Universidad de Jaén

Differential and integral Calculus of several variables with applications to economics. Introduction to differential equations.

THEORETICAL CONTENTS

Unit 1.   Limits and continuity of real-valued functions of several real variables . The space R^n. Real-valued functions of several real variables. Limits of real-valued functions of several real variables. Continuity of real-valued functions of several real variables.

Unit 2. Differentiability of real-valued functions of several real variables.   Partial derivatives. Directional derivatives. Differential of real-valued functions of several real variables. Applications to economics.

Unit 3. Vector-valued functions of several real variables.   Limits, continuity and differentiability of vector-valued functions. The Chain Rule. Homogeneous functions. Applications to economics.

Unit 4. Optimization of real-valued functions of several real variables.   Quadratic forms. Unconstrained optimization. Optimization with equality constraints. Applications to economics.

Unit 5. Integration of real-valued functions of several real variables.   Double integral construction. Double integrals over rectangular domains. Double integrals over general bounded regions.

Unit 6. Introduction to differential equations.   Basic concepts and notation. Integration methods for some types of first and second order ordinary differential equations. Applications to economics.

PRACTICAL CONTENTS

Written exercises and computer sessions related to the theoretical contents.

Lectures (M1, M3, M4, M5): Theoretical contents and related practical examples will be developed in these sessions.

Seminars (M6, M7, M8, M10, M12, M13): 15 one-hour long classroom sessions will be devoted for solving problems, with special emphasis on applications to economics. Additionally, 15 one-hour long computer lab sessions will be devoted for solving problems by using the software Mathematica.

Students with special educational needs should contact the Student Attention Service (Servicio de Atención y Ayudas al Estudiante) in order to receive the appropriate academic support

1. Detail: 
   • S2. THEORETICAL CONCEPTS: 6 points (60%): Final written exam about the theoretical concepts and related exercises. Learning results R1 and R4.
   • S3. CLASSROOM EXERCISES: 2 points (20%): Short classroom tests. Learning results R1, R2 and R4.
   • S4. COMPUTER LAB PRACTICES: 2 points (20%): Computer exam. Computer guidelines may be used in the exam. Learning results R1, R3 and R4.
2. Marks from S3 and S4 will be maintained during the current academic year.
3. The final continuous grade will be the sum of the marks obtained from S2, S3, S4. A minimum of 3 points (out of 10) in S2 is required in order to consider this sum.
4. Assessment of S2 and/or S4 could be performed during the ordinary classroom sessions if the number of students of the group allows it.
5. Without assessment of S2, students will appear as "NOT SHOWN" in the grade list for the corresponding official exam call.
6. As an exception, the grade given by the sum of the marks of the final written exam (S2) and the computer exam (S4), weighted 80% and 20%, respectively, could be considered as the final grade for each student at each official exam call, with the appropriate justification.