A 100% online Professional master’s degree that will allow you to delve into Material Physics and apply this science with current technology" 

The scientific community that focuses its studies on Material Physics continues to make progress and provide society with greater knowledge about new properties of existing resources, the development of nanomaterials and the promotion of other technological, biological or health disciplines. A progress, where engineering professionals can make a great contribution thanks to direct technique application and physics concepts.

At the same time, the need to find new, more effective, efficient and sustainable materials has driven this area, both from the private and public sectors. An expanding field of study for engineering specialists who wish to thrive in the field of Material Physics. For this reason, TECH has created this Professional master’s degree, where over course of 12 months, the graduate will obtain the necessary knowledge about fluid mechanics, advanced thermodynamics and optics.

All this, in addition, with a university program that has educational tools in which the latest academic teaching technology has been used. Therefore, through video conferences, detailed videos or case study simulations, students will be able to delve, in a much more dynamic way, into symmetries and conservation laws, the handling of Navier-Stokes equations or the connection between the microscopic structure (atomic, nanometric or micrometric) and the macroscopic material properties.

This way, TECH offers engineering professionals the most advanced and exhaustive knowledge on Material Physics. All this through an exclusively online program that you can access whenever and wherever you want. Students only need an electronic device (computer, tablet or cell phone) with Internet connection to be able to view the information on the virtual platform. Also, with the Relearning system, you will be able to reduce the long hours of study normally spent in other methodologies.

Excel in the field of new materials discovery, thanks to the solid concepts you will acquire in this program"

This Professional master’s degree in Material Physics contains the most complete and up-to-date program on the market. The most important features include:

• Practical case studies are presented by experts in Physics 
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• Theoretical lessons, questions to the expert, debate forums on controversial topics, and individual reflection assignments 
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TECH adapts to you and has therefore created a university program, where you can distribute the teaching load according to your personal needs"

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Gain essential knowledge about magnetostatics in both material media and vacuum with this university program"

This Professional master’s degree has been structured in 10 modules which will allow students to delve into optics, classical mechanics, electromagnetism, statistical physics or Material Physics itself. The Relearning method, based on content reiteration, as well as the multimedia teaching material, will enhance learning. Likewise, students will be able to access this program's content 24 hours a day from any computer with Internet connection.

The multimedia resource library will be available 24 hours a day. Access it easily from your computer with internet connection"

Module 1. Optics 

1.1. Waves: Introduction 

1.1.1. Wave Motion Equation 
1.1.2. Plane Waves 
1.1.3. Spherical Waves 
1.1.4. Harmonic Solution of the Wave Equation 
1.1.5. Fourier Analysis 

1.2. Wavelet Superposition 

1.2.1. Superposition of Waves of the Same Frequency 
1.2.2. Superposition of Waves of Different Frequency 
1.2.3. Phase Velocity and Group Velocity 
1.2.4. Superposition of Waves with Perpendicular Electric Vectors 

1.3. Electromagnetic Theory of Light 

1.3.1. Maxwell's Macroscopic Equations 
1.3.2. The Material Response 
1.3.3. Energy Relations 
1.3.4. Electromagnetic Waves 
1.3.5. Homogeneous and Isotropic Linear Medium 
1.3.6. Transversality of Plane Waves 
1.3.7. Energy Transport 

1.4. Isotropic Media 

1.4.1. Reflection and Refraction in Dielectrics 
1.4.2. Fresnel Formulas 
1.4.3. Dielectric Media 
1.4.4. Induced Polarization 
1.4.5. Classical Lorentz Dipole Model 
1.4.6. Propagation and Diffusion of a Light Beam 

1.5. Geometric Optics 

1.5.1. Paraxial Approximation 
1.5.2. Fermat's Principle 
1.5.3. Trajectory Equation 
1.5.4. Propagation in Non-Uniform Media 

1.6. Image Formation 

1.6.1. Image Formation in Geometrical Optics 
1.6.2. Paraxial Optics 
1.6.3. Abbe's Invariant 
1.6.4. Increases 
1.6.5. Centered Systems 
1.6.6. Focuses and Focal Planes 
1.6.7. Planes and Main Points 
1.6.8. Thin Lenses 
1.6.9. System Coupling 

