• Network solution methods: KVL, KCL, Node And Mesh Analysis
• Network Theorems: Thevenin’s, Norton’s, Superposition and Maximum Power Transfer Theorem

• Resonance
• Transient Response of dc & ac networks
• Sinusoidal Steady-State Analysis
• Balanced Three-Phase Circuits
• Two-Port Networks
• Complex Power And Power Factor in ac circuits
• Star-Delta Transformation

Section 3- Electromagnetic Fields

• Electric Field Intensity
• Coulomb’s Law
• Electric Flux Density
• Divergence
• Gauss’s Law
• Electric field and potential due to point, line, plane and spherical charge distributions
• Effect Of Dielectric Medium
• Biot-Savart’s Law
• Capacitance Of Simple Configurations
• Ampere’s Law
• Curl
• Self And Mutual Inductance Of Simple Configurations
• Lorentz Force
• Inductance
• Faraday’s Law
• Magnetomotive Force
• Magnetic Circuits
• Reluctance

• Average Value Calculation for any General Periodic Waveform
• Shifting and Scaling Properties
• Representation of Continuous and Discrete-Time Signals
• Linear Time-Invariant and Causal Systems
• Laplace Transform and Z Transform
• R.M.S. Value
• Sampling Theorem
• Fourier Series Representation of Continuous and Discrete-Time Periodic Signals
• Applications of Fourier Transform for Continuous and Discrete-Time Signals 

• Single-phase transformer: Equivalent Circuit, Open Circuit And Short Circuit Tests, Phasor Diagram, Regulation And Efficiency
• Three-phase transformers: connections, vector groups, parallel operation

• Electromechanical Energy Conversion Principles
• Auto-Transformer
• DC machines: separately excited, series and shunt, motoring and generating
• mode of operation and their characteristics, speed control of dc motors 
• Three-phase induction machines: principle of operation, types, performance, torque-speed characteristics, no-load and blocked-rotor tests, equivalent circuit, starting and speed control
• Synchronous machines: cylindrical and salient pole machines, performance and characteristics, regulation and parallel operation of generators, starting of synchronous motors
• Types Of Losses And Efficiency Calculations Of Electric Machines

• Models And Performance Of Transmission Lines And Cables
• Basic Concepts Of Electrical Power Generation
• Ac And Dc Transmission Concepts
• Economic Load Dispatch (With And Without Considering Transmission Losses)
• Electric Field Distribution And Insulators
• Series And Shunt Compensation
• Distribution Systems
• Bus Admittance Matrix
• Per-Unit Quantities
• Gauss- Seidel And Newton-Raphson Load Flow Methods
• Power Factor Correction
• Voltage And Frequency Control
• Symmetrical Components
• Principles of Over-Current, Differential, Directional And Distance Protection
• Symmetrical and Unsymmetrical Fault Analysis
• Circuit Breakers
• System stability concepts
• Equal Area Criterion

• Feedback Principle
• Mathematical Modelling And Representation Of Systems
• Transfer Function
• Transient And Steady-State Analysis Of Linear Time-Invariant Systems
• Block Diagrams And Signal Flow Graphs
• Stability Analysis Using Routh-Hurwitz And Nyquist Criteria
• Root Loci
• Bode Plots
• Lag, Lead And Lead-Lag Compensators
• Solution Of State Equations Of LTI Systems
• P, PI And PID Controllers
• State-Space Model 

• Measurement Of Voltage, Current, Power, Energy And Power Factor
• Bridges And Potentiometers
• Instrument Transformers
• Oscilloscopes, Error Analysis
• Phase, Time and Frequency measurement
• Digital Voltmeters And Multimeters
• Time And Frequency Measurement

• Simple diode circuits: Clamping, Clipping, Rectifiers
• Amplifiers: Biasing, Equivalent Circuit and Frequency Response

• Oscillators And Feedback Amplifiers
• Operational amplifiers: characteristics and applications; single stage active filters
• Active Filters: Sallen Key, Butterwoth, VCOs and timers, combinatorial and sequential logic circuits, multiplexers, demultiplexers, Schmitt triggers, sample and hold circuits, A/D and D/A converters.

• Static V-I characteristics and firing/gating circuits for Thyristor, MOSFET, IGBT; DC to DC conversion 
• Buck, Boost And Buck-Boost Converters
• Single and Three-Phase Configuration Of Uncontrolled Rectifiers
• Bidirectional ac to dc Voltage Source Converters
• Voltage And Current Commutated Thyristor Based Converters
• Magnitude And Phase Of Line Current Harmonics For Uncontrolled and Thyristor-Based Converters
• Single-Phase And Three-Phase Voltage And Current Source Inverters
• Power Factor And Distortion Factor Of ac to dc Converters
• Sinusoidal Pulse Width Modulation