**Algebra & Geometry:**Solution of equations, Linear algebra: Determinants, Matrices, Vector algebra and Solid geometry.**Calculus:**Differential calculus, Partial differentiation, Integral calculus, Multiple integrals, Vector calculus.**Series:**Infinite Series and Fourier Series.**Differential Equations:**Differential equations of first order and their applications, Linear differential equations and their applications, Differential equations of different types, Series solution of differential equations and special functions, Partial differential equations and their applications.**Complex Analysisc:**Complex numbers and functions, Calculus of complex functions.**Transforms:**Laplace Transforms, Fourier transforms and Z-transforms.**Numerical Techniques:**Empirical Laws and Curve fitting, Statistical methods, Probability and Distributions, Sampling and Inference, Numerical methods, Finite differences and Interpolation, Difference equations, Numerical solution of Ordinary and Partial differential equations, Linear programming.**Special Topics:**Calculus of variations, Integral equations, Discrete mathematics, Tensors.

**Table of Contents****Unit I: Algebra, Vectors and Geometry**

- Solution of Equations
- Linear Algebra: Determinants, Matrices
- Vector Algebra and Solid Geometry

**Unit II: Calculus**

- Differential Calculus & Its Applications
- Partial Differentiation & Its Applications
- Integral Calculus & Its Applications
- Multiple Integrals & Beta, Gamma Functions
- Vector Calculus & Its Applications

**Univ III: Series**

- Infinite Series
- Fourier Series & Harmonic Anslysis

**Unit IV: Differential Equations**

- Differential Equations of First Order
- Applications of Differential Equations of First Order
- Linear Differential Equations
- Applications of Linear Differential Equations
- Differential Equations of Other Types
- Series Solution of Differential Equations and Special Functions
- Partial Differential Equations
- Applications of Partial Differential Equations

**Unit V: Complex Analysis**

- Complex Numbers and Functions
- Calculus of Complex Functions

**Unit VI: Transforms**

- Laplace Transforms
- Fourier Transforms
- Z-Transforms

**Unit VII: Numerical Techniques**

- Empirical Laws and Curve-fitting
- Statistical Methods
- Probability and Distributions
- Sampling and Inference
- Numerical Solution of Equations
- Finite Differences and Interpolation
- Numerical Differentiation and Integration
- Difference Equations
- Numerical Solution of Ordinary Differential Equations
- Numerical Solution of Partial Differential Equations
- Linear Programming

**Unit VIII: Special Topics**

- Calculus of Variations
- Integral Equations
- Discrete Mathematics
- Tensor Analysis
- Useful Information
- Tables
- Answers to Problems
- Index

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