1.7. Optical Instruments 

1.7.1. The Human Eye 
1.7.2. Photographic and Projection Instruments 
1.7.3. Telescopes 
1.7.4. Near Vision Instruments: Compound Magnifier and Microscope 

1.8. Anisotropic Media 

1.8.1. Polarization 
1.8.2. Electrical Susceptibility Index Ellipsoid 
1.8.3. Wave Equation in Anisotropic Media 
1.8.4. Propagation Conditions 
1.8.5. Refraction in Anisotropic Media 
1.8.6. Fresnel Construction 
1.8.7. Construction with the Index Ellipsoid 
1.8.8. Retarders 
1.8.9. Absorbent Anisotropic Media 

1.9. Interference 

1.9.1. General Principles and Interference Conditions
1.9.2. Wavefront Split Interference 
1.9.3. Young's Stripes 
1.9.4. Amplitude Division Interferences 
1.9.5. Michelson's Interferometer 
1.9.6. Interference of Multiple Beams Obtained by Amplitude Division 
1.9.7. Fabry-Perot’s Interferometer 

1.10. Diffraction 

1.10.1. The Huygens-Fresnel Principle 
1.10.2. Fresnel and Fraunhofer Diffraction 
1.10.3. Fraunhofer's Diffraction through an Aperture 
1.10.4. Limitation of the Resolutive Power of the Instruments 
1.10.5. Fraunhofer Diffraction by Various Apertures 
1.10.6. Double Slit 
1.10.7. Diffraction Grating 
1.10.8. Introduction to Kirchhoff's Scalar Theory 

Module 2. Classical Mechanics I 

2.1. Kinematics and Dynamics: Review 

2.1.1. Newton’s Law  
2.1.2. Reference Systems 
2.1.3. Motion Equation of Particles 
2.1.4. Conservation Theorems 
2.1.5. Particle System Dynamics 

2.2. More Newtonian Mechanics 

2.2.1. Conservation Theorems for Particle Systems 
2.2.2. Universal Gravity Law 
2.2.3. Force Lines and Equipotential Surfaces 
2.2.4. Limitations of Newtonian Mechanics 

2.3. Kinematics of Rotations 

2.3.1. Fundamentals of Mathematics 
2.3.2. Infinitesimal Rotations 
2.3.3. Angular Velocity and Acceleration 
2.3.4. Rotational Reference Systems 
2.3.5. Coriolis Force 

2.4. Rigid Solid Study 

2.4.1. Rigid Solid Kinematics 
2.4.2. Inertia Tensor of Rigid Solids 
2.4.3. Main Inertia Axes  
2.4.4. Steiner and Perpendicular Axes Theorems 
2.4.5. Kinetic Energy of Rotation 
2.4.6. Angular Momentum 

2.5. Symmetries and Conservation Laws 

2.5.1. Conservation Theorem of Linear Momentum 
2.5.2. Conservation Theorem of Angular Momentum 
2.5.3. Energy Conservation Theorem 
2.5.4. Classical Mechanic Symmetries: Galileo Group 

2.6. Coordinate Systems: Euler Angles 

2.6.1. Coordinate Systems and Changes 
2.6.2. Euler Angles 
2.6.3. Euler Equations 
2.6.4. Stability Around a Major Axis 

2.7. Rigid Solid Dynamics Applications 

2.7.1. Spherical Pendulum 
2.7.2. Free Symmetrical Top Movement 
2.7.3. Symmetrical Top Movement with a Fixed Point 
2.7.4. Gyroscopic Effect 

2.8. Movement Under Central Forces 

2.8.1. Introduction to Central Force Fields 
2.8.2. Reduced Mass 
2.8.3. Trajectory Equation 
2.8.4. Central Field Orbits 
2.8.5. Centrifugal Energy and Effective Potential 

2.9. Kepler's Problem 

2.9.1. Planetary Motion - Kepler's Problem 
2.9.2. Approximate Solution to Kepler's Equation 
2.9.3. Kepler's Laws 
2.9.4. Bertrand's Theorem 
2.9.5. Stability and Perturbation Theory 
2.9.6. 2-Body Problem 

2.10. Collisions 

2.10.1. Elastic and Inelastic Shocks: Introduction 
2.10.2. Center of Mass Coordinate System 
2.10.3. Laboratory Coordinate System 
2.10.4. Elastic Shock Kinematics 
2.10.5. Particle Dispersion - Rutherford's Dispersion Formula 
2.10.6. Effective Section 

