Mathematics for Economics
|
|
- Arthur Morris Russell
- 6 years ago
- Views:
Transcription
1 Mathematics for Economics third edition Michael Hoy John Livernois Chris McKenna Ray Rees Thanasis Stengos The MIT Press Cambridge, Massachusetts London, England
2 c 2011 Massachusetts Institute of Technology All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher. This book was set in Helvetica and Times Roman by Westchester Book Group. Printed and bound in the United States of America. Library of Congress Cataloging-in-Publication Data Mathematics for economics / Michael Hoy... [et al.]. 3rd ed. p. cm. Includes index. ISBN (hbk. : alk. paper) ISBN (pbk. : alk. paper) 1. Economics, Mathematical. I. Hoy, Michael, 1953 Sept. 22 HB135. M dc
3 Contents Preface Part I xiii Introduction and Fundamentals Chapter 1 Introduction What Is an Economic Model? How to Use This Book Conclusion 9 Chapter 2 Review of Fundamentals Sets and Subsets Numbers Some Properties of Point Sets in R n Functions 41 Chapter 3 Sequences, Series, and Limits Definition of a Sequence Limit of a Sequence Present-Value Calculations Properties of Sequences Series 84 Part II Univariate Calculus and Optimization Chapter 4 Continuity of Functions Continuity of a Function of One Variable Economic Applications of Continuous and Discontinuous Functions 113
4 viii CONTENTS Chapter 5 The Derivative and Differential for Functions of One Variable Definition of a Tangent Line Definition of the Derivative and the Differential Conditions for Differentiability Rules of Differentiation Higher Order Derivatives: Concavity and Convexity of a Function Taylor Series Formula and the Mean-Value Theorem 185 Chapter 6 Optimization of Functions of One Variable Necessary Conditions for Unconstrained Maxima and Minima Second-Order Conditions Optimization over an Interval 220 Part III Linear Algebra Chapter 7 Systems of Linear Equations Solving Systems of Linear Equations Linear Systems in n-variables 250 Chapter 8 Matrices General Notation Basic Matrix Operations Matrix Transposition Some Special Matrices 293 Chapter 9 Determinants and the Inverse Matrix Defining the Inverse Obtaining the Determinant and Inverse of a 3 3 Matrix The Inverse of an n n Matrix and Its Properties Cramer s Rule 329 Chapter 10 Some Advanced Topics in Linear Algebra Vector Spaces The Eigenvalue Problem Quadratic Forms 378
5 CONTENTS ix Part IV Multivariate Calculus Chapter 11 Calculus for Functions of n-variables Partial Differentiation Second-Order Partial Derivatives The First-Order Total Differential Curvature Properties: Concavity and Convexity More Properties of Functions with Economic Applications Taylor Series Expansion* 464 Chapter 12 Optimization of Functions of n-variables First-Order Conditions Second-Order Conditions Direct Restrictions on Variables 491 Chapter 13 Constrained Optimization Constrained Problems and Approaches to Solutions Second-Order Conditions for Constrained Optimization Existence, Uniqueness, and Characterization of Solutions 520 Chapter 14 Comparative Statics Introduction to Comparative Statics General Comparative-Statics Analysis The Envelope Theorem 554 Chapter 15 Concave Programming and the Kuhn-Tucker Conditions The Concave-Programming Problem Many Variables and Constraints 575 Part V Integration and Dynamic Methods Chapter 16 Integration The Indefinite Integral The Riemann (Definite) Integral Properties of Integrals 605
6 x CONTENTS 16.4 Improper Integrals Techniques of Integration 623 Chapter 17 An Introduction to Mathematics for Economic Dynamics Modeling Time 634 Chapter 18 Linear, First-Order Difference Equations Linear, First-Order, Autonomous Difference Equations The General, Linear, First-Order Difference Equation 656 Chapter 19 Nonlinear, First-Order Difference Equations The Phase Diagram and Qualitative Analysis Cycles and Chaos 673 Chapter 20 Linear, Second-Order Difference Equations The Linear, Autonomous, Second-Order Difference Equation The Linear, Second-Order Difference Equation with a Variable Term 708 Chapter 21 Linear, First-Order Differential