GATE - 2013: Engineering Mathematics (English)

Table of Contents
1. Linear Algebra 
1.1 Introduction
1.2 Algebra of Matrices
1.3 Determinants
1.4 Inverse of Matrix
1.5 Rank of Matrix
1.6 Subspaces: Basis and Dimension 
1.7 System of Linear Equations
1.8 Eigen Values and Eigen Vectors
2. Calculus
2.1 Limit
2.2 Continuity
2.3 Differentiability
2.4 Mean Value Theorems
2.5 Computing the Derivative
2.6 Application of Derivatives
2.7 Partial Derivatives 
2.8 Total Derivatives
2.9 Maxima and Minima (of function of two variables) 
2.10 Theorems of Integral Calculus
2.11 Definite Integrals
2.12 Applications of Integration
2.13 Multiple Integrals and their applications
2.14 Vectors
3. Differential Equations
3.1 Introduction
3.2 Differential Equations of first order
3.3 Linear differential equations (of nth order)
3.4 Two other methods of finding particular integral
4. Complex Functions
4.1 Introduction
4.2 Complex Functions
4.3 Limit of a complex function
4.4 Derivative of f(z)
4.5 Analytic Functions
4.6 Complex Integration
4.7 Cauchy's Theorem
4.8 Cauchy's Integral Formulae
4.9 Series of Complex terms
4.10 Zeroes and singularities (poles) of an analytic function
4.11 Residues
5. Probability and Statistics 
5.1 Probability Fundamentals 
5.2 Statistics 
5.3 Probability Distributions
6. Numerical Methods
6.1 Introduction
6.2 Numerical Solution of system of linear equations
6.3 Numerical solution of non linear equations
6.4 Numerical Integration by trapezoidal and Simpson's rules
6.5 Numerical Solutions of ordinary differential equations
7. Laplace Transforms
7.1 Introduction
7.2 Definitions 
7.3 Transforms of elementary functions
7.4 Properties of Laplace transforms
7.5 Evaluation of integrals by Laplace Transforms
7.6 Inverse Laplace Transforms
7.7 Unit Step function
7.8 Second shifting property
7.9 Unit Impulse function
7.10. Periodic Functions