Syllabus for GATE Mathematics ExamLinear Algebra- Vector spaces
- Basis and dimension
- Linear transformations
- Matrix algebra
- Eigenvalues and eigenvectors
- Orthogonality
- Gaussian elimination
Calculus- Limits, continuity and differentiability
- Mean value theorem
- Taylor series
- Evaluation of definite and improper integrals
- Partial derivatives
- Maxima and minima
- Multiple integrals
Ordinary Differential Equations (ODE)- First order ODE
- Second order linear ODE
- Higher order linear ODE with constant coefficients
- Cauchy’s and Euler’s equations
- Laplace transforms
Partial Differential Equations (PDE)- Classification of second order PDE
- Solution of wave equation, heat equation and Laplace equation
Complex Analysis- Analytic functions
- Cauchy-Riemann equations
- Contour integration
- Cauchy’s integral theorem and integral formula
- Taylor and Laurent series
Numerical Methods- Solution of algebraic and transcendental equations
- Bisection method
- Newton-Raphson method
- Interpolation and extrapolation
- Numerical integration
- Gauss elimination
- Gauss-Seidel method
Probability and Statistics- Probability spaces
- Conditional probability
- Mean, median, mode and standard deviation
- Random variables
- Binomial, Poisson and normal distributions
- Correlation and regression
Discrete Mathematics- Propositional and first order logic
- Sets, relations and functions
- Permutations, combinations and counting
- Graph theory
- Trees and spanning trees
Real Analysis- Sequences and series of real numbers
- Continuity
- Differentiability
- Riemann integral
- Improper integrals
Linear Programming- Linear programming problems
- Simplex method
- Duality
Marks Weightage- Linear Algebra: 10-12 marks
- Calculus: 8-10 marks
- ODE: 6-8 marks
- PDE: 6-8 marks
- Complex Analysis: 4-6 marks
- Numerical Methods: 6-8 marks
- Probability and Statistics: 8-10 marks
- Discrete Mathematics: 6-8 marks
- Real Analysis: 8-10 marks
- Linear Programming: 4-6 marks
EduRev provides Mock Test Series for GATE Mathematics Exam to help students prepare effectively and efficiently for the exam.
This course is helpful for the following exams: Mathematics