GATE Section-XE-A Engineering Mathematics Syllabus
Course Structure
| Units |
Topics |
| Unit 1 |
Linear Algebra |
| Unit 2 |
Calculus |
| Unit 3 |
Vector Calculus |
| Unit 4 |
Complex Variables |
| Unit 5 |
Ordinary Differential Equations |
| Unit 6 |
Partial Differential Equations |
| Unit 7 |
Probability and Statistics |
| Unit 8 |
Numerical Methods |
Course Syllabus
Unit 1: Linear Algebra
- Algebra of matrices
- Inverse and rank of a matrix
- System of linear equations
- Symmetric, skew-symmetric and orthogonal matrices
- Determinants
- Eigenvalues and eigenvectors
- Diagonalisation of matrices
- Cayley-Hamilton Theorem
Unit 2: Calculus
Chapter 1: Functions of single variable
- Limit, continuity and differentiability
- Mean value theorems
- Indeterminate forms and L'Hospital's rule
- Maxima and minima
- Taylor's theorem
- Fundamental theorem and mean value-theorems of integral calculus
- Evaluation of definite and improper integrals
- Applications of definite integrals to evaluate areas and volumes
Chapter 2: Functions of two variables
- Limit, continuity and partial derivatives
- Directional derivative
- Total derivative
- Tangent plane and normal line
- Maxima, minima and saddle points
- Method of Lagrange multipliers
- Double and triple integrals, and their applications
Chapter 3: Sequence and Series
- Convergence of sequence and series
- Tests for convergence
- Power series
- Taylor's series
- Fourier Series
- Half range sine and cosine series
Unit 3: Vector Calculus
Gradient, divergence and curl
Line and surface integrals
Green's theorem, Stokes theorem and Gauss divergence theorem (without proofs)
Unit 4: Complex Variables
- Analytic functions
- Cauchy-Riemann equations
- Line integral, Cauchy's integral theorem and integral formula (without proof)
- Taylor's series and Laurent series
- Residue theorem (without proof) and its applications
Unit 5: Ordinary Differential Equations
- First order equations (linear and nonlinear)
- Higher order linear differential equations with constant coefficients
- Second order linear differential equations with variable coefficients
- Method of variation of parameters
- Cauchy-Euler equation
- Power series solutions
- Legendre polynomials, Bessel functions of the first kind and their properties
Unit 6: Partial Differential Equations
- Classification of second order linear partial differential equations
- Method of separation of variables
- Laplace equation
- Solutions of one dimensional heat and wave equations
Unit 7: Probability and Statistics
- Axioms of probability
- Conditional probability
- Bayes' Theorem
- Discrete and continuous random variables −
- Binomial
- Poisson
- Normal distributions
- Correlation and linear regression
Unit 8: Numerical Methods
Solution of systems of linear equations using LU decomposition
Gauss elimination and Gauss-Seidel methods
Lagrange and Newton's interpolations
Solution of polynomial and transcendental equations by Newton-Raphson method
Numerical integration by trapezoidal rule
Simpson's rule and Gaussian quadrature rule
Numerical solutions of first order differential equations by Euler's method and 4th order Runge-Kutta method
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