Equations Autonomous Equations Nonautonomous Equations 731 Chapter 22 Nonlinear, First-Order Differential Equations Autonomous Equations and Qualitative Analysis Two Special Forms of Nonlinear, First-Order Differential Equations 748 Chapter 23 Linear, Second-Order Differential Equations The Linear, Autonomous, Second-Order Differential Equation The Linear, Second-Order Differential Equation with a Variable Term 772 Chapter 24 Simultaneous Systems of Differential and Difference Equations Linear Differential Equation Systems Stability Analysis and Linear Phase Diagrams Systems of Linear Difference Equations 825
7 CONTENTS xi Chapter 25 Optimal Control Theory The Maximum Principle Optimization Problems Involving Discounting Alternative Boundary Conditions on x(t ) Infinite Time Horizon Problems Constraints on the Control Variable Free-Terminal-Time Problems (T Free) 909 Answers 921 Index 953
MATHEMATICS FOR ECONOMISTS. An Introductory Textbook. Third Edition. Malcolm Pemberton and Nicholas Rau. UNIVERSITY OF TORONTO PRESS Toronto Buffalo
MATHEMATICS FOR ECONOMISTS An Introductory Textbook Third Edition Malcolm Pemberton and Nicholas Rau UNIVERSITY OF TORONTO PRESS Toronto Buffalo Contents Preface Dependence of Chapters Answers and Solutions
More informationMathematics for Economics and Finance
Mathematics for Economics and Finance Michael Harrison and Patrick Waldron B 375482 Routledge Taylor & Francis Croup LONDON AND NEW YORK Contents List of figures ix List of tables xi Foreword xiii Preface
More informationMathematical Formulas for Economists
Mathematical Formulas for Economists Springer-Verlag Berlin Heidelberg GmbH Bernd Luderer. Volker Nollau Klaus Vetters Mathematical Formulas for Economists With 58 Figures and 6 Tables, Springer Professor
More informationCOMPARATIVE STATICS ANALYSIS in ECONOMICS
COMPARATIVE STATICS ANALYSIS in ECONOMICS This page is intentionally left blank COMPARATIVE STATICS ANALYSIS in ECONOMICS Kevin M. Currier Department of Economics Oklahoma State University \ > World Scientific
More informationAdvanced Calculus of a Single Variable
Advanced Calculus of a Single Variable Tunc Geveci Advanced Calculus of a Single Variable 123 Tunc Geveci Department of Mathematics and Statistics San Diego State University San Diego, CA, USA ISBN 978-3-319-27806-3
More informationMatrix Calculus and Kronecker Product
Matrix Calculus and Kronecker Product A Practical Approach to Linear and Multilinear Algebra Second Edition This page intentionally left blank Matrix Calculus and Kronecker Product A Practical Approach
More informationOptimization: Insights and Applications. Jan Brinkhuis Vladimir Tikhomirov PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD
Optimization: Insights and Applications Jan Brinkhuis Vladimir Tikhomirov PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD Contents Preface 0.1 Optimization: insights and applications xiii 0.2 Lunch, dinner,
More informationNonlinear Parabolic and Elliptic Equations
Nonlinear Parabolic and Elliptic Equations Nonlinear Parabolic and Elliptic Equations c. V. Pao North Carolina State University Raleigh, North Carolina Plenum Press New York and London Library of Congress
More informationChemistry by Computer. An Overview of the Applications of Computers in Chemistry
Chemistry by Computer An Overview of the Applications of Computers in Chemistry Chemistry by Computer An Overview of the Applications of Computers in Chemistry Stephen Wilson Theoretical Chemistry Department
More informationVARIATIONS INTRODUCTION TO THE CALCULUS OF. 3rd Edition. Introduction to the Calculus of Variations Downloaded from
INTRODUCTION TO THE CALCULUS OF VARIATIONS 3rd Edition This page intentionally left blank INTRODUCTION TO THE CALCULUS OF VARIATIONS 3rd Edition Bernard Dacorogna Ecole Polytechnique Fédérale Lausanne,
More informationEngineering Mathematics
Thoroughly Revised and Updated Engineering Mathematics For GATE 2017 and ESE 2017 Prelims Note: ESE Mains Electrical Engineering also covered Publications Publications MADE EASY Publications Corporate
