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Class Calculus II

  • Presentation

    Presentation

    Provides knowledge, skills and mathematical tools essential for Engineering studies: describe and solve static and dynamic problems and optimize solutions in a space of any dimension; calculate lengths, areas and volumes.

  • Code

    Code

    ULHT39-714
  • Syllabus

    Syllabus

    Vectors. Dot product and cross product. Parametric equations of lines and planes.

    Vector-valued functions. Limits and continuity. Differentiability.

    Unit tangent, normal and binormal vectors.

    Integration, length of a curve. Curvature.

    Speed and acceleration.

    Cylindrical surfaces.

    Functions of several variables

    Level curves.

    Limits and continuity. Topological notions in Rn.

    Polar coordinates.

    Partial derivatives. Partial derivatives of higher order.

    Differentiability, tangent planes.

    The chain rule.

    Derivatives of implicitly defined functions.

    Directional derivative and gradient.

    Hessian matrix. Maxima and minima.

    Lagrange multipliers.

    Multiple integrals

    Cylindrical and spherical coordinates.

    Double and triple integrals. Change of variables. Applications.

  • Objectives

    Objectives

    Aims to deepen and develop the mastery of vector calculus as a tool to solve geometric problems involving lines and planes in two and more dimensions; functional description of static and dynamic phenomena in various dimensions; expand and consolidate the essential knowledge of differential and integral calculus in Rn and its application to concrete problems in order to expand the mastery of the concepts presented in the course and develop independent reasoning. Solve optimization problems using the identification of extreme points fo functions of several variables; Describe the properties of the Riemann integral. Use the notions of double and triple integral in the calculation of areas and volumes.

  • Teaching methodologies and assessment

    Teaching methodologies and assessment

    Series of exercises will be proposed with the aim of consolidating knowledge and stimulating problem-solving skills. The evaluation of the discipline, expressed on a scale from 0 to 20 points, will be made at different times, including 2 midterms (40% + 50%) and individual work to be developed outside the classroom (10%). If the weighted average of these evaluations is equal to or greater than 9.5, the student will be successful in the subject, otherwise the student will be able to attend a global frequency. In the final exam, the student can improve the grade. The minimum passing grade for these assessments is also 9.5. Assessment criteria are explained at the beginning of the semester.

  • References

    References

    ANTON, H., Calculus. 10ª ed. EUA: John Wiley & Sons, 2012

    BAPTISTA, M. O. BAPTISTA, M. O., Matemática: integrais duplos, triplos, de linha e de superfície, Lisboa: Edições Sílabo, 2001.

    FERREIRA, M.A.M., Matemática. Exercícios cálculo diferencial em Rn, Lisboa: Edições Sílabo, 1994.

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