Description

Fields and Waves presents the first contact in the student's degree with the phenomena of electromagnetic waves, which are the physical medium for transmission of information at almost instantaneous speed. Mathematical modeling of electromagnetic fields that
provide insights into the behavior of electromagnetic waves in real environments will be introduced.
English Friendly subject: International students may request from the teachers: a) materials and bibliographic references in English, b) tutoring sessions in English, c) exams and assessments in English.

Requirements

Before taking this course, it’s helpful (but not always mandatory) to have completed:

• Mathematics: Calculus 1 (V05G301V01101)
• Mathematics: Calculus 2 (V05G301V01106)

Instructors

Pino García, Antonio

Contents

1. Vector and differential analysis of fields

• 1.1 Scalar and vector fields
• 1.2 Systems of coordinates in space
• 1.3 Vector Algebra
• 1.4 Integral operators
• 1.5 Differential operators
• 1.6 Properties of operators

2. Electrostatics

• 2.1 Electric charge
• 2.2 Electric field and its properties
• 2.3 Electric potential
• 2.4 Electric permittivity
• 2.5 Gauss law
• 2.6 Equations of Poisson and Laplace. Capacitance

3. Magnetostatics

• 3.1 Electric current
• 3.2 Magnetic field and its properties
• 3.3 Magnetic permeability
• 3.4 Ampere's Law
• 3.5 Self-induction

4. Maxwell model

• 4.1 Maxwell's equations in integral form
• 4.2 Differential form of Maxwell's equations
• 4.3 Boundary conditions
• 4.4 Harmonic time variation and phasor notation
• 4.5 Energy and power density

5. Fundamentals and characteristics of waves

• 5.1 Wave equation in the phasor domain
• 5.2 Solutions in rectangular coordinates
• 5.3 Wave parameters: frequency, wavelength, propagation constant, impedance
• 5.4 Poynting vector and average power density
• 5.5 Progressive waves on lossy and lossless media
• 5.6 Polarization

6. Waves in the presence of obstacles

• 6.1 Wave incidence on conductors
• 6.2 Incidence on discontinuity between two media
• 6.3 Incident, reflected and transmitted wave
• 6.4 Standing wave diagram
• 6.5 Power transmission

Practical / Problem Sets

P1. Vector algebra and coordinate systems

• Review of operations with vectors in space
• Vector representation in Cartesian, cylindrical, and spherical systems
• Differential elements of length, area, and volume

P2. Electrostatics

• Circulation integral of the electric field
• Electric dipole
• Charge densities (linear, surface, volume)
• Potential and electric field of charge distributions
• Superposition principle
• Far field
• Electric displacement vector flow
• Gauss theorem (integral and differential forms)
• Capacitors
• Image theory

P3. Magnetostatics

• Surface and volume current densities
• Magnetic field of current distributions
• Superposition principle
• Ampere’s Law (integral and differential forms)
• Self-induction
• Image theory

P4. Maxwell’s model

• Faraday’s Law and Ampere-Maxwell Law applications
• Phasor and time-domain representation of EM fields
• Applications of Maxwell’s equations

P5. Fundamentals and characteristics of waves

• Plane wave propagation
• Wave parameters
• Wave polarization
• Phasor and time-domain representation of plane waves

P6. Waves in the presence of obstacles

• Wave incidence on metallic plane
• Incidence between dielectric media
• Standing waves

Learning Outcomes

B3

• CG3: Knowledge of basic subjects and technologies that enables the student to learn new methods and technologies, as well as providing versatility to face and adapt to new situations

C1

• CE1 / FB1: Ability to solve mathematical problems in Engineering
• Application of knowledge in:
  • Linear algebra
  • Geometry and differential geometry
  • Differential and integral calculus
  • Differential and partial differential equations
  • Numerical methods and algorithms
  • Statistics and optimization

C3

• CE3 / FB3: Comprehension and command of basic concepts related to:
  • General laws of mechanics
  • Thermodynamics
  • Electromagnetic fields and waves
  • Electromagnetism
• Application of these concepts to solve Engineering problems

D3

• CT3: Awareness of the need for lifelong learning and continuous quality improvement
• Demonstrates:
  • Flexible and open attitude
  • Ethical mindset toward different opinions and situations
  • Respect for non-discrimination (sex, race, religion)
  • Respect for fundamental rights and accessibility

Recommended Readings and Tools

Students are recommended to review all the basic operations with complex numbers and trigonometric functions, as well as the different techniques for solving systems of linear equations, calculating derivatives of elementary functions and calculating immediate integrals.

