Analysis and Linear Algebra for Finance: Part I Patrick Roger Download free books at Patrick Roger Analysis and Linear Algebra for Finance: Part I Patrick ROGER LaRGE Research Center EM Strasbourg Business School University of Strasbourg Download free eBooks at bookboon.com Analysis and Linear Algebra for Finance: Part I First edition © 2013 Patrick Roger & bookboon.com (Ventus Publishing ApS) ISBN 978-87-403-0412-1 Download free eBooks at bookboon.com                                Analysis and Linear Algebra for  Finance: Part I Contents                                          Contents Introduction     1 Preliminaries            1.1   Sets and subsets             Binary relations    1.2   17 1.3 Mappings 20 1.4    Topology of  25                                    Functions of one variable 43            2.1 Definitions and notations 44 2.2 Limits and continuity           2.3 Differentiation 360° thinking Logarithms      2.4     and  exponential   functions                     2.5 Polynomial approximations and Taylor formula  Deloitte & Touche LLP and affiliated entities 360° thinking 50 61 70 75 360° thinking Discover the truth at www.deloitte.ca/careers © Deloitte & Touche LLP and affiliated entities Discover the truth at www.deloitte.ca/careers Download free eBooks at bookboon.com © Deloitte & Touche LLP and affiliated entities at www.deloitte.ca/careers Discover the truth Click on the ad to read more © Deloitte & Touche LLP and affiliated entities Dis 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 98 Improper integrals 4 Matrices 101 4.1 Definitions 101 4.2 Elementary algebra on matrices 104 4.3 Linear equations 115 Increase your impact with MSM Executive Education For almost 60 years Maastricht School of Management has been enhancing the management capacity of professionals and organizations around the world through state-of-the-art management education Our broad range of Open Enrollment Executive Programs offers you a unique interactive, stimulating and multicultural learning experience Be prepared for tomorrow’s management challenges and apply today For more information, visit www.msm.nl or contact us at +31 43 38 70 808 or via admissions@msm.nl For more information, visit www.msm.nl or contact us at +31 43 38 70 808 the globally networked management school or via admissions@msm.nl Executive Education-170x115-B2.indd Download free eBooks at bookboon.com 18-08-11 15:13 Click on the ad to read more Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                                                                          Download free eBooks at bookboon.com Introduction Analysis and Linear Algebra for Finance: Part I Preliminaries                                                                                                                                                                                                                              Download free eBooks at bookboon.com Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                                                                      Download free eBooks at bookboon.com Preliminaries Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                                                                    Download free eBooks at bookboon.com Preliminaries Analysis and Linear Algebra for Finance: Part I     Preliminaries                                                       GOT-THE-ENERGY-TO-LEAD.COM We believe that energy suppliers should be renewable, too We are therefore looking for enthusiastic new colleagues with plenty of ideas who want to join RWE in changing the world Visit us online to find out what we are offering and how we are working together to ensure the energy of the future Download free eBooks at bookboon.com 10 Click on the ad to read more Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                         Download free eBooks at bookboon.com 113 Matrices Analysis and Linear Algebra for Finance: Part I     Matrices                                                                                                                                                                                                                                                                                                         Download free eBooks at bookboon.com 114 Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                    Download free eBooks at bookboon.com 115 Matrices Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                      Download free eBooks at bookboon.com 116 Matrices Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                            Download free eBooks at bookboon.com 117 Matrices Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                               Download free eBooks at bookboon.com 118  Matrices Analysis and