More informationControlled Markov Processes and Viscosity Solutions
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming, H. Mete Soner Controlled Markov Processes and Viscosity Solutions Second Edition Wendell H. Fleming H.M. Soner Div. Applied Mathematics
More informationElementary Linear Algebra with Applications Bernard Kolman David Hill Ninth Edition
Elementary Linear Algebra with Applications Bernard Kolman David Hill Ninth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM JE England and Associated Companies throughout the world Visit
More informationUNIVERSITY OF NORTH ALABAMA MA 110 FINITE MATHEMATICS
MA 110 FINITE MATHEMATICS Course Description. This course is intended to give an overview of topics in finite mathematics together with their applications and is taken primarily by students who are not
More informationSpringerBriefs in Mathematics
SpringerBriefs in Mathematics For further volumes: http://www.springer.com/series/10030 George A. Anastassiou Advances on Fractional Inequalities 123 George A. Anastassiou Department of Mathematical Sciences
More informationADVANCED ENGINEERING MATHEMATICS
ADVANCED ENGINEERING MATHEMATICS DENNIS G. ZILL Loyola Marymount University MICHAEL R. CULLEN Loyola Marymount University PWS-KENT O I^7 3 PUBLISHING COMPANY E 9 U Boston CONTENTS Preface xiii Parti ORDINARY
More informationCONTENTS. Preface Preliminaries 1
Preface xi Preliminaries 1 1 TOOLS FOR ANALYSIS 5 1.1 The Completeness Axiom and Some of Its Consequences 5 1.2 The Distribution of the Integers and the Rational Numbers 12 1.3 Inequalities and Identities
More informationPhysics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition
Physics for Scientists & Engineers with Modern Physics Douglas C. Giancoli Fourth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the
More informationEngineering. Mathematics. GATE 2019 and ESE 2019 Prelims. For. Comprehensive Theory with Solved Examples
Thoroughly Revised and Updated Engineering Mathematics For GATE 2019 and ESE 2019 Prelims Comprehensive Theory with Solved Examples Including Previous Solved Questions of GATE (2003-2018) and ESE-Prelims
More informationCALCULUS. C. HENRY EDWARDS The University of Georgia, Athens. DAVID E. PENNEY The University of Georgia, Athens. Prentice Hall
CALCULUS C. HENRY EDWARDS The University of Georgia, Athens DAVID E. PENNEY The University of Georgia, Athens Prentice Hall Pearson Education International CONTENTS ABOUT THE AUTHORS PREFACE XI xiii CHAPTER
More informationMathematics for Chemists
Mathematics for Chemists MATHEMATICS FOR CHEMISTS D. M. Hirst Department of Molecular Sciences, university of Warwick, Coventry M D. M. Hirst 1976 All rights reserved. No part of this publication may be
More informationEconomics 101A (Lecture 3) Stefano DellaVigna
Economics 101A (Lecture 3) Stefano DellaVigna January 24, 2017 Outline 1. Implicit Function Theorem 2. Envelope Theorem 3. Convexity and concavity 4. Constrained Maximization 1 Implicit function theorem
More informationCalculus from Graphical, Numerical, and Symbolic Points of View, 2e Arnold Ostebee & Paul Zorn
Calculus from Graphical, Numerical, and Symbolic Points of View, 2e Arnold Ostebee & Paul Zorn Chapter 1: Functions and Derivatives: The Graphical View 1. Functions, Calculus Style 2. Graphs 3. A Field
More informationEconomic Foundations of Symmetric Programming
Economic Foundations of Symmetric Programming QUIRINO PARIS University of California, Davis B 374309 CAMBRIDGE UNIVERSITY PRESS Foreword by Michael R. Caputo Preface page xv xvii 1 Introduction 1 Duality,
More informationRAGNAR FRISCH MAXIMA AND MINIMA THEORY AND ECONOMIC APPLICATIONS IN COLLABORA TION WITH A. NATAF SPRJNGER-SCIENCE+BUSJNESS MEDIA, B.V.
MAXIMA AND MINIMA RAGNAR FRISCH MAXIMA AND MINIMA THEORY AND ECONOMIC APPLICATIONS IN COLLABORA TION WITH A. NATAF SPRJNGER-SCIENCE+BUSJNESS MEDIA, B.V. MAXIMA ET MINIMA Theorie et applications economiques
More informationOptimisation theory. The International College of Economics and Finance. I. An explanatory note. The Lecturer and Class teacher: Kantorovich G.G.
