Calculus II

It is recommended some knowledge of subjects of year 1 first semester mathematics (Mathematical Analysis I and Linear Algebra).

Activities theoreticaI (Lecture); PraticaI (Exercises – mathematicaI and computacionaI impIementation) and Lab (Laboratory work, programming in MatIab, MapIe, Maxima and GeoGebra)
Progress assessment – There are two options:
First option: A midterm exam and/or a finaI written exam worth 100% of the finaI grade. Second option: Continuous evaIuation
–   A midterm exam and/or a finaI written exam worth 60% of the finaI grade
–   TheoreticaI-PracticaI activities (programming of mathematicaI methods) worth 40% of the finaI grade
For purposes of caIcuIating the finaI grade, weighted average of the tests and works, the student must have a minimum score of 6.5 (out of 20) on the exam.
Students receiving a grade higher than 18 (on a grading scaIe of 1 to 20) are required to do an extra written and/or oraI test. If students choose not to do this extra test, the finaI grade wiII remain 18.

The main aims of this course unit are to teach students:
The important role of mathematics as a fundamental basis within the engineering fields; The use and application of mathematics software, such as Matlab, Maple and Maxima; The use of mathematics as an auxiliary tool for analytical computational matter.
At the end of this course unit the learner is expected to be able:
To develop skills of abstraction, demonstration, 3D Visualization and representation, algorithms and programming of numerical methods.
To understand and apply programmed matter and other matters related to the topics covered in study plan of this course unit.

Functions of Two or More Variables; Limits and Continuity; Partial Derivatives; Differentiability and Chain Rules; Tangent Planes; Total Differentials; Differentiability; Directional Derivatives and Gradients; Maxima and Minima of functions of two variables; Lagrange Multipliers.
Double Integrals Over Nonrectangular Regions; Double Integrals in Polar Coordinates; Area and Surface Area; Triple Integrals; Volume of Solids; Centroid; Center of Gravity; Triple Integrals in Cylindrical and Spherical Coordinates; Change of Variables in Multiple Integrals; Jacobians.
Introduction to Numerical Methods using Matlab. Solutions of Equations in one Variable: The Bisection Method; Newton’s Method; Interpolation and Polynomial Approximation: Divided Differences; Numerical Differentiation and Integration; Trapezoid Rule and Simpson Rule; Initial-Value Problems for Ordinary Differential Equations: Euler’s Method and Runge-Kutta Methods.
Programming in Matlab and CAS.

NAO