Code: | M1029 | Acronym: | M1029 | Level: | 100 |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mathematics |
Active? | Yes |
Responsible unit: | Department of Mathematics |
Course/CS Responsible: | Bachelor in Landscape Architecture |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
L:AP | 34 | Official Study Plan | 1 | - | 6 | 56 | 162 |
The aim of this course is that the student:
- masters basic concepts and results of Euclidean plane geometry, including isometries;
- masters basic techniques of differential and recognizes some of its applications;
- masters some basic concepts of probability and statistics;
specially those necessary for geographic information course units.
1) Statics and numerical methods:
Sum symbol; average, variance, standard deviation; Least squares line; Correlation coefficient.
2) Trigonometry:
Oriented angles; Trigonometric circle; Measure of an angle. Parametric equation of a circle. Sine,cossine and tangent of an angle.
3) Geometry:
Coordinate axes and point coordinates; Distance between two points; Circle and sphere equations.
Planar symmetry (translations, reflections, homothety);
Vectors: Scalar product of vectors; Angle defined by two vectors; Perpendicularity among vectors, lines and planes.
Equations for lines and planes (implicit and parametric); Slope of a line on a plane; Slopes of perpendicular lines; Parallelism among vectors and planes.
4) Functions:
Graphs; Image of a set; Injective, surjective and bijective functions; Composion; Inverse function. Trigonometric functions: Sine, cossine and tangent; Properties: periodicity, parity, zeros and local extremes; Graphs; Inverse functions.
5) Continuity and differentiation of real valued functions of one real variable:
Intuitive approach to limits and continuity of functions; Sum, difference, product and quotient of functions and composion of functions. Continuity of polynomial, rational, trigonometric, exponential and logarithm functions.
6) Derivative of a function at a given point; Geometric interpretation; Derivative of sums, differences, products and quotients of functions; Derivative of composed and inverse functions; Derivative of polynomial, rational, trigonometric, exponential and logarithm functions.
Derivative rules and reference functions; tangent line to graphs.
Presentation of topics in lectures, including the relevant examples.
Exercises presented in the course's homepage, solved in example classes.
designation | Weight (%) |
---|---|
Teste | 100,00 |
Total: | 100,00 |
designation | Time (hours) |
---|---|
Estudo autónomo | 106,00 |
Frequência das aulas | 52,00 |
Total: | 158,00 |
The final mark is either the sum of the classifications in 3 tests or approval in exam in the second exam period.
The first test is for 6 points and the other are for 7 points. For approval in the tests the student should obtain a total of at least 9,50 points.
During the exam period there is an additional test divided in 3 parts, each corresponding to a test, so that each student can improve the classification obtained in a test or tests.
A minimum of 9.5 in the exam is required for approval.
An additional test, either written or oral, may be asked of students aiming at marks over 18 out of 20.
The student can add up to 2 points to the final mark (to a maximum of 20 points) by solving extra given exercises: 4 exercises, more difficult than those solved at the xample classes, corresponding to different parts of the program, each quoted to 0,5 points. At one of the final classes, the students will present an exercise.
The student can add up to 2 points to the final mark (to a maximum of 20 points) by solving extra given exercises: 4 exercises, more difficult than those solved at the xample classes, corresponding to different parts of the program, each quoted to 0,5 points. At one of the final classes, the students will present an exercise.