The International College of Economics and Finance The course syllabus Optimisation theory The eighth semester I. An explanatory note The Lecturer and Class teacher: Kantorovich G.G. Requirements to students:
More informationPHASE PORTRAITS OF PLANAR QUADRATIC SYSTEMS
PHASE PORTRAITS OF PLANAR QUADRATIC SYSTEMS Mathematics and Its Applications Managing Editor: M. HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 583 PHASE PORTRAITS
More informationEC /11. Math for Microeconomics September Course, Part II Problem Set 1 with Solutions. a11 a 12. x 2
LONDON SCHOOL OF ECONOMICS Professor Leonardo Felli Department of Economics S.478; x7525 EC400 2010/11 Math for Microeconomics September Course, Part II Problem Set 1 with Solutions 1. Show that the general
More informationCOUNTING. Solutions Manual. 2nd Edition. Counting Downloaded from by on 02/19/18. For personal use only.
COUNTING Solutions Manual 2nd Edition This page intentionally left blank COUNTING Solutions Manual 2nd Edition Koh Khee Meng National University of Singapore, Singapore Tay Eng Guan Nanyang Technological
More informationES10006: Core skills for economists: Mathematics 2
ES10006: Core skills for economists: Mathematics 2 Seminar 10 Problem set no. 7: Questions 6 and 7 Simultaneous difference equations The direct method The following system of n = 2 linear difference equations
More informationMULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS
T H I R D E D I T I O N MULTIVARIABLE CALCULUS, LINEAR ALGEBRA, AND DIFFERENTIAL EQUATIONS STANLEY I. GROSSMAN University of Montana and University College London SAUNDERS COLLEGE PUBLISHING HARCOURT BRACE
More informationHANDBOOK OF ELECTRONICS FORMULAS, SYMBOLS AND DEFINITIONS
HANDBOOK OF ELECTRONICS FORMULAS, SYMBOLS AND DEFINITIONS HANDBOOK OF ELECTRONICS FORMULAS, SYMBOLS AND DEFINITIONS Second Edition John R. Brand Inm!I VAN NOSTRAND REINHOLD ~ New York ISBN-13: 978-1-4684-6493-1
More informationGLOBAL EDITION. Thomas. CALCULUS Early Transcendentals Thirteenth Edition in SI Units
GLOBAL EDITION Thomas CALCULUS Early Transcendentals Thirteenth Edition in SI Units Editor-in-Chief: Deirdre Lynch Senior Acquisitions Editor: William Hoffman Assistant Acquisitions Editor, Global Editions:
More informationControlled Markov Processes and Viscosity Solutions
Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming, H. Mete Soner Controlled Markov Processes and Viscosity Solutions Second Edition Wendell H. Fleming H.M. Soner Div. Applied Mathematics
More informationProbability Theory, Random Processes and Mathematical Statistics
Probability Theory, Random Processes and Mathematical Statistics Mathematics and Its Applications Managing Editor: M.HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume
More informationFor Bonnie and Jesse (again)
SECOND EDITION A P P L I E D R E G R E S S I O N A N A L Y S I S a n d G E N E R A L I Z E D L I N E A R M O D E L S For Bonnie and Jesse (again) SECOND EDITION A P P L I E D R E G R E S S I O N A N A
More informationProgress in Nonlinear Differential Equations and Their Applications Volume 18
Progress in Nonlinear Differential Equations and Their Applications Volume 18 Editor Haim Brezis Universite Pierre et Marie Curie Paris and Rutgers University New Brunswick, N.J. Editorial Board A. Bahri,
More informationUNIVERSITY OF SOUTHAMPTON ECONOMICS SERIES MATHEMATICS FOR ECONOMISTS AND SOCIAL SCIENTISTS
UNIVERSITY OF SOUTHAMPTON ECONOMICS SERIES MATHEMATICS FOR ECONOMISTS AND SOCIAL SCIENTISTS UNIVERSITY OF SOUTHAMPTON ECONOMICS SERIES Now available OUTPUT, INFLATION AND GROWTH: AN INTRODUCTION TO MACRO-ECONOMICS
More informationBusiness Calculus
Business Calculus 978-1-63545-025-5 To learn more about all our offerings Visit Knewtonalta.com Source Author(s) (Text or Video) Title(s) Link (where applicable) OpenStax Senior Contributing Authors: Gilbert