Planned Activities

Lecturing

• Exhibition by the professor of the contents of the subject
• Includes:
  • Theoretical foundations
  • Guidelines for assignments, exercises, or projects
• Competencies developed: B3, C1, C3, D3

Case studies

• Analysis of real facts, problems, or events to:
  • Understand and interpret situations
  • Propose and test hypotheses
  • Contrast data
  • Diagnose and explore alternative solutions
• Applied in both large and medium-sized groups
• Competencies developed: B3, C1, C3, D3

Problem solving

• Application of knowledge to specific situations
• Focus on:
  • Developing practical skills
  • Procedural understanding of the subject
• Conducted in computer labs
• Use of electromagnetic simulators
• Competencies developed: B3, C1, C3, D3

Assessment Methods and Criteria

Evaluation Activities

Problem and/or exercise solving (ECa)

• Description:
  ECa. Individual proof where students must develop appropriate or correct solutions through the exercise of routines, the application of formulas or algorithms, the application of procedures for transforming available information and the interpretation of results
• Qualification: 35
• Training and Learning Results:
  B3, C1, C3, D3

Problem and/or exercise solving (ECc)

• Description:
  ECc. Individual proof where students must develop appropriate or correct solutions through the exercise of routines, the application of formulas or algorithms, the application of procedures for transforming available information and the interpretation of results
• Qualification: 35
• Training and Learning Results:
  B3, C1, C3, D3

Problem and/or exercise solving (Short question tests)

• Description:
  Short question tests. Test in which the student has to solve a series of brief problems, applying the acquired knowledge
• Qualification: 5
• Training and Learning Results:
  B3, C1, C3, D3

Case studies (Deliverables)

• Description:
  Deliverables. Test for individual evaluation of the competences that includes the approach of a practical case. Students develop the analysis of the situation in order to know it, interpret it, solve it, generate hypothesis, contrast data, reflect, complete knowledge, diagnose it and train in alternative solution procedures
• Qualification: 25
• Training and Learning Results:
  B3, C1, C3, D3

Other comments on the Evaluation

• Following the policy guidelines of the Center, students can choose between:
  • Continuous assessment
  • Global (exam-only) assessment at the end of the term
• In all evaluation tests, the competences B3, C1, C3 and D3 will be evaluated

1. CONTINUOUS ASSESSMENT

The system of continuous assessment (EC) will consist of:

• a) A problem solving deliverables, worked in practical classes or on-line tests on topics 1, 2 and 3
  • Qualification: ECa (maximum 3 points)
  • Must reach 50% to count toward final grade
• b) A problem solving session on topics 1, 2 and 3
  • Qualification: ECb
  • Subtotal: EC1 = ECa + ECb (max 10 points)
• c) A problem solving deliverables, worked in practical classes or on-line tests on topics 4, 5 and 6
  • Qualification: ECc (maximum 3 points)
  • Must reach 50% to count
• d) A problem solving session on topics 4, 5 and 6
  • Qualification: ECd
  • Subtotal: EC2 = ECc + ECd (max 10 points)
• Final grade calculation:
  EC = (EC1 + EC2) / 2
• Condition:
  If either EC1 or EC2 is less than 3 (30%), the final grade is capped at 4.9 (Suspense)
• Planning of assessments approved by Academic Committee (CAG)
• Review process announced before each test
• Continuous assessment tests are not recoverable
• Taking ECb or ECd implies acceptance of continuous assessment system

2. EXAM-ONLY ASSESSMENT

• Mandatory for students not following continuous assessment
• One exam covering topics 1 to 6, divided into:
  • EC1 (topics 1–3)
  • EC2 (topics 4–6)
• Each part: maximum 10 points
• Final grade = average of both parts
• Must reach at least 30% in each part
• Continuous assessment students may take one or both parts to improve grades
• Best mark is retained

3. EXTRAORDINARY EXAM

• Divided into:
  • EX1 (topics 1–3, max 10 points)
  • EX2 (topics 4–6, max 10 points)
• Students may choose:
  • EX1 only
  • EX2 only
  • Both
• Best score between EC* and EX* retained
• Final grade = average
• Must reach 30% minimum in each part

4. END OF PROGRAM EXAM

• Same format as extraordinary exam
• Both parts compulsory
• Previous marks cannot be used

5. OBSERVATIONS

• Any student taking in-person tests (ECb, ECd, EC1, EC2, EX1, EX2) is considered presented
• Partial marks (EC1, EC2, EX1, EX2) are valid only for the same academic year
• Passing criteria:
  • Final grade ≥ 5
  • At least 30% in each part
• If one part <30%, final grade capped at 4.9 (Suspenso)
• Attendance to practices or submissions is not mandatory except for graded tests
• Plagiarism:
  • Final grade = 0 (Suspenso)
  • Reported to Center Head
• Use of generative AI (IAG):
  • Allowed
  • Must be ethical, critical, and responsible
  • Results must be verified
  • Recommended to declare tools used
• English Friendly subject:
  • Resources and bibliography in English
  • Tutoring in English
  • Exams and assessments in English upon request