Module 3. Electromagnetism 

3.1. Vector Calculus: Review 

3.1.1. Vector Operations 

3.1.1.1. Scalar Products 
3.1.2.1. Vectorial Products 
3.1.3.1. Mixed Products 
3.1.4.1. Triple Product Properties 

3.1.2. Vector Transformation 

3.1.2.1. Differential Calculus 
3.1.2.1. Gradient 
3.1.2.2. Divergence 
3.1.2.3. Rotational 
3.1.2.4. Multiplication Rules 

3.1.3. Integral Calculus 

3.1.3.1. Line, Surface and Volume Integrals 
3.1.3.2. Fundamental Calculus Theorem 
3.1.3.3. Fundamental Gradient Theorem 
3.1.3.4. Fundamental Divergence Theorem 
3.1.3.5. Fundamental Rotational Theorem 

3.1.4. Dirac Delta Function 
3.1.5. Helmholtz Theorem 

3.2. Coordinate Systems and Transformations 

3.2.1. Line, Surface and Volume Element 
3.2.2. Cartesian Coordinates 
3.2.3. Polar Coordinates 
3.2.4. Spherical Coordinates 
3.2.5. Cylindrical Coordinates 
3.2.6. Coordinate Change 

3.3. Electric Field 

3.3.1. Point Charges
3.3.2. Coulomb's Law
3.3.3. Electric Field and Field Lines 
3.3.4. Discrete Charge Distributions 
3.3.5. Continuous Load Distributions 
3.3.6. Divergence and Rotational Electric Field 
3.3.7. Electric Field Flow: Gauss’ Theorem

3.4. Electric Potential 

3.4.1. Electric Potential Definition 
3.4.2. Poisson's Equation 
3.4.3. Laplace's Equation 
3.4.4. Potential Charge Distribution Calculation 

3.5. Electrostatic Energy 

3.5.1. Electrostatic Work 
3.5.2. Discrete Charge Distribution Energy 
3.5.3. Continuous Charge Distribution Energy 
3.5.4. Electrostatic Equilibrium Conductors 
3.5.5. Induced Charges 

3.6.  Vacuum Electrostatics 

3.6.1. Laplace's Equation in One, Two and Three Dimensions 
3.6.2. Laplace’s Equation - Boundary Conditions and Uniqueness Theorems 
3.6.3. Image Method  
3.6.4. Variable Separation 

3.7. Multi-Polar Expansion 

3.7.1. Approximate Potentials Away from the Source 
3.7.2. Multi-Polar Development 
3.7.3. Mono-Polar Term 
3.7.4. Di-Polar Term 
3.7.5. Coordinate Origins in Multipole Expansions 
3.7.6. Electric Field of an Electric Dipole 

3.8. Electrostatics in Material Media I 

3.8.1. Dielectric Field 
3.8.2. Dielectric Types 
3.8.3. Vector Displacement 
3.8.4. Gauss's Law in Dielectric Presence 
3.8.5. Boundary Conditions 
3.8.6. Electric Field within Dielectrics 

3.9. Electrostatics in Material Media II: Linear Dielectrics 

3.9.1. Electrical Susceptibility 
3.9.2. Electrical Permittivity 
3.9.3. Dielectric Constant 
3.9.4. Dielectric Systems Energy 
3.9.5. Dielectric Forces 

3.10. Magnetostatics 

3.10.1. Magnetic Induction Field 
3.10.2. Electric Currents 
3.10.3. Magnetic Field Calculation: Biot and Savart's Law 
3.10.4. Lorentz Force 
3.10.5. Divergence and Rotational Magnetic Field 
3.10.6. Ampere's Law 
3.10.7. Magnetic Vector Potential 

Module 4. Classical Mechanics II 

4.1. Oscillations 

4.1.1. Simple Harmonic Oscillator 
4.1.2. Damped Oscillator 
4.1.3. Forced Oscillator 
4.1.4. Fourier Series 
4.1.5. Green's Function 
4.1.6. Non-Linear Oscillators 

4.2. Coupled Oscillations I 

4.2.1. Introduction 
4.2.2. Coupling of Two Harmonic Oscillators 
4.2.3. Normal Trends 
4.2.4. Weak Coupling 
4.2.5. Forced Vibrations of Coupled Oscillators 