More informationTopics in Number Theory
Topics in Number Theory THE UNIVERSITY SERIES IN MATHEMATICS Series Editor: Joseph J. Kohn Princeton University THE CLASSIFICATION OF FINITE SIMPLE GROUPS Daniel Gorenstein VOLUME 1: GROUPS OF NONCHARACTERISTIC
More informationPROCEEDINGS OF THE EIGHTH SYMPOSIUM IN APPLIED MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY. Held at the University of Chicago April 12-13, 1956
http://dx.doi.org/10.1090/psapm/008 PROCEEDINGS OF THE EIGHTH SYMPOSIUM IN APPLIED MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY Held at the University of Chicago April 12-13, 1956 COSPONSORED BY THE
More informationPURE MATHEMATICS Unit 1
PURE MATHEMATICS Unit 1 FOR CAPE EXAMINATIONS DIPCHAND BAHALL CAPE is a registered trade mark of the Caribbean Examinations Council (CXC). Pure Mathematics for CAPE Examinations Unit 1 is an independent
More informationAPPLIED NONLINEAR CONTROL. Jean-Jacques E Slotine WeipingLi
APPLIED NONLINEAR CONTROL Jean-Jacques E Slotine WeipingLi Applied Nonlinear Control JEAN-JACQUES E. SLOTlNE Massachusetts Institute of Technology WEIPING LI Massachusetts Institute of Technologv Prentice
More informationIB Mathematics Standard Level Revision guide
IB Mathematics Standard Level Revision guide F.G. Groeneveld TopClassTutors.ORG Copyright 2016 by F. Groeneveld All rights reserved. No part of this publication may be reproduced, distributed, or transmitted
More informationFRACTIONAL CALCULUS IN PHYSICS
APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS APPLICATIONS OF FRACTIONAL CALCULUS IN PHYSICS Editor Universitat Mainz and Universitat Stuttgart Germany Vfe World Scientific «Singapore New Jersey London
More informationUndergraduate Texts in Mathematics
Undergraduate Texts in Mathematics Editors S. Axler F.W. Gehring K.A. Ribet Springer Books on Elementary Mathematics by Serge Lang MATH! Encounters with High School Students 1985, ISBN 96129-1 The Beauty
More informationNumerical Methods. Scientists. Engineers
Third Edition Numerical Methods for Scientists and Engineers K. Sankara Rao Numerical Methods for Scientists and Engineers Numerical Methods for Scientists and Engineers Third Edition K. SANKARA RAO Formerly,
More informationCALCULUS GARRET J. ETGEN SALAS AND HILLE'S. ' MiIIIIIIH. I '////I! li II ii: ONE AND SEVERAL VARIABLES SEVENTH EDITION REVISED BY \
/ / / ' ' ' / / ' '' ' - -'/-' yy xy xy' y- y/ /: - y/ yy y /'}' / >' // yy,y-' 'y '/' /y , I '////I! li II ii: ' MiIIIIIIH IIIIII!l ii r-i: V /- A' /; // ;.1 " SALAS AND HILLE'S
More informationA FIRST COURSE IN INTEGRAL EQUATIONS
A FIRST COURSE IN INTEGRAL EQUATIONS This page is intentionally left blank A FIRST COURSE IN INTEGRAL EQUATIONS Abdul-M ajid Wazwaz Saint Xavier University, USA lib World Scientific 1M^ Singapore New Jersey
More informationWritten as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year
Written as per the revised G Scheme syllabus prescribed by the Maharashtra State Board of Technical Education (MSBTE) w.e.f. academic year 2012-2013 Basic MATHEMATICS First Year Diploma Semester - I First
More informationGraduate Texts in Mathematics 51
Graduate Texts in Mathematics 51 Editorial Board F. W. Gehring P. R. Halmos M anaging Editor c. C. Moore Wilhelm Klingenberg ACoursein Differential Geometry Translated by David Hoffman Springer Science+Business
More informationUndergraduate Texts in Mathematics. Editors J. H. Ewing F. W. Gehring P. R. Halmos
Undergraduate Texts in Mathematics Editors J. H. Ewing F. W. Gehring P. R. Halmos Springer Books on Elemeritary Mathematics by Serge Lang MATH! Encounters with High School Students 1985, ISBN 96129-1 The
More informationQUANTUM MECHANICS USING COMPUTER ALGEBRA
QUANTUM MECHANICS USING COMPUTER ALGEBRA Includes Sample Programs in C++, SymbolicC++, Maxima, Maple, and Mathematica 2nd Edition This page intentionally left blank QUANTUM MECHANICS USING COMPUTER ALGEBRA
