MATHEMATICS 1

MATHEMATICS 1

Marco Isopi, Michele Aleandri

Instructional goals

The course provides students with the basic mathematical tools needed in economics, management, finance, and insurance. Students will also get acquainted with setting up and solving mathematical problems, with the aid of many examples. By the end of the course, students will be able to tackle and solve non trivial mathematical exercises, together with a clear understanding of the most important theoretical results discussed in the class.

Intended learning outcomes

Knowledge and understanding: the aim of the course is to provide students with a wide range of mathematical tools in order to understand and solve theoretical and applied problems in the economic, business and financial fields. Applying knowledge and understanding: students will possess the methodological tools that will allow them to apply the basic quantitative knowledge acquired during the course to the working contexts in which they will operate: they will therefore be able to apply quantitative tools to decision making in the business environment, to the analysis of economic phenomena and to solving problems in the economic and business environment Autonomy of judgment: at the end of the class, students will have a working knowledge of quantitative tools useful for understanding economic and managerial phenomena. To this end, standard and non-standard problems will be presented to the students. Students will develop a critical ability in identifying the most suitable solution to the proposed problems. Communication skills: Students will be stimulated to develop communication skills through written papers and oral interviews. Student will describe their acquired skills but will also highlight the relationships between the theoretical concepts and the most important economic-managerial applications. Learning skills: students will have acquired not only adequate skills and knowledge to pass the exam, but above all ability to update and improve their skills in the field of Mathematics applied to economics and management. Students will have to learn how the general theory can in turn be applied to concrete problems as frequently met in economic studies and how economic reality is a stimulus for the improvement of theoretical concepts.

Course Contents

An introduction to single-variable and two variables calculus, with applications to economics.

Reference Books

- Calculus (C): James Stewart, Calculus Early Trascendentals, 8th edition, Brooks/Cole - Other freely available online material posted on the course's webpage.

Teaching Methods

Teaching will consist of the following activities: - classroom and online teaching; - classroom and online TA sessions; - weekly tests. The presence of multimedia content available on the Moodle platform (videos, slides, tutorials) as well as the tutoring activity and office hours provided by the teachers and their collaborators provides the opportunity to create a stable interaction between class and teacher giving the opportunity to check in real time skills acquired by students and their ability to apply them to the solution of different problems and their capability to argue their choices.

Assessment Method

The exam will take place in several steps: Written exam: Students will read the exam text on their laptop. The exam will be divided into two parts. The first part consists of multiple choice or numerical questions. The answers must be given directly on your laptop. The second consists of open-ended questions that must be solved out on sheets to be delivered by the end of the test. Phones must be turned off during the exam. The written test can also take place as two distinct tests: - The first partial test, called the midterm test, takes place in the middle of the semester (the date will be announced in the first weeks of the course). - The second partial test, called the final test, takes place on the days scheduled for the first (December) session. The grade will be a weighted average between the first part and the second part. If the student fails any of the two partial tests, she/he will only be able to retake the complete written test (on the entire syllabus) in the next available exam session. Bonus points During each week of the course a quiz on the learn.luiss.it page is arranged. Depending on the number of quizzes attempted and the grade received, each student can receive up to 2 points that will be added to the written text grade only if the written exam is passed on the first two exam sessions (December and January/February of the same academic year). At the beginning of the session, students have access to their graded papers and can ask for clarifications about the grading.

Thesis assignment criteria

Interview with the teacher after passing the exam.

Does the syllabus cover sustainability topics?

No

Week 1 Contenuto sessioni on line e on campus

The real line. Space R^2 (rectangles, subsets distance, vectors). A review of analytical geometry. Some elementary functions. Exponential functions. Inverse functions and logarithms. Domain of function. TA session on the lectures of the present week.

Week 2 Contenuto sessioni on line e on campus

New functions from old functions. Functions in 2 variables, domain and sign. Utility functions (Cobb-Douglas). TA session on the lectures of the present week.

Week 3 Contenuto sessioni on line e on campus

Function limits. Computing limits using the laws of limits. Asymptotes and continuity. TA session on the lectures of the present week.

Week 4 Contenuto sessioni on line e on campus

Derivatives and rates of change. The derivative as a function. Rules of differentiation: derivatives of polynomials and exponential functions. Product and quotient rules. TA session on the lectures of the present week.

Week 5 Contenuto sessioni on line e on campus

Derivatives of composite functions. Derivatives of logarithmic functions. Applications of the derivative: Taylor expansion. Maximum and minimum values. TA session on the lectures of the present week.

Week 6 Contenuto sessioni on line e on campus

Midterm week

Week 7 Contenuto sessioni on line e on campus

Graph of a function. Integrals: Antiderivatives. The definite integral. The fundamental theorem of calculus. TA session on the lectures of the present week.

Week 8 Contenuto sessioni on line e on campus

Indefinite integrals. Integration by substitution. Integration by parts. TA session on the lectures of the present week.

Week 9 Contenuto sessioni on line e on campus

Partial derivatives. Tangent plane and linear approximation. TA session on the lectures of the present week.

Week 10 Contenuto sessioni on line e on campus

Taylor approximation. Directional derivatives and gradient vector. Implicit differentiation. TA session on the lectures of the present week.

Week 11 Contenuto sessioni on line e on campus

Chain rule and implicit function theorem. Stationary points of function in two variables. Unconstrained optimization. TA session on the lectures of the present week.

Week 12 Contenuto sessioni on line e on campus

Constrained optimization. Lagrange multipliers. TA session on the lectures of the present week.