Elements of Mathematics for Economics and Finance / / by Vassilis C. Mavron, Timothy N. Phillips

• Autore: Mavron Vassilis C.
• Pubblicazione: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023
• Edizione: 2nd ed. 2023.
• Descrizione fisica: 1 online resource (390 pages)
• Disciplina: 260
• Soggetto topico: Mathematics; Economics; Finance, Public; Business; Management science; Game theory; Public Economics; Applications of Mathematics; Business and Management; Game Theory
• Persona (resp. second.): PhillipsTim <1967->
• Nota di contenuto: Intro -- Preface -- Preface to the Second Edition -- Contents -- 1 Essential Skills -- 1.1 Introduction -- 1.2 Numbers -- 1.2.1 Addition and Subtraction -- 1.2.2 Multiplication and Division -- 1.2.3 Evaluation of Arithmetical Expressions -- 1.3 Fractions -- 1.3.1 Multiplication and Division -- 1.4 Decimal Representation of Numbers -- 1.4.1 Standard Form -- 1.5 Percentages -- 1.6 Powers and Indices -- 1.7 Simplifying Algebraic Expressions -- 1.7.1 Multiplying Brackets -- 1.7.2 Factorization -- 2 Linear Equations -- 2.1 Introduction -- 2.2 Solution of Linear Equations -- 2.3 Solution of Simultaneous Linear Equations -- 2.4 Graphs of Linear Equations -- 2.4.1 Slope of a Straight Line -- 2.5 Budget Lines -- 2.6 Supply and Demand Analysis -- 2.6.1 Multicommodity Markets -- 3 Quadratic Equations -- 3.1 Introduction -- 3.2 Graphs of Quadratic Functions -- 3.3 Quadratic Equations -- 3.4 Applications to Economics -- 4 Functions of a Single Variable -- 4.1 Introduction -- 4.2 Limits -- 4.3 Polynomial Functions -- 4.4 Continuity -- 4.5 Reciprocal Functions -- 4.6 Inverse Functions -- 5 The Exponential and Logarithmic Functions -- 5.1 Introduction -- 5.2 Exponential Functions -- 5.3 Logarithmic Functions -- 5.4 Returns to Scale of Production Functions -- 5.4.1 Cobb-Douglas Production Functions -- 5.5 Compounding of Interest -- 5.6 Applications of the Exponential Function in EconomicModelling -- 6 Differentiation -- 6.1 Introduction -- 6.2 Rules of Differentiation -- 6.2.1 Constant Functions -- 6.2.2 Linear Functions -- 6.2.3 Power Functions -- 6.2.4 Sums and Differences of Functions -- 6.2.5 Product of Functions -- 6.2.6 Quotient of Functions -- 6.2.7 The Chain Rule -- 6.3 Exponential and Logarithmic Functions -- 6.4 Marginal Functions in Economics -- 6.4.1 Marginal Revenue and Marginal Cost -- 6.4.2 Marginal Propensities. ; 6.5 Approximation to Marginal Functions -- 6.6 Higher Order Derivatives -- 6.7 Production Functions -- 7 Maxima and Minima -- 7.1 Introduction -- 7.2 Local Properties of Functions -- 7.2.1 Increasing and Decreasing Functions -- 7.2.2 Concave and Convex Functions -- 7.3 Local or Relative Extrema -- 7.4 Global or Absolute Extrema -- 7.5 Points of Inflection -- 7.6 Optimization of Production Functions -- 7.7 Optimization of Profit Functions -- 7.8 Other Examples -- 8 Partial Differentiation -- 8.1 Introduction -- 8.2 Functions of Two or More Variables -- 8.3 Partial Derivatives -- 8.4 Higher Order Partial Derivatives -- 8.5 Partial Rate of Change -- 8.6 The Chain Rule and Total Derivatives -- 8.7 Some Applications of Partial Derivatives -- 8.7.1 Implicit Differentiation -- 8.7.2 Elasticity of Demand -- 8.7.3 Utility -- 8.7.4 Production -- 8.7.5 Graphical Representations -- 9 Optimization -- 9.1 Introduction -- 9.2 Unconstrained Optimization -- 9.3 Constrained Optimization -- 9.3.1 Substitution Method -- 9.3.2 Lagrange Multipliers -- 9.3.3 The Lagrange Multiplier λ: An Interpretation -- 9.4 Iso Curves -- 10 Matrices and Determinants -- 10.1 Introduction -- 10.2 Matrix Operations -- 10.2.1 Scalar Multiplication -- 10.2.2 Matrix Addition -- 10.2.3 Matrix Multiplication -- 10.3 Solutions of Linear Systems of Equations -- 10.4 Cramer's Rule -- 10.5 More Determinants -- 10.6 Special Cases -- 10.7 Eigenvalues and Eigenvectors -- 11 Integration -- 11.1 Introduction -- 11.2 Rules of Integration -- 11.3 Definite Integrals -- 11.4 Definite Integration: Area and Summation -- 11.5 Producer's Surplus -- 11.6 Consumer's Surplus -- 11.7 Integration by Substitution -- 11.8 Partial Fractions in Integration -- 11.9 Integration by Parts -- 12 Linear Difference Equations -- 12.1 Introduction -- 12.2 Difference Equations -- 12.3 First Order Linear Difference Equations. ; 12.4 Stability -- 12.5 The Cobweb Model -- 12.6 Second Order Linear Difference Equations -- 12.6.1 Complementary Solutions -- 12.6.2 Particular Solutions -- 12.6.3 Stability -- 13 Differential Equations -- 13.1 Introduction -- 13.2 First Order Linear Differential Equations -- 13.2.1 Stability -- 13.3 Nonlinear First Order Differential Equations -- 13.3.1 Separation of Variables -- 13.3.2 Integrating Factors -- 13.4 Solow Differential Equation -- 13.5 Second Order Linear Differential Equations -- 13.5.1 The Homogeneous Case -- 13.5.2 The General Case -- 13.5.3 Stability -- A Differentials -- B Answers to Self-Assessment Questions -- Index.
• Sommario/riassunto: Based on over 15 years’ experience in the design and delivery of successful first-year courses, this book equips undergraduates with the mathematical skills required for degree courses in economics, finance, management, and business studies. The book starts with a summary of basic skills and takes its readers as far as constrained optimisation helping them to become confident and competent in the use of mathematical tools and techniques that can be applied to a range of problems in economics and finance. Designed as both a course text and a handbook, the book assumes little prior mathematical knowledge beyond elementary algebra and is therefore suitable for students returning to mathematics after a long break. The fundamental ideas are described in the simplest mathematical terms, highlighting threads of common mathematical theory in the various topics. Features of the book include: a systematic approach: ideas are touched upon, introduced gradually and then consolidated through the use of illustrative examples; several entry points to accommodate differing mathematical backgrounds; numerous problems, with full solutions, and exercises to illustrate the theory and applications; key learning objectives and self-assessment questions provided for each chapter; full solutions to exercises, available to lecturers via the web. Vass Mavron is Emeritus Professor of Mathematics at Aberystwyth University. Tim Phillips is Professor of Applied Mathematics in the School of Mathematics at Cardiff University.
• Titolo autorizzato: Elements of Mathematics for Economics and Finance
• ISBN: 9783031439100; 3031439104
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910765489203321
• Lo trovi qui: Univ. Federico II
• Serie: Classroom Companion: Economics, . 2662-2890