More informationApplied Multivariate Statistical Analysis Richard Johnson Dean Wichern Sixth Edition
Applied Multivariate Statistical Analysis Richard Johnson Dean Wichern Sixth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
More informationSTRUCTURE Of ECONOMICS A MATHEMATICAL ANALYSIS
THIRD EDITION STRUCTURE Of ECONOMICS A MATHEMATICAL ANALYSIS Eugene Silberberg University of Washington Wing Suen University of Hong Kong I Us Irwin McGraw-Hill Boston Burr Ridge, IL Dubuque, IA Madison,
More informationMathematics for Chemists
Mathematics for Chemists Mathematics for Chemists P. G. Francis Department of Chemistry, University of Hull LONDON NEW YORK Chapman and Hall First p u b l 1984 i s ~ d by Clulpmml and Hall LId I I New
More informationNumerical Data Fitting in Dynamical Systems
Numerical Data Fitting in Dynamical Systems Applied Optimization Volume 77 Series Editors: Panos M. Pardalos University of Florida, U.S.A. Donald Hearn University of Florida, U.S.A. The titles published
More informationNonlinear Programming (NLP)
Natalia Lazzati Mathematics for Economics (Part I) Note 6: Nonlinear Programming - Unconstrained Optimization Note 6 is based on de la Fuente (2000, Ch. 7), Madden (1986, Ch. 3 and 5) and Simon and Blume
More informationSTATISTICAL ANALYSIS WITH MISSING DATA
STATISTICAL ANALYSIS WITH MISSING DATA SECOND EDITION Roderick J.A. Little & Donald B. Rubin WILEY SERIES IN PROBABILITY AND STATISTICS Statistical Analysis with Missing Data Second Edition WILEY SERIES
More informationThomas Fischer Weiss. Cellular Biophysics. Volume 1: Transport. A Bradford Book The MIT Press Cambridge, Massachusetts London, England
Thomas Fischer Weiss Cellular Biophysics Volume 1: Transport A Bradford Book The MIT Press Cambridge, Massachusetts London, England 1996 Massachusetts Institute of Technology All rights reserved. No part
More informationIntroductory Statistics Neil A. Weiss Ninth Edition
Introductory Statistics Neil A. Weiss Ninth Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at:
More informationMaple in Calculus. by Harald Pleym. Maple Worksheets Supplementing. Edwards and Penney. CALCULUS 6th Edition Early Transcendentals - Matrix Version
Maple in Calculus by Harald Pleym Maple Worksheets Supplementing Preface Edwards and Penney CALCULUS 6th Edition Early Transcendentals - Matrix Version These worksheets provide a comprehensive Maple supplement
More informationDifferential Equations and Linear Algebra C. Henry Edwards David E. Penney Third Edition
Differential Equations and Linear Algebra C. Henry Edwards David E. Penney Third Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world
More informationSignals and Systems with MATLAB Applications
Signals and Systems with MATLAB Applications Second Edition Steven T. Karris www.orchardpublications.com Signals and Systems with MATLAB Applications, Second Edition Copyright 2003. All rights reserved.
More informationGeometrical Properties of Differential Equations Downloaded from by on 05/09/18. For personal use only.
This page intentionally left blank Applications of Lie Group Analysis in Financial Mathematics Ljudmila A. Bordag University of Applied Sciences Zittau/Görlitz, Germany World Scientific NEW JERSEY LONDON
More informationStatistics for Social and Behavioral Sciences
Statistics for Social and Behavioral Sciences Advisors: S.E. Fienberg W.J. van der Linden For other titles published in this series, go to http://www.springer.com/series/3463 Haruo Yanai Kei Takeuchi
More informationThe Practice Book for Conceptual Physics. Paul G. Hewitt Eleventh Edition
The Practice Book for Conceptual Physics Paul G. Hewitt Eleventh Edition Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on
More information9TH EDITION. George B. Thomas, Jr. Massachusetts Institute of Technology. Ross L. Finney. With the collaboration of Maurice D.
