## Prakhar Shrivastava is teaching live on Unacademy Plus

ENGINEERING MATHEMATICS PROBABLITY AND STATISTICS By Prakhar Shrivastava

Educator's Introduction Prakhar Shrivastava I am an Industrial and production engineering graduate JEC, Jabalpur GATE 2016 AIR 03 (PI) GATE SCORE 989/1000 Cracked written and interview for IEOR, IIT B Currently pursuing PGDIE from NITIE, Mumbai (One of the 15 centers of excellence including IIT's and IIM's) My hobbies - Tennis, Street plays and big time Foodie

Section 1: Engineering Mathematics Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green's theorems. Differential equations: First order equations (linear and nonlinear): higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems Laplace transforms solutions of heat, wave and Laplace's equations. Complex variables: Analytic functions: Cauchy-Riemann equations; Cauchy's integral theorem and integral formula: Taylor and Laurent series. Probability and Statistics: Definitions of probability, sampling theorems, conditional probability: mean, median, mode and standard deviation; random variables. binomial, Poisson and normal distributions Numerical Methods: Numerical solutions of linear and non-linear algebraic equations: integration by trapezoidal and Simpson's rules; single and multi-step methods for differential equations.

Pathway 1. Probability and statistics 2. Differential equations 3. Complex variables 4. Linear algebra 5. Calculus - Derivatives 1. Linear algebra 2. Calculus - Derivatives, Integrals and theorems 3. Differential equations 4. Complex variables 5. Probability and statistics 6. Numerical methods Integrals and theorems 6. Numerical methods Efficiency increases with smart study

PRACTISE,!!!! 1. Probability and statistics - 50-70 Questions 2. Differential equations 50-60 questions from each type 3. Complex variables 40 unique questions at least 4. Linear algebra - 70 questions 5. Calculus Derivatives, Integrals and theorems 150-180 6. Numerical methods 25-30 questions Can score 12-13 marks easily 15

TIMELINE 1. Probability and statistics - 4-5 days to learn and practice 2. Differential equations 5 days to learn and practice 3. Complex variables 5 days to learn and practice 4. Linear algebra 3 days to learn and practice 5. Calculus Derivatives, Integrals and theorems 9-11 days to learn and practice 6. Numerical methods 3-4 days to learn and practice All of you can do it ! Your willingness motivates Us

Probability and Statistics 1. Definition of Probability and basic operations 2. Sampling theorem 8. Conditional probability 4. Mean, median, mode and standard deviation 5. Random variables 6. Distributions