Mathematics II

Universidade Católica Portuguesa

Course Description

  • Course Name

    Mathematics II

  • Host University

    Universidade Católica Portuguesa

  • Location

    Lisbon, Portugal

  • Area of Study

    Economics, Mathematics

  • Language Level

    Taught In English

  • Prerequisites

    Students should master matrix calculus and differential and integral calculus for real-valued functions of a
    single variable. This course has as prerequisite the Mathematics for Business & Economics course.

  • Course Level Recommendations

    Upper

    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

    7.5
  • Recommended U.S. Semester Credits
    3
  • Recommended U.S. Quarter Units
    5

  • Overview

    COURSE OVERVIEW
    The Mathematics II course provides students with the mathematical tools from differential and integral
    calculus for functions of several variables and methods for solving differential equations.

    LEARNING OBJECTIVES
    Upon completion of this course, students will be able to work with real-valued functions of several real
    variables and to solve differential equations in order to apply them to problems in Economics and
    Management.

    TEACHING AND LEARNING METHODOLOGY
    The content is presented in theoretical classes, promoting the understanding of concepts in the abstract,
    and is then applied to solving exercises in practical classes.

    COURSE CONTENT
    Part I – Integration methods
    1. Integration by parts
    2. Integration by substitution
    3. Integration of rational functions

    Part II – Differential calculus in Rn
    1. Domain of a real function of several variables. Graphical representation. Level curves
    2. Limits and continuity of real functions of several variables
    3. Partial derivatives
    4. Chain rule
    5. Directional derivatives. Gradient. Tangent planes and normal lines.
    6. Differentials
    7. Homogeneous functions. Euler theorem
    8. Maxima and minima of functions of several variables
    9. Lagrange multipliers. Karush–Kuhn–Tucker conditions
    10. Graphical analysis of extrema. Applications to Economy and Management

    Part III – Integral calculus in R2
    1. Double integrals. Fubini’s theorem
    2. Reversing the order of integration
    3. Changing variables

    Part IV – First order differential equations
    1. Separable equations
    2. Linear equations
    3. Exact equations. Reducible to exact equations
    4. Substitution method. Homogeneous equations and Bernoulli’s equations

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