9TH EDITION Calculus and Analytic Geometry George B. Thomas, Jr. Massachusetts Institute of Technology Ross L. Finney With the collaboration of Maurice D. Weir Naval Postgraduate School ^ Addison-Wesley
More informationMATHEMATICAL ECONOMICS: OPTIMIZATION. Contents
MATHEMATICAL ECONOMICS: OPTIMIZATION JOÃO LOPES DIAS Contents 1. Introduction 2 1.1. Preliminaries 2 1.2. Optimal points and values 2 1.3. The optimization problems 3 1.4. Existence of optimal points 4
More informationThe Foundations of Real Analysis A Fundamental Course with 347 Exercises and Detailed Solutions
The Foundations of Real Analysis A Fundamental Course with 347 Exercises and Detailed Solutions Richard Mikula BrownWalker Press Boca Raton The Foundations of Real Analysis: A Fundamental Course with 347
More informationLIBRARY OF MATHEMATICS edited by
LIBRARY OF MATHEMATICS edited by WALTER LEDERMANN D.Sc., Ph.D., F.R.S.Ed., Professor of Mathematics, University of Sussex Linear Equations Sequences and Series Differential Calculus Elementary Differential
More informationMathematical Economics. Lecture Notes (in extracts)
Prof. Dr. Frank Werner Faculty of Mathematics Institute of Mathematical Optimization (IMO) http://math.uni-magdeburg.de/ werner/math-ec-new.html Mathematical Economics Lecture Notes (in extracts) Winter
More informationApplied Regression Modeling
Applied Regression Modeling Applied Regression Modeling A Business Approach Iain Pardoe University of Oregon Charles H. Lundquist College of Business Eugene, Oregon WILEY- INTERSCIENCE A JOHN WILEY &
More informationMathematics for Engineers and Scientists
Mathematics for Engineers and Scientists Fourth edition ALAN JEFFREY University of Newcastle-upon-Tyne B CHAPMAN & HALL University and Professional Division London New York Tokyo Melbourne Madras Contents
More informationOptimization Tutorial 1. Basic Gradient Descent
E0 270 Machine Learning Jan 16, 2015 Optimization Tutorial 1 Basic Gradient Descent Lecture by Harikrishna Narasimhan Note: This tutorial shall assume background in elementary calculus and linear algebra.
More informationFollow links Class Use and other Permissions. For more information, send to:
COPYRIGHT NOTICE: Stephen L. Campbell & Richard Haberman: Introduction to Differential Equations with Dynamical Systems is published by Princeton University Press and copyrighted, 2008, by Princeton University
More informationDifferential and Integral
Noavaran Sharif Publication Differential and Integral Volume 1 Authors: Maryam Shafiebeyk Mohammadi Somayeh Mashayekhi Hossein Pourbashash (Faculty Member of Adiban Higher Education Institute) Title: Differential
More informationAmbrosio Dancer Calculus of Variations and Partial Differential Equations
Ambrosio Dancer Calculus of Variations and Partial Differential Equations Springer-Verlag Berlin Heidelberg GmbH L. Ambrosio N. Dancer Calculus of Variations and Partial Differential Equations Topics on
More informationPRESENTATION OF MATHEMATICAL ECONOMICS SYLLABUS FOR ECONOMICS HONOURS UNDER CBCS, UNIVERSITY OF CALCUTTA
PRESENTATION OF MATHEMATICAL ECONOMICS SYLLABUS FOR ECONOMICS HONOURS UNDER CBCS, UNIVERSITY OF CALCUTTA Kausik Gupta Professor of Economics, University of Calcutta Introductory Remarks The paper/course
More informationNonlinear Optimization: What s important?
