Chapter 1 Interpolation and Curve Fitting
1.1 Introduction
1.2 Finite Differences
1.3 Interpolation
1.4 Error in Polynomial Interpolation
1.5 Lagrange’s Interpolation Formula for Unequal Intervals
1.6 Spline Interpolation
1.7 Curve Fitting
Chapter 2 Numerical Techniques
2.1 Introduction
2.2 Graphical Method
2.3 Bisection Method
2.4 Method of False Position Method (Regula - Falsi Method)
2.5 Iteration Method
2.6 Newton - Raphson Method
2.7 Matrix Decomposition Methods (LU Decomposition Method)
2.8 Gauss - Seidel and Jacobi Iteration Method
2.9 Numerical Differentiation
2.10 Numerical Integration
2.11 Solution of Ordinary Differential Equations by Taylor’s Series Method
2.12 Picard’s Method
2.13 Solution of Ordinary Differential Equation by Euler’s Method
2.14 Solution of Ordinary Differential Equation by Runge - Kutta Methods
2.15 Predictor - Corrector Methods
Chapter 3 Fourier Series
3.1 Introduction
3.2 Limit of a Function
3.3 Continuity
3.4 Periodic Functions
3.5 Fourier Series
3.6 Dirichlet’s Conditions
3.7 Euler’s Formulae
3.8 Jump of a Function
3.9 Fourier Series for Discontinuous Functions
3.10 Even and Odd Functions
3.11 Change of Interval
3.12 Half - Range Series
Chapter 4 Fourier Transforms
4.1 Introduction
4.2 Integral Transforms
4.3 Fourier Integral
4.4 Complex Form of Fourier Integral
4.5 Fourier Transforms and Inversion Transforms
4.6 Finite Fourier Transforms and Their Inverse
4.7 Parseval’s Identity
4.8 Applications of Fourier Transforms
Chapter 5 Partial Differential Equations and Their Applications
5.1 Introduction
5.2 Formation of Partial Differential Equations
5.3 Solution of Partial Differential Equations of First Order
5.4 Solution of Linear PDEs
5.5 Non - Linear Partial Differential Equations of First Order
5.6 Classification of Second - order PDEs
5.7 Equations Reducible to Standard Forms
5.8 Charpit’s Method
5.9 Method of Separation of Variables
5.10 Solution of One - Dimensional Wave Equation
5.11 Solution to Two - Dimensional Wave Equation
5.12 Solution of One - Dimensional Heat Equation
5.13 Steady Two - Dimensional Heat Problems: Laplace’s Equation
5.14 Solution of Laplace Equation in Two Dimensions
Chapter 6 Vector Calculus and Its Applications
6.1 Introduction
6.2 Vector Algebra
6.3 Differentiation of a Vector
6.4 Gradient of a Scalar Point Function
6.5 Divergence and Curl
6.6 Flux, Solenoidal Vector, Irrotational Vector, Conservative Vector Field, Scalar Potential
6.7 Vector Integration
6.8 Surface and Volume Integrals
6.9 Green’s Theorem in the Plane
6.10 Gauss Divergence Theorem
6.11 Stokes’ Theorem
Important Points and Formulas
Exercises
Answers
Question Paper 2014