PE GATE Syllabus : Mathemaics

Mathematics Petroleum Engineering GATE syllabus

Linear Algebra: 

• Matrix algebra, 
• Systems of linear equations, 
• Eigen values and eigenvectors. 

Calculus: 

• Functions of single variable, 
• Limit, continuity and differentiability, 
• Taylor series, 
• Mean value theorems, 
• Evaluation of definite and improper integrals, 
• Partial derivatives, 
• Total derivative, 
• Maxima and minima, 
• Gradient, Divergence and Curl, 
• Vector identities, 
• Directional derivatives, 
• Line, Surface and Volume integrals, 
• Stokes, Gauss and Green’stheorems. 

Differential equations: 

• First order equations (linear and nonlinear), 
• Higher order linear differential equations with constant coefficients, 
• Cauchy’s and Euler’s equations, 
• Initial and boundary value problems, 
• Laplace transforms, 
• Solutions of one dimensional heat and wave equations and Laplace equation. 

Complex variables: 

• Complex number, 
• polar form of complex 
• number, triangle inequality. 

Probability and Statistics: 

• Definitions of probability and sampling theorems, 
• Conditional probability, 
• Mean, median, mode and standard deviation, 
• Random variables, 
• Poisson, Normal and Binomial distributions, 
• Linear regression analysis. 

Numerical Methods: 

• Numerical solutions of linear and non-linear algebraic equations. 
• Integration by trapezoidal and Simpson’s rule. 
• Single and multi-step methods for numerical solution of differential equations. 

  

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