# GATE 2015 Engineering Mathematics Online Crash Course

Comprehensive Online Coaching for GATE Engineering Mathematics.

13 Weeks

Course Start Date: 3 May 2013

tutorials

live classes

test

The Engineering Mathematics section of GATE 2014 Exam may seem daunting due to its generic and vast nature. However, believe us it is one of the easiest sections to prepare, provided you get the right resources and guidance. **Enroll Now **in this gate course online and get taught by an experienced faculty for the GATE Engineering Mathematics exam.

Engineering Mathematics in GATE 2014 will play a vital role in maximizing your score.

**In fact, a good performance in Engineering Mathematics will ensure you securing the minimum qualification marks in GATE 2014 exam.**

**Why you should Enroll in this Course?**

This GATE online coaching provides a Quick guide to most troubling section of GATE 2014 exam – Engineering Mathematics.

This GATE coaching provides full Engineering Mathematics preparation with live classes, online material & doubt clearing sessions that benefits both new and old aspirants equally.

Package of this Engineering Mathematics Course:

45 Live Online Classes of an hour each.

Online Study Material.

**Note: **This GATE 2014 Engineering Mathematics Online Crash Course will run for 2 months. Classes must be booked 48 hours in advance.

**Detail Course Outline of this Engineering Mathematics Course:**

**Linear Algebra: **Algebra of matrices, inverse, rank, system of linear equations, symmetric, skew symmetric and orthogonal matrices. Hermitian, skew-Hermitian and unitary matrices, eigen values and eigen vectors, diagonalisation of matrices, Cayley-Hamilton Theorem.

**Calculus: **Functions of single variable, limit, continuity and differentiability, Mean value theorems, Indeterminate forms and L'Hospital rule, Maxima and minima, Taylor's series, Fundamental and mean value-theorems of integral calculus. Evaluation of definite and improper integrals, Beta and Gamma functions, Functions of two variables, limit, continuity, partial derivatives, Euler's theorem for homogeneous functions, total derivatives, maxima and minima, Lagrange method of multipliers, double and triple integrals and their applications, sequence and series, tests for convergence, power series, Fourier Series, Half range sine and cosine series.

**Complex variables: **Analytic functions, Cauchy-Riemann equations, Application in solving potential problems, Line integral, Cauchy's integral theorem and integral formula (without proof), Taylor's and Laurent' series, Residue theorem (without proof) and its applications.

**Vector Calculus: **Gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green's theorems (without proofs) applications.

**Ordinary Differential Equations: **First order equation (linear and nonlinear), Second order linear differential equations with variable coefficients, Variation of parameters method, higher order linear differential equations with constant coefficients, Cauchy- Euler's equations, power series solutions, Legendre polynomials and Bessel functions of the first kind and their properties.

**Partial Differential Equations: **Separation of variables method, Laplace equation, solutions of one dimensional heat and wave equations.

**Probability and Statistics: **Definitions of probability and simple theorems, conditional probability, Bayes Theorem, random variables, discrete and continuous distributions, Binomial, Poisson, and normal distributions, correlation and linear regression.

**Numerical Methods: **Solution of a system of linear equations by L-U decomposition, Gauss-Jordan and Gauss-Seidel Methods, Newton's interpolation formulae, Solution of a polynomial and a transcendental equation by Newton-Raphson method, numerical integration by trapezoidal rule, Simpson's rule and Gaussian quadrature, numerical solutions of first order differential equation by Euler's method and 4th order Runge-Kutta method.

Language of instruction: English

Er. Himanshu Vasistha holds a B.Tech in Mechanical Engineering and is a Marine Engineering Class 3 MNZ. He has more 6 years of teaching experience for Mathematics and Engineering topics for IES and GATE & has been associated with best GATE coaching institutes. He has these publications to his credit:

Presentation on Potential of Computerized Engine Control in Future- A Review at Trends in Mechanical Engineering at CIET, Jansala

Presentation on the topic EDM in Nuclear Power Plants- A review at National Conference on “Emerging Trends in Manufacturing Systems” (ETMS-2005) held at JMIT Radaur, Yamuna Nagar.

Presentation on Power Electronics and Bluetooth in Automobiles at Inauguration of SAE Collegiate Club.

He lives in Chandigarh and is associated as an expert consultant and coach with many reputed IES and GATE training academies.