4.3. Coupled Oscillations II 

4.3.1. General Theory of Coupled Oscillations 
4.3.2. Normal Coordinates 
4.3.3. Multiple Oscillator Coupling: Continuous Boundary and Vibrating Wire 
4.3.4. Wave Equation 

4.4. Special Relativity Theory 

4.4.1. Inertial Reference Systems  
4.4.2. Galileo’s Invariance 
4.4.3. Lorentz Transformations 
4.4.4. Relative Velocities 
4.4.5. Linear Relativistic Momentum 
4.4.6. Relativistic Invariants 

4.5. Tensor Formalism of Special Relativity 

4.5.1. Quadrivectors 
4.5.2. Quadrimomentum and Quadriposition 
4.5.3. Relativistic Energy 
4.5.4. Relativistic Forces 
4.5.5. Relativistic Particle Collisions 
4.5.6. Particle Disintegrations 

4.6. Introduction to Analytical Mechanics 

4.6.1. Links and Generalized Coordinates 
4.6.2. Mathematical Tools: Variance Calculation 
4.6.3. Definition of Action 
4.6.4. Hamilton Principle: Extreme Action 

4.7. Lagrangian Formulation 

4.7.1. Lagrangian Definition 
4.7.2. Variance Calculation 
4.7.3. Euler-Lagrange Equations 
4.7.4. Conserved Quantities 
4.7.5. Extension to Non-Holonomous Systems 

4.8. Hamiltonian Formulation 

4.8.1. Phasic Space 
4.8.2. Legendre Transformations: Hamiltonian 
4.8.3. Canonical Equations 
4.8.4. Conserved Quantities 

4.9. Analytical Mechanics-Extension 

4.9.1. Poisson Parentheses 
4.9.2. Lagrange Multipliers and Bond Forces 
4.9.3. Liouville Theorem 
4.9.4. Virial Theorem 

4.10. Analytical Relativistic Mechanics and Classical Field Theory 

4.10.1. Charge Movement in Electromagnetic Fields 
4.10.2. Lagrangian of a Free relativistic particle 
4.10.3. Interaction Lagrangian 
4.10.4. Classical Field Theory: Introduction 
4.10.5. Classical Electrodynamics 

Module 5. Electromagnetism II 

5.1.  Magnetism in Material Mediums 

5.1.1. Multi-Polar Development 
5.1.2. Magnetic Dipole 
5.1.3. Field Created by a Magnetic Material 
5.1.4. Magnetic Intensity 
5.1.5. Types of Magnetic Materials: Diamagnetic, Paramagnetic and Ferromagnetic 
5.1.6. Border Conditions 

5.2. Magnetism in Material Media II 

5.2.1. Auxiliary Field H 
5.2.2. Ampere's Law in Magnetized Media 
5.2.3. Magnetic Susceptibility 
5.2.4. Magnetic Permeability 
5.2.5. Magnetic Circuits 

5.3. Electrodynamics 

5.3.1. Ohm's Law 
5.3.2. Electromotive Force 
5.3.3. Faraday's Law and its Limitations 
5.3.4. Mutual Inductance and Self-Inductance 
5.3.5. Induced Electric Field 
5.3.6. Inductance 
5.3.7. Magnetic Field Energy 

5.4. Maxwell's Equations 

5.4.1. Displacement Current 
5.4.2. Maxwell's Equations in Vacuum and in Material Media 
5.4.3. Boundary Conditions 
5.4.4. Solution Uniqueness 
5.4.5. Electromagnetic Energy 
5.4.6. Electromagnetic Field Drive 
5.4.7. Angular Momentum of Electromagnetic Fields 

5.5. Conservation Laws 

5.5.1. Electromagnetic Energy 
5.5.2. Continuity Equation 
5.5.3. Poynting's Theorem 
5.5.4. Newton's Third Law in Electrodynamics 

5.6. Waves electromagnetic: Introduction 

5.6.1. Wave Motion 
5.6.2. Wave Equation 
5.6.3. Electromagnetic Spectrum 
5.6.4. Plane Waves 
5.6.5. Sine Waves 
5.6.6. Boundary Conditions: 
5.6.7. Polarization 