Nonlinear Optimization: What s important? Julian Hall 10th May 2012 Convexity: convex problems A local minimizer is a global minimizer A solution of f (x) = 0 (stationary point) is a minimizer A global
More informationQUANTUM MECHANICS. For Electrical Engineers. Quantum Mechanics Downloaded from
Quantum Mechanics Downloaded from www.worldscientific.com QUANTUM MECHANICS For Electrical Engineers Quantum Mechanics Downloaded from www.worldscientific.com This page intentionally left blank Quantum
More informationStochastic Optimization Methods
Stochastic Optimization Methods Kurt Marti Stochastic Optimization Methods With 14 Figures 4y Springer Univ. Professor Dr. sc. math. Kurt Marti Federal Armed Forces University Munich Aero-Space Engineering
More informationMicroeconomics I. September, c Leopold Sögner
Microeconomics I c Leopold Sögner Department of Economics and Finance Institute for Advanced Studies Stumpergasse 56 1060 Wien Tel: +43-1-59991 182 soegner@ihs.ac.at http://www.ihs.ac.at/ soegner September,
More informationPopulation Games and Evolutionary Dynamics
Population Games and Evolutionary Dynamics William H. Sandholm The MIT Press Cambridge, Massachusetts London, England in Brief Series Foreword Preface xvii xix 1 Introduction 1 1 Population Games 2 Population
More informationGAME PHYSICS SECOND EDITION. дяййтаййг 1 *
GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers
More informationMATH2070 Optimisation
MATH2070 Optimisation Nonlinear optimisation with constraints Semester 2, 2012 Lecturer: I.W. Guo Lecture slides courtesy of J.R. Wishart Review The full nonlinear optimisation problem with equality constraints
More informationMathematics for Physicists and Engineers
Mathematics for Physicists and Engineers Klaus Weltner Sebastian John Wolfgang J. Weber Peter Schuster Jean Grosjean Mathematics for Physicists and Engineers Fundamentals and Interactive Study Guide 2nd
More informationNumerical Methods for the Solution of Ill-Posed Problems
Numerical Methods for the Solution of Ill-Posed Problems Mathematics and Its Applications Managing Editor: M.HAZEWINKEL Centre for Mathematics and Computer Science, Amsterdam, The Netherlands Volume 328
More informationMaximum Principles in Differential Equations
Maximum Principles in Differential Equations Springer New York Berlin Heidelberg Barcelona Hong Kong London Milan Paris Singapore Tokyo Murray H. Protter Hans F. Weinberger Maximum Principles in Differential
More informationin this web service Cambridge University Press
CONTINUUM MECHANICS This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behavior of continuous materials.
More informationMathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS
Mathematics Syllabus UNIT I ALGEBRA : 1. SETS, RELATIONS AND FUNCTIONS (i) Sets and their Representations: Finite and Infinite sets; Empty set; Equal sets; Subsets; Power set; Universal set; Venn Diagrams;
More informationGradient Descent. Dr. Xiaowei Huang
Gradient Descent Dr. Xiaowei Huang https://cgi.csc.liv.ac.uk/~xiaowei/ Up to now, Three machine learning algorithms: decision tree learning k-nn linear regression only optimization objectives are discussed,
More informationMathematical Methods and Economic Theory
Mathematical Methods and Economic Theory Anjan Mukherji Subrata Guha C 263944 OXTORD UNIVERSITY PRESS Contents Preface SECTION I 1 Introduction 3 1.1 The Objective 3 1.2 The Tools for Section I 4 2 Basic
More informationMVE165/MMG631 Linear and integer optimization with applications Lecture 13 Overview of nonlinear programming. Ann-Brith Strömberg
MVE165/MMG631 Overview of nonlinear programming Ann-Brith Strömberg 2015 05 21 Areas of applications, examples (Ch. 9.1) Structural optimization Design of aircraft, ships, bridges, etc Decide on the material
More informationMultivariate Analysis in The Human Services
Multivariate Analysis in The Human Services INTERNATIONAL SERIES IN SOCIAL WELFARE Series Editor: William J. Reid State University of New York at Albany Advisory Editorial Board: Weiner W. Boehm Rutgers,
More informationPharmaceutical Mathematics with Application to Pharmacy
Pharmaceutical Mathematics with Application to Pharmacy (ii) (iii) Pharmaceutical Mathe ematics with Application to Pharmacy D.H. Panchaksharappa Gowda Assistant Professor, J.S.S. College of Pharmacy,
More informationOptimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations
Martino Bardi Italo Capuzzo-Dolcetta Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations Birkhauser Boston Basel Berlin Contents Preface Basic notations xi xv Chapter I. Outline
More informationCHAPTER 2: QUADRATIC PROGRAMMING
CHAPTER 2: QUADRATIC PROGRAMMING Overview Quadratic programming (QP) problems are characterized by objective functions that are quadratic in the design variables, and linear constraints. In this sense,
More informationAnalysis and Control of Age-Dependent Population Dynamics
Analysis and Control of Age-Dependent Population Dynamics MATHEMATICAL MODELLING: Theory and Applications VOLUME I I This series is aimed at publishing work dealing with the definition, development and
More informationCE 191: Civil and Environmental Engineering Systems Analysis. LEC 05 : Optimality Conditions
CE 191: Civil and Environmental Engineering Systems Analysis LEC : Optimality Conditions Professor Scott Moura Civil & Environmental Engineering University of California, Berkeley Fall 214 Prof. Moura
More information