101212 - MATHEMATICS III

Subject type: Basic

Coordinator: Julián Horrillo Tello

Trimester: First term

Credits: 6

It is the last subject of mathematics and provides basic tools in the training of the engineer. The course enables the student to understand and / or solve mathematical problems, which may arise in engineering, related to analysis and linear algebra.

The learning outcomes specify the specific measure of the competencies worked on.
This subject contributes to the following learning outcomes specified for the subject to which it belongs:

• LO1: Correctly apply the fundamental concepts of differential and integral calculus, linear algebra and geometry, developing the ability to apply them to problems in engineering.
• LO2: Use appropriately the differential equations in modeling and problem solving in engineering.
• LO3: Use the mathematical tools needed to solve analytical and numerical problems.
• LO4: Use the basic concepts of non-deterministic analysis and statistics in engineering problems.
• LO5: Analyze and critique the results of engineering problems.

The classes will be master classes (development of the theory and practical examples) and participatory (conceptual questions, guided resolution of exercises and presentation of exercises by the students).
1. The teacher will explain in class the theoretical and practical concepts (examples), emphasizing the most important aspects and leaving some content for individual study. The teacher will also ask conceptual questions regarding the concepts explained.
2. It is advisable for students to try to solve the proposed exercises individually or in pairs. Some will be solved by the teacher and / or the students in class in a participatory way.
3. Students can complete the class contents and the notes with the books of the bibliography.

Topic 1: Introduction to complex numbers

1. Origin of numbers C and operations with C
2. Polar shape of the C
3. Trigonometric shape - exponential
4. Complex roots of an equation

Topic 2: Limits and derivatives in complexes

1. Complex functions
2. Derivability of complex functions
3. Integration of complex functions. Primitives

Topic 3: Elementary functions

1. Complex polynomial function
2. Complex exponential function
3. Complex logarithmic function
4. Complex trigonometric functions

Topic 4: Diagonalization of matrices

1. Linear application
2. Characteristic polynomial, vaps and veps
3. Diagonalization of matrices_I
4. Diagonalization of matrices_II

Topic 5: Ordinary Differential Equations (ODE)

1. Separable ordinary differential equations
2. Linear ordinary differential equations
3. Exact ordinary differential equations
4. Exercises EDO I
5. Exercises EDO II
6. Mathematical models
7. Mathematical model exercises

Topic 6: Laplace transform (TL)

1. Laplace transform
2. Inverse Laplace transform

Master class: development of theory and practical examples.
Participatory class: collaborative instruction with conceptual questions and resolution of guided exercises (collect evidence of learning of almost all expected results, serve as a guide for self-assessment of the student and their active participation in class).
Resolution and presentation of exercises: resolution and presentation of exercises by students (collect evidence of all expected results).
Assessment exercises that gather general and more specific evidence of learning.

70% testing

There will be two exams during the course (35% each test), a first partial (3 first topics) and a final exam with 5 questions each. Those who have failed the first exam will have to take this part in the final exam. Those who have passed the first part-time will not need to take the final exam (the first part-time is subject-free). Students who fail the final exam will go to recovery. The maximum grade for the retake is 6 points and the evaluable exercises are not compatible with the retake. To opt for an average between the two exams, you must get a minimum of 5 points in the first exam and 4 points in the second exam. To the average grade obtained between the two exams, as long as it is a minimum grade of 4, the score obtained from the evaluable exercises will be added (30%).

30% Active participation in class

It will be evaluated based on the participation in class and the answers to the questions that the teacher will propose during the development of the classes.

Krasnov, m et al. 1990. Higher mathematics course for engineers. Mir. Moscow

Notes of the subject

Boyce, W .; DiPrima, R. (1990). Differential equations. Mexico: Limusa Noriega Editores.

Schaum (1971). Complex variable. Madrid: Mc Graw-Hill