Calculus II
Objectives
In this course, applications of Differential Calculus in R , and the fundamental tools of Optimization and Integration will be developed, n allowing the formulation and mathematical development of models in Economics and Management.
General characterization
Code
1310
Credits
7
Responsible teacher
Áurea Quintino | Madina Karamysheva | Tânia Silva
Hours
Weekly - Available soon
Total - Available soon
Teaching language
Portuguese and English
Prerequisites
Mandatory precedence: 1301. Calculus I
Bibliography
Main references:
• Pires, C., Cálculo para Economia e Gestão, Escolar Editora, 2011. (PT)
• Simon, C.P., Blume, L., Mathematics for Economists, W.W. Norton & Company, Inc, 1994. (EN)
• Dias Agudo, F.R., Análise Real, Livraria Escolar Editora, 2ª edição, 1994.
Excepto tópicos 6.5 e 6.6
• Campos Ferreira, J., Introdução à Análise em , Publicação electrónica (https://math.tecnico.ulisboa.pt/textos/iarn.pdf), DM, IST, 2003.
Excepto tópicos 6.5 e 6.6
• Sydsæter, K. et al., Further Mathematics for Economic Analysis, Prentice Hall, 2005.
Teaching method
Video Lectures
Lessons with a mix of theory and practice Exposition of concepts Solved
exercises Proposed exercises Quizzes Midterm test Final Exam.
As this is a Mathematics course, the presentation of concepts followed by exercises, solved in class or proposed for autonomous work, allows the students to be guided in a first contact with the ideas that they're exposed to and to consolidate the understanding of these ideas through an independent process of critical analysis and resolution of exercises.
Evaluation method
1. Enrolment Type: Normal
1.1. Regular Season
Best grade of the following two:
10%: Quizzes (average grade)
30%: Midterm Test
60%: Final Exam (minimum grade of 8.5) or
30%: Midterm Test
70%: Final Exam (minimum grade of 8.5) 1.2.
Resit Season
1.2.1. Choosing Final Exam only (in the week prior to the
Final Exam): 100% Final Exam
1.2.2. Choosing continuous assessment (in the week prior
to the Final Exam):
Best grade of the following two:
10%: Quizzes (average grade)
30%: Midterm Test
60%: Final Exam (minimum grade of 8.5)
or
30%: Midterm Test
70%: Final Exam (minimum grade of 8.5)
2. Enrolment Type: Grade Improvement
Regular Season or Resit Season
2.1. Choosing Final Exam only (in the week prior to the
Final Exam): 100% Final Exam
2.2. Choosing continuous assessment (in the week prior to
the Final Exam):
Best grade of the following two:
10%: Quizzes (average grade)
30%: Midterm Test
60%: Final Exam (minimum grade of 8.5)
or
30%: Midterm Test 70%: Final Exam (minimum grade of 8.5)
Subject matter
Theorems
Composite Function Theorem
Euler's Theorem
Mean Value Theorem
Taylor's Theorem
Inverse Function Theorem
Implicit Function Theorem
Optimization
Pre - Optimization
Unconstrained
Optimization Optimization with Equality Constraints
Optimization with Inequality Constraints
Integration
Antiderivatives
Simple
Integrals
Double
Integrals