Linear Algebra for Finance: Part I     Matrices                                                                       Download free eBooks at bookboon.com 119 Click on the ad to read more Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                                 Download free eBooks at bookboon.com 120 Matrices Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                                                                                Download free eBooks at bookboon.com 121 Matrices Analysis and Linear Algebra for Finance: Part I                                                                                                                                                                                                                     Download free eBooks at bookboon.com                 122       Matrices Analysis and Linear Algebra for Finance: Part I    Matrices                                                                                                                                                                                                                                         Download free eBooks at bookboon.com 123               Analysis and Linear Algebra for Finance: Part I Index Index right, 63 second-order, 68 bijection, 22 exterior, 30 bound infimum, 28 frontier, 30 lower, 27, 49 function, 44 supremum, 28 affine, 44 upper, 27, 49 bounded, 49 compound, 67 concave, 61 cardinality, continuous, 55 closure, 30 convex, 61 compact, 31 decreasing, 46 complement, 32 derivative, 62 Consol bond, 36 differentiable, 62 domain, 44 derivative, 62 even, 45 higher order, 68 increasing, 46 left, 63 left-continuous, 56 boundary, 30 Turning a challenge into a learning curve Just another day at the office for a high performer Accenture Boot Camp – your toughest test yet Choose Accenture for a career where the variety of opportunities and challenges allows you to make a difference every day A place where you can develop your potential and grow professionally, working alongside talented colleagues 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monotonic, 57 product by a real number, 106 odd, 45 square, 102 range, 44 substraction, 106 Riemann-integrable, 87 transpose, 104 right-continuous, 55 triangular, 102 maximum image, 20 global, 50 inclusion, 11 local, 49 injection, 22 method integral Gauss, 120 improper, 98 substitution, 118 of a step function, 83 minimum Riemann, 87 global, 49 local, 49 interior, 30 intersection, 12 interval, 28 limit, 50 ordering, 17 complete, 18 partial, 18 infinite, 53 left, 52 partition, 15 right, 51 pre-ordering, 17 Mac Laurin formula, 78 range, 20 mapping, 20 bijective, 22 relation identity, 24 asymmetric, 17 image, 20 binary, 17 injective, 22 equivalence, 19 inverse, 23 graph, 20 one-to-one, 22 ordering, 17 range, 20 refl?exive, 17 surjective, 22 symmetric, 17 transitive, 17 matrix, 101 reciprocal, 22 diagonal, 102 identity, 110 sequence, 32 inverse, 110 adjacent, 41, 87 invertible, 110 arithmetic, 36 Download free eBooks at bookboon.com 125 Analysis and Linear Algebra for Finance: Part I Index Cauchy, 34 lower bound, 27 convergence, 33 neighborhood, 29 decreasing, 37 null, 10 geometric, 36 open, 30 increasing, 37 partition, 14 set, subset, 11 boundary, 30 union, 12 bounded, 28, 31 upper bound, 27 cardinality, step function, 82 closed, 30 subdivision, 82 closure, 30 subset, 11 compact, 31, 35 surjection, 22 complement, 12 system element, Cramer, 117 empty, 10 homogeneous, 117 exterior, 30 impossible, 117 frontier, 30 indeterminate, 117 inclusion, 11 square, 117 interior, 29, 30 intersection, 12 Taylor The Wake the only emission we want to leave behind QYURGGF 'PIKPGU /GFKWOURGGF 'PIKPGU 6WTDQEJCTIGTU 2TQRGNNGTU 2TQRWNUKQP 2CEMCIGU 2TKOG5GTX 6JG FGUKIP QH GEQHTKGPFN[ OCTKPG RQYGT CPF RTQRWNUKQP UQNWVKQPU KU ETWEKCN HQT /#0 &KGUGN 6WTDQ 2QYGT EQORGVGPEKGU CTG QHHGTGF YKVJ VJG YQTNFoU NCTIGUV GPIKPG RTQITCOOG s JCXKPI QWVRWVU URCPPKPI HTQO  VQ  M9 RGT GPIKPG )GV WR HTQPV (KPF QWV OQTG CV YYYOCPFKGUGNVWTDQEQO Download free eBooks at bookboon.com 126 Click on the ad to read more Analysis and Linear Algebra for Finance: Part I expansion, 79 formula, 78 Mac-Laurin, 78 Index union, 12 variable dependent, 44 independent, 44 Download free eBooks at bookboon.com 127 ... Preliminaries Analysis and Linear Algebra for Finance: Part I Download free eBooks at bookboon.com Preliminaries 26 Analysis and Linear Algebra for Finance: Part I      Preliminaries... bookboon.com 12 Preliminaries Analysis and Linear Algebra for Finance: Part I Download free eBooks at bookboon.com Preliminaries 13 Analysis and Linear Algebra for Finance: Part I    ... truth Click on the ad to read more © Deloitte & Touche LLP and affiliated entities Dis Analysis and Linear Algebra for Finance: Part I Contents 3 Integrals 81 3.1 Integral of a step function 81