Advanced Calculus for Economics and Finance

This textbook provides a comprehensive introduction to mathematical calculus. Written for advanced undergraduate and graduate students, it teaches the fundamental mathematical concepts, methods and tools required for various areas of economics and the social sciences, such as optimization and measure theory. The reader will be introduced to topological, metric and normed spaces, learning about numerical sequences, series, and differential and integral calculus. These concepts are introduced using the axiomatic approach as a tool for logical reasoning, consistency, and formalization of ideas. The book follows a theorem-proving approach, stressing the limitations of applying the different theorems, while providing thought-provoking counter-examples. Each chapter features exercises that facilitate learning and allow students to apply and test important concepts and tools.

Teaches mathematics for economics and finance Written for advanced undergraduate and graduate students Features exercises that facilitate learning

Autorentext
Giulio Bottazzi is a Professor of Economics at the Scuola Superiore Sant'Anna in Pisa (Italy) where he has taught courses in mathematics and statistics since 2010. He graduated at the Parma University and holds a PhD in Theoretical Physics from Milano University. He is the author of several papers published in international journals. His research interests range from industrial dynamics to financial economics, encompassing experimental economics, economic geography, theoretical and empirical aspects of market interactions and applied econometrics. He is the author of several software packages for data analysis and simulation of economic models.

Inhalt
Chapter 1. Preliminaries.- Chapter 2. Topology.- Chapter 3. Metric Spaces.- Chapter 4. Normed Spaces.- Chapter 5. Sequences and Series.- Chapter 6. Differential Calculus of functions of one variable.- Chapter 7. Functions of several variables.- Chapter 8. Integral Calculus.- Chapter 9. Measure Theory.