Università degli Studi di Roma "Tor Vergata"

1. Course introduction. Cash flow diagrams. Financing and Investments. Inflation.
Projects and Investment alternatives.Time value of money.
Interest rate, interest earned. Opportunity cost.

2. Simple interest. Compound interest. Excercises.

3. Compound and Simple interest: A graphical comparison.
Nominal and effective interest rates. Exercises.Cash Flows Equivalence.

4. Cash Flows Equivalence: formulas and factors. Excercises. Bases for comparison of alternatives. Present Worth.

5. Present Worth. Future Worth. Future Worht and Present Worth with simple interest. Exercises.

6. Annual Equivalent. Future Worht, Annual Equivalent and Present Worth: a comparison.
Payback Period. Exercises.

7. Incremental Investment.Exercises.

8. Exercises (interest and related formuals). Introduction to IRR.

9. Internal rate of return.
MARR. Cost of capital. Computation of the Internal Rate of Return. Financing: IRR, PW, FW. Exercises.

10. Alternatives with unequal lives (case I, II and III). Alternative A0. Project Balance. Exercises.

11. Advanced Exercises (part1).

12. Innovation, new projects and development of alternatives (part 1)

13. Advanced Exercises (part2).

14. Innovation, new projects and development of alternatives (part 2)

15. Advanