Curricular Unit:Code:
Mathematics II831MAT2
Year:Level:Course:Credits:
1UndergraduateComputer Systems Engineering7 ects
Learning Period:Language of Instruction:Total Hours:
Spring SemesterPortuguese/English91
Learning Outcomes of the Curricular Unit:
This curricular unit is a complement to the previous Matemática I, in order to provide a deeper knowledge on some of the mathematical issues covered before. The aim is to provide more advanced mathematical tools, deepening the student’s mathematical knowledge.
The expected learning outcomes for this curricular unit are:
- To interpret and mathematically equate real problems, using the concepts of multivariable functions, multiple integrals and differential equations;
- To select and adequately apply the mathematical tools available for solving these problems;
- To interpret and critically analyze the results obtained.
Syllabus:
Multiple Integrals - double integrals and triple integrals. First-Order Differential Equations - separable differential equations, linear equations, Bernoulli equations and exact equations. Second-Order Linear Differential Equations – homogeneous constant coefficients equations, Euler-Cauchy equations, non-homogeneous equations using method of undetermined coefficients and using Variation of Parameters.
Demonstration of the Syllabus Coherence with the Curricular Unit's Objectives:
The syllabus presented covers the essential areas of knowledge and consistently achieves the objectives, since all the topics included in the program – multiple integrals and differential equations - cover the main aspects of the study that will enable students to select and properly apply mathematical tools in engineering problems solving.
Teaching Methodologies (Including Evaluation):
The teaching methodologies are mainly expositive, interrogative and demonstrative, both during classes and tutorial orientation sessions. Emphasis is given to the interpretation and mathematically equation of real problems, and to the proper selection and application of mathematical tools in problem solving. Problems and exercises are proposed, for resolution in classroom and individual study hours. Particular attention is given to the physical interpretation of the studied phenomena, trying to make a solid connection between theory and practice.
The evaluation is continuous, and includes the following items:
- Individual written tests (95%);
- Student performance, taking into account class attendance, the resolution of exercises outside classes, the attitude and active participation in class and in tutorial orientation (5%).
Demonstration of the Coherence between the Teaching Methodologies and the Learning Outcomes:
The proposed methodologies are consistent with the objectives set for the course since they were planned in order to enhance physical interpretation of the studied phenomena, trying to make a solid connection between theory and practice. It is expected, therefore to help students to develop the ability to apply such techniques in solving engineering problems.
Reading:
[1] Anton, H.; Bivens, I; Davis, S. Cálculo – Volume 2, Bookman
[2] Smith, Robert T. e Minton, Roland B. “Calculus – second edition”, McGraw-Hill
[3] Larson, R.; Hostetler, R.P.; Edwards, B.H. Cálculo – Volume 2, McGraw Hill
[4] Kreyszig, E. - “Advanced Engineering Mathematics”, Wiley, 7th Edition