5.7. Electromagnetic Waves in Vacuums 

5.7.1. Wave Equation for Electric Fields and Magnetic Induction 
5.7.2. Monochromatic Waves 
5.7.3. Electromagnetic Wave Energy 
5.7.4. Electromagnetic Wave Momentum 

5.8. Electromagnetic Waves in Material Media 

5.8.1. Flat Dielectric Waves 
5.8.2. Flat Conductor Waves 
5.8.3. Wave Propagation in Linear Media 
5.8.4. Medium Dispersive 
5.8.5. Reflection and Refraction 

5.9. Waves in Confined Mediums I 

5.9.1. Maxwell's Guide Equations 
5.9.2. Dielectric Guides 
5.9.3. Modes in a Guide 
5.9.4. Propagation speed 
5.9.5. Rectangular Guide 

5.10. Waves in Confined Mediums 

5.10.1. Resonant Cavities 
5.10.2. Transmission Lines 
5.10.3. Transitional Regime 
5.10.4. Permanent Regime 

Module 6. Advanced Thermodynamics 

6.1. Formalism of Thermodynamics 

6.1.1. Laws of Thermodynamics 
6.1.2. The Fundamental Equation 
6.1.3. Internal Energy: Euler's Form 
6.1.4. Gibbs-Duhem Equation 
6.1.5. Legendre Transformations 
6.1.6. Thermodynamic Potentials 
6.1.7. Maxwell's Relations for a Fluid 
6.1.8. Stability Conditions 

6.2. Microscopic Description of Macroscopic Systems I 

6.2.1. Microstates and Macrostates: Introduction 
6.2.2. Phase Space 
6.2.3. Collectivities 
6.2.4. Microcanonical Collectivity 
6.2.5. Thermal Equilibrium 

6.3. Microscopic Description of Macroscopic Systems II 

6.3.1. Discrete Systems 
6.3.2. Statistical Entropy 
6.3.3. Maxwell-Boltzmann Distribution 
6.3.4. Pressure 
6.3.5. Effusion 

6.4. Canonical Collectivity 

6.4.1. Partition Function 
6.4.2. Ideal Systems 
6.4.3. Energy Degeneration 
6.4.4. Behavior of the Monoatomic Ideal Gas at a Potential 
6.4.5. Energy Equipartition Theorem 
6.4.6. Discrete Systems 

6.5. Magnetic Systems 

6.5.1. Thermodynamics of Magnetic Systems 
6.5.2. Classical Paramagnetism 
6.5.3. ½" Spin Paramagnetism
6.5.4. Adiabatic Demagnetization 

6.6. Phase Transitions 

6.6.1. Classification of Phase Transitions 
6.6.2. Phase Diagrams 
6.6.3. Clapeyron Equation 
6.6.4. Vapor-Condensed Phase Equilibrium 
6.6.5. The Critical Point 
6.6.6. Ehrenfest's Classification of Phase Transitions 
6.6.7. Landau's Theory 

6.7. Ising's Model 

6.7.1. Introduction 
6.7.2. One-Dimensional Chain 
6.7.3. Open One-Dimensional Chain 
6.7.4. Mean Field Approximation 

6.8. Real Gases 

6.8.1. Comprehensibility Factor: Virial Development 
6.8.2. Interaction Potential and Configurational Partition Function
6.8.3. Second Virial Coefficient 
6.8.4. Van der Waals Equation 
6.8.5. Lattice Gas 
6.8.6. Corresponding States Law 
6.8.7. Joule and Joule-Kelvin Expansions 

6.9. Photon Gas 

6.9.1. Boson Statistics Vs. Fermion Statistics 
6.9.2. Energy Density and Degeneracy of States 
6.9.3. Planck Distribution 
6.9.4. Equations of State of a Photon Gas 

6.10. Macrocanonical Collectivity 

6.10.1. Partition Function 
6.10.2. Discrete Systems 
6.10.3. Fluctuations 
6.10.4. Ideal Systems 
6.10.5. The Monoatomic Gas 
6.10.6. Vapor-Solid Equilibrium 

Module 7. Material Physics 

7.1. Materials Science and Solid State 

7.1.1. Field of Study of Materials Science 
7.1.2. Classification of Materials According to the Type of Bonding 
7.1.3. Classification of Materials According to Their Technological Applications 
7.1.4. Relationship between Structure, Properties and Processing 

