Calculus II

Universidad Carlos III de Madrid

Course Description

  • Course Name

    Calculus II

  • Host University

    Universidad Carlos III de Madrid

  • Location

    Madrid, Spain

  • Area of Study

    Biomedical Engineering, Calculus

  • Language Level

    Taught In English

  • Prerequisites


    Calculus I
    Linear Algebra

  • Course Level Recommendations


    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

  • Recommended U.S. Semester Credits
  • Recommended U.S. Quarter Units
  • Overview

    Calculus II (257 - 15531)
    Study: Bachelor in Biomedical Engineering
    Semester 2/Spring Semester
    1st Year Course/Lower Division

    Please note: this course is cross-listed under the majority of engineering departments. Students should select the course from the department that best fits their area of study.

    Students are Expected to have completed:
    Calculus I, Linear Algebra

    Compentences and Skills that will be Acquired and Learning Results:

    The student will be able to formulate, solve and understand mathematically the problems arising in Biomedical Engineering. To do so it is necessary to be familiar with the n-dimensional Euclidean space, making a special emphasis in dimensions 2 and 3, visualizing the more important subsets. He/she must be able to manage (scalar and vector) functions of several variables, as well as their continuity, differentiability, and integrability properties. The student must solve optimization problems with and without restrictions and will apply the main theorems of integration of scalar and vector functions to compute, in particular, lengths, areas and volumes, moments of inertia, and heat flow.

    Description of Contents: Course Description

    1. Differential Calculus in several variables
    1.1. R^n as an Euclidean space; topology
    1.2. Scalar and vector functions of n variables
    1.3. Limits and continuity
    1.4. Differentiability

    2. Local properties of functions
    2.1. Higher-order derivatives
    2.2. Differential operations on scalar and vector functions: geometrical properties
    2.3. Free and constrained optimization

    3. Integral Calculus on R^n
    3.1. Double and triple integrals
    3.2. Changes of variables and applications

    4. Integrals over curves and surfaces
    4.1. Line and path integrals
    4.2. Surface integrals
    4.3. Integral theorems of vector analysis in R^2 and R^3

    Learning Activities and Methodology:

    The learning methodology will include:
    - Attendance to master classes, in which core knowledge will be presented that the students must acquire. The recommended bibliography will facilitate the students' work
    - Resolution of exercises by the student that will serve as a self-evaluation method and to acquire the necessary skills
    - Exercise classes, in which problems proposed to the students are discussed
    - Fortnightly tests
    - Final Exam
    - Tutorial sessions
    - The instructors may propose additional homework and activities

    Assessment System:

    - Fortnightly tests (average over top 4 scores) 40%
    - Final exam (60%)

    Basic Bibliography:

    J. E. Marsden and A. J. Tromba. Vector Calculus, 6th. edition. W. H. Freeman. 2012
    M. D. Weir, J. Hass, and G. B. Thomas. Thomas¿ Calculus, Multivariable. Addison-Wesley. 2010

    Additional Bibliography:

    J. Stewart. Calculus. Cengage. 2008
    M. Besada, F. J. García, M. A. Mirás, and C. Vázquez. Cálculo de varias variables. Cuestiones y ejercicios resueltos. Garceta. 2011
    M. J. Strauss, G. L. Bradley, and K. J. Smith. Multivariable Calculus. Prentice Hall. 2002
    P. Pedregal Tercero. Cálculo Vectorial, un enfoque práctico. Septem Ediciones. 2001
    R. Larson and B. H. Edwards. Calculus II, 9th. edition. Cengage. 2009
    S. Salas, E. Hille, and G. Etgen. Calculus. One and several variables. Wiley. 2007
    T. M. Apostol. Calculus. Wiley. 1975

Course Disclaimer

Courses and course hours of instruction are subject to change.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.


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