Analysis and linear algebra for finance part i

Patrick Roger

Analysis and Linear Algebra for Finance:
Part I

Patrick ROGER
LaRGE Research Center
EM Strasbourg Business School
University of Strasbourg

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Analysis and Linear Algebra for Finance: Part I
First edition
© 2013 Patrick Roger & bookboon.com (Ventus Publishing ApS)
ISBN 978-87-403-0412-1

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             

           

 

Analysis

and Linear
Algebra for 
Finance:
Part I

Contents

              
              
          

Contents

   

Introduction

6

1 
Preliminaries
  
      

7

1.1  
Sets
and subsets
   

       
Binary relations
   1.2
 

8

1.3

Mappings

20

1.4   
Topology
of           
  
 

                   
2

Functions of one variable

  
  

2.1   
Deinitions
and

notations
2.2
2.3

17
25
43
44

Limits and continuity

50

 Diferentiation
        

61

Logarithms
     2.4
  
 and
 exponential
  functions
   
   













2.5
Polynomial approximations and Taylor
formula



70
75

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Analysis and Linear Algebra for Finance: Part I

Contents

3

Integrals

81

3.1

Integral of a step function

81

3.2

General case

86

3.3

Computations

94

3.4

Improper integrals

98

4

Matrices

101

4.1

Deinitions

101

4.2

Elementary algebra on matrices

104

4.3

Linear equations

115

360°
thinking

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Analysis and Linear Algebra for Finance: Part I






             
             
          
           
          
          
            
         
          
          
            
           
       
         
          
             
         

           
            
          
         
         
             



          
  


          

6
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Introduction


Analysis and Linear Algebra for Finance: Part I

Preliminaries

 

         
          
            
        
          
           
             
          
 
        
          
            
            
          
            

             
              
            


          



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Analysis and Linear Algebra for Finance: Part I



  

            
          
            
        



  

            
           

            
              
          
           
       
             
          
            
           
            
    



  

             
      
                   



            
   
              
      

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Preliminaries


Analysis and Linear Algebra for Finance: Part I

   



              
      

 

          


               
  
                  
                
      
          
       




 

              
       


           



              
             
             
              
  
             
    
               
               
             

9
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