7.2. Crystalline Structures 

7.2.1. Order and Disorder: Basic Concepts 
7.2.2. Crystallography: Fundamental Concepts 
7.2.3. Review of Basic Crystal Structures: Simple Metallic and Ionic Structures 
7.2.4. More Complex Crystal Structures (Ionic and Covalent) 
7.2.5. Structure of Polymers 

7.3. Defects in Crystalline Structures 

7.3.1. Classification of Imperfections 
7.3.2. Structural Defects 
7.3.3. Punctual Defects 
7.3.4. Other Imperfections 
7.3.5. Dislocations 
7.3.6. Interfacial Defects 
7.3.7. Extended Defects 
7.3.8. Chemical Imperfections 
7.3.9. Substitutional Solid Solutions 
7.3.10. Interstitial Solid Solutions 

7.4. Phase Diagrams  

7.4.1. Fundamental Concepts  

7.4.1.1. Solubility Limit and Phase Equilibrium 
7.4.1.2. Interpretation and Use of Phase Diagrams: Gibbs Phase Rule 

7.4.2. 1 Component Phase Diagram 
7.4.3. 2 Component Phase Diagram  

7.4.3.1. Total Solubility in the Solid State 
7.4.3.2. Total Insolubility in the Solid State 
7.4.3.3. Partial Solubility in the Solid State 

7.4.4. 3 Component Phase Diagram 

7.5. Mechanical Properties 

7.5.1. Elastic Deformation 
7.5.2. Plastic Deformation 
7.5.3. Mechanical Testing 
7.5.4. Fracture 
7.5.5. Fatigue 
7.5.6. Fluence 

7.6. Electrical Properties 

7.6.1. Introduction 
7.6.2. Conductivity. Conductors 
7.6.3. Semiconductors 
7.6.4. Polymers 
7.6.5. Electrical Characterization 
7.6.6. Insulators 
7.6.7. Conductor-Insulator Transition 
7.6.8. Dielectrics 
7.6.9. Dielectric Phenomena 
7.6.10. Dielectric Characterization 
7.6.11. Materials of Technological Interest 

7.7. Magnetic Properties 

7.7.1. Origin of Magnetism 
7.7.2. Materials with Magnetic Dipole Moment 
7.7.3. Types of Magnetism 
7.7.4. Local Field 
7.7.5. Diamagnetism 
7.7.6. Paramagnetism 
7.7.7. Ferromagnetism 
7.7.8. Antiferromagnetism 
7.7.9. Ferrimagnetism 

7.8. Magnetic Properties II 

7.8.1. Domains 
7.8.2. Hysteresis 
7.8.3. Magnetostriction 
7.8.4. Materials of Technological Interest: Magnetically Soft and Hard 
7.8.5. Characterization of Magnetic Materials 

7.9. Thermal Properties 

7.9.1. Introduction 
7.9.2. Heat Capacity 
7.9.3. Thermal Conduction 
7.9.4. Expansion and Contraction 
7.9.5. Thermoelectric Phenomena 
7.9.6. Magnetocaloric Effect 
7.9.7. Characterization of Thermal Properties

7.10. Optical Properties: Light and Matter 

7.10.1. Absorption and Re-Emission 
7.10.2. Light Sources 
7.10.3. Energy Conversion 
7.10.4. Optical Characterization 
7.10.5. Microscopy Techniques 
7.10.6. Nanostructures 

Module 8. Analog and Digital Electronics 

8.1. Circuit Analysis

8.1.1. Element Constraints 
8.1.2. Connection Constraints 
8.1.3. Combined Constraints 
8.1.4. Equivalent Circuits 
8.1.5. Voltage and Current Division 
8.1.6. Circuit Reduction 

8.2. Analog Systems 

8.2.1. Kirchoff's Laws 
8.2.2. Thévenin's Theorem 
8.2.3. Norton's Theorem 
8.2.4. Introduction to Semiconductor Physics 

8.3. Devices and Characteristic Equations  

8.3.1. Diode 
8.3.2. Bipolar Transistors (BJTs) and MOSFETs 
8.3.3. Pspice Model 
8.3.4. Characteristic Curves 
8.3.5. Regions of Operation 

