Curricular Unit: Code: Mathematics I 831MAT1 Year: Level: Course: Credits: 1 Undergraduate Computer Systems Engineering 7 ects Learning Period: Language of Instruction: Total Hours: Winter Semester Portuguese/English 91 Learning Outcomes of the Curricular Unit: The main objective is to create solid bases of mathematical knowledge (concepts of function, derivative and integral), and to promote logical and methodological thinking, indispensables for any engineer to face the challenges that may arise in professional practice.At the end of the course the student will possess the following skills:- Ability to interpret and mathematically equate real problems, using the concepts of functions, derivatives and integrals;- Ability to select and adequately apply the mathematical tools available for solving these problems;- Ability to interpret and critically analyze the results obtained. Syllabus: 1. Real Valued Functions.1.1. Functions in R: Basic concepts. Domain and range of a function. Exponential and logarithmic functions. Trigonometric functions. Derivatives. Rules of differentiation. Optimization problems.1.2. Functions in Rn. Partial derivatives. Chain rule. Gradient vector and directional derivatives.2. Integrals and Primitives.2.1. Indefinite integration. Integration techniques.2.2. Definite integrals. Fundamental Theorem of Calculus. 3. Matrices and Determinants.3.1. Matrices. Matrix operations. Inverse of a matrix. Solving systems of linear equations.3.2. Determinants. Determinants calculus. Cramer’s rule. 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 - differentiability, integrals and primitives, matrices and determinants - 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:  Larson, R.; Hostetler, R.P.; Edwards, B.H. Cálculo – Volume 1, McGraw Hill, 2006. Larson, R.; Hostetler, R.P.; Edwards, B.H. Cálculo – Volume 2, McGraw Hill, 2006. Anton, H.; Bivens, I; Davis, S. Cálculo – Volume 1, Bookman, 2014. Anton, H.; Bivens, I; Davis, S. Cálculo – Volume 2, Bookman, 2007. Smith, R. T.; Minton, R. B. Calculus – second edition, McGraw-Hill, 2011. Sullivan, M. Precalculus – seventh edition, Prentice Hall, 2015. Anton, H.; Busby, R.C. Álgebra Linear Contemporânea, Bookman, 2005 Croft, A. & Davison, R. Mathematics for Engineers, Pearson Education, 2015. Wolfram Alpha: www.wolframalpha.com