Content

1. Complex Numbers 

1.1 Introduction

1.2 Basic operations on complex numbers

1.3 Modulus and arguments of complex numbers

1.4 Properties of modulus and arguments

1.5 De–Moiver’s theorem   

1.6 Roots of a polynomial equations   

2. Sequences and Series    

2.1 Introduction   

2.2 Sequences   

2.3 Series

2.4 Approximation of functions by series 

3. Partial Differentiations

3.1 Introduction   

3.2 Partial derivatives    

3.3 Rules of partial differentiations  (Chain Rules)     

3.4 Higher order partial derivatives     

3.5 Maxima and minima 

4. Differential Equations 

4.1 Introduction   

4.2 An Order and degree of differential equations    

4.3 General and particular solution of differential equations     

4.4 Differential equations of 1st order and 1st degree   

4.5 Homogeneous differential equations 

4.6 Non homogeneous differential equations     

4.7 Exact differential equations

4.8 Integrating Factors (I.F.)

4.9 Linear differential equations    

4.10 Applications of differential equations

5. Matrices and System of Linear Equations

5.1 Introduction   

5.2 Elementary transformations    

5.3 Rank of a matrix  

5.4 Row echelon form of a matrix  

5.5 System of linear equations      

5.6 Homogeneous system of linear equations  

5.7 Non homogeneous system of linear equations

6. Vector Spaces

6.1 Introduction   

6.2 Euclidean N–space 

6.3 General vector space    

6.4 Subspaces   

6.5 Linear combination 

6.6 Linear independence and dependence   

6.7 Eigenvalues and eigenvectors 

6.8 Diagonalization of matrices