8.4. Amplifiers  

8.4.1. Amplifier Operation 
8.4.2. Equivalent Circuits of Amplifiers 
8.4.3. Feedback 
8.4.4. Frequency Domain Analysis 

8.5. Amplification Stages 

8.5.1. BJT and MOSFET Amplifier Function 
8.5.2. Polarization 
8.5.3. Equivalent Small-Signal Model 
8.5.4. Single-Stage Amplifiers 
8.5.5. Frequency Response 
8.5.6. Connection of Amplifier Stages in Cascade 
8.5.7. Differential Torque 
8.5.8. Current Mirrors and Application as Active Loads 

8.6. Operational Amplifier and Applications  

8.6.1. Ideal Operational Amplifier 
8.6.2. Deviations from Ideality 
8.6.3. Sinusoidal Oscillators 
8.6.4. Comparators and Relaxation Oscillators 

8.7. Logic Functions and Combinational Circuits  

8.7.1. Information Representation in Digital Electronics 
8.7.2. Boolean Algebra 
8.7.3. Simplification of Logic Functions 
8.7.4. Two-Level Combinational Structures 
8.7.5. Combinational Functional Modules 

8.8. Sequential Systems  

8.8.1. Concept of Sequential System 
8.8.2. Latches, Flip-Flops and Registers 
8.8.3. State Tables and State Diagrams: Moore and Mealy Models 
8.8.4. Synchronous Sequential Systems Implementation 
8.8.5. General Structure of a Computer 

8.9. MOS Digital Circuits 

8.9.1. Inverters 
8.9.2. Static and Dynamic Parameters 
8.9.3. Combinational MOS Circuits 

8.9.3.1. Step Transistor Logic 
8.9.3.2. Implementing Latches and Flip-Flops 

8.10. Bipolar and Advanced Technology Digital Circuits 

8.10.1. BJT Switch. BTJ Digital Circuits 
8.10.2. TTL Transistor-Transistor Logic Circuits 
8.10.3. Characteristic Curves of a Standard TTL 
8.10.4. Emitter-Coupled Logic Circuits ECL 
8.10.5. Digital Circuits with BiCMOS 

Module 9. Statistical Physics 

9.1. Stochastic Processes 

9.1.1. Introduction 
9.1.2. Brownian Motion 
9.1.3. Random Walk 
9.1.4. Langevin Equation 
9.1.5. Fokker-Planck Equation 
9.1.6. Brownian Engines 

9.2. Review of Statistical Mechanics 

9.2.1. Collectivities and Postulates 
9.2.2. Microcanonical Collectivity 
9.2.3. Canonical Collectivity 
9.2.4. Discrete and Continuous Energy Spectra 
9.2.5. Classical and Quantum Limits. Thermal Wavelength 
9.2.6. Maxwell-Boltzmann Statistics 
9.2.7. Energy Equipartition Theorem 

9.3. Ideal Gas of Diatomic Molecules 

9.3.1. The Problem of Specific Heats in Gases 
9.3.2. Internal Degrees of Freedom 
9.3.3. Contribution of Each Degree of Freedom to the Heat Capacity 
9.3.4. Polyatomic Molecules 

9.4. Magnetic Systems 

9.4.1. ½ Spin Systems  
9.4.2. Quantum Paramagnetism 
9.4.3. Classical Paramagnetism 
9.4.4. Superparamagnetism 

9.5. Biological Systems 

9.5.1. Biophysics 
9.5.2. DNA Denaturation 
9.5.3. Biological Membranes 
9.5.4. Myoglobin Saturation Curve. Langmuir Isotherm 

9.6. Systems with Interaction 

9.6.1. Solids, Liquids, Gases 
9.6.2. Magnetic Systems. Ferro-Paramagnetic Transition 
9.6.3. Weiss Model 
9.6.4. Landau Model 
9.6.5. Ising's Model 
9.6.6. Critical Points and Universality 
9.6.7. Monte Carlo Method. Metropolis Algorithm 

9.7. Quantum Ideal Gas 

9.7.1. Distinguishable and Indistinguishable Particles 
9.7.2. Microstates in Quantum Statistical Mechanics 
9.7.3. Calculation of the Macrocanonical Partition Function in an Ideal Gas 
9.7.4. Quantum Statistics: Bose-Einstein and Fermi-Dirac Statistics 
9.7.5. Ideal Gases of Bosons and Fermions 

9.8. Ideal Boson Gas 

9.8.1. Photons. Black Body Radiation 
9.8.2. Phonons. Heat Capacity of the Crystal Lattice 
9.8.3. Bose-Einstein Condensation 
9.8.4. Thermodynamic Properties of Bose-Einstein Gas 
9.8.5. Critical Temperature and Density 

9.9. Ideal Gas for Fermions 

9.9.1. Fermi-Dirac Statistics 
9.9.2. Electron Heat Capacity 
9.9.3. Fermion Degeneracy Pressure 
9.9.4. Fermi Function and Temperature 

9.10. Elementary Kinetic Theory of Gases 

9.10.1. Dilute Gas in Equilibrium  
9.10.2. Transport Coefficients 
9.10.3. Thermal Conductivity of the Crystalline Lattice and Electrons 
9.10.4. Gaseous Systems Composed of Moving Molecules 

Module 10. Fluid Mechanics 

10.1. Introduction to Fluid Physics 

10.1.1. No-Slip Condition 
10.1.2. Classification of Flows 
10.1.3. Control System and Volume 
10.1.4. Fluid Properties 

10.1.4.1. Density 
10.1.4.2. Specific Gravity 
10.1.4.3. Vapor Pressure 
10.1.4.4. Cavitation 
10.1.4.5. Specific Heat 
10.1.4.6. Compressibility 
10.1.4.7. Speed of Sound 
10.1.4.8. Viscosity 
10.1.4.9. Surface Tension 

10.2. Fluid Statics and Kinematics 

10.2.1. Pressure 
10.2.2. Pressure Measuring Devices 
10.2.3. Hydrostatic Forces on Submerged Surfaces 
10.2.4. Buoyancy, Stability and Motion of Rigid Solids 
10.2.5. Lagrangian and Eulerian Description 
10.2.6. Flow Patterns 
10.2.7. Kinematic Tensors 
10.2.8. Vorticity 
10.2.9. Rotationality 
10.2.10. Reynolds Transport Theorem 

10.3. Bernoulli and Energy Equations 

10.3.1. Conservation of Mass 
10.3.2. Mechanical Energy and Efficiency 
10.3.3. Bernoulli's Equation 
10.3.4. General Energy Equation 
10.3.5. Stationary Flow Energy Analysis 

10.4. Fluid Analysis  

10.4.1. Conservation of Linear Momentum Equations 
10.4.2. Conservation of Angular Momentum Equations 
10.4.3. Dimensional Homogeneity 
10.4.4. Variable Repetition Method 
10.4.5. Buckingham's Pi Theorem 

10.5. Flow in Pipes 

10.5.1. Laminar and Turbulent Flow 
10.5.2. Inlet Region 
10.5.3. Minor Losses 
10.5.4. Networks 

10.6. Differential Analysis and Navier-Stokes Equations 

10.6.1. Conservation of Mass 
10.6.2. Current Function 
10.6.3. Cauchy Equation 
10.6.4. Navier-Stokes Equation 
10.6.5. Dimensionless Navier-Stokes Equations of Motion 
10.6.6. Stokes Flow 
10.6.7. Inviscid Flow 
10.6.8. Irrotational Flow 
10.6.9. Boundary Layer Theory. Clausius Equation 

10.7. External Flow 

10.7.1. Drag and Lift 
10.7.2. Friction and Pressure 
10.7.3. Coefficients 
10.7.4. Cylinders and Spheres  
10.7.5. Aerodynamic Profiles 

10.8. Compressible Flow 

10.8.1. Stagnation Properties 
10.8.2. One-Dimensional Isentropic Flow 
10.8.3. Nozzles 
10.8.4. Shock Waves 
10.8.5. Expansion Waves 
10.8.6. Rayleigh Flow 
10.8.7. Fanno Flow 

10.9. Open Channel Flow 

10.9.1. Classification 
10.9.2. Froude Number 
10.9.3. Wave Speed 
10.9.4. Uniform Flow 
10.9.5. Gradually Varying Flow 
10.9.6. Rapidly Varying Flow 
10.9.7. Hydraulic Jump 

10.10. Non-Newtonian Fluids 

10.10.1. Standard Flows 
10.10.2. Material Functions 
10.10.3. Experiments 
10.10.4. Generalized Newtonian Fluid Model 
10.10.5. Generalized Linear Viscoelastic Fluid Model 
10.10.6. Advanced Constitutive Equations and Rheometry 

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