Contents

1. Analytical Geometry of Two Dimensions  

1.1 Introduction     

1.2 Change of axes (Transformation of Axis)  

1.3 Invariants 

1.4 Removal of product term xy   

1.5 Conic sections   

1.6 Central conics   

1.7 Reduction to standard form   

2. Analytical Geometry of Three Dimensions 

2.1 Co-ordinates in space  

2.2 Distance of a point from the origin

2.3 Distance between two points  

2.4 Section formula  

2.5 Direction cosines

2.6 Angle between two lines in terms of D.C.S.     

2.7 The plane  

2.8 The straight lines     

3. Sphere   

3.1 Equation of a sphere   

3.2 Sphere passing through the circle of intersection of the given sphere and plane     

3.3 Intersection of a sphere with the line   

3.4 Tangent plane    

3.5 The condition of tangency    

3.6 Condition for orthogonality 

3.7 Section of a sphere by a plane     

4. System of Linear Equations 

4.1 Introduction     

4.2 Matrices   

4.3 Submatrix of a matrix  

4.4 Rank of a matrix 

4.5 Echelon form of a matrix     

4.6 System of linear equations   

4.7 System of homogeneous linear equations   

4.8 Gauss-elimination method

1. Continuous Function  

1.1 Continuity of a function     

1.2 Discontinuity of a function 

1.3 Combination of continuous function 

1.4 Properties of continuous functions on intervals

2. Differentiation

2.1 Introduction

2.2 The mean value theorems

2.3 L’ hospital’s rule     

2.4 Successive differentiation   

2.5 Taylor’s theorem 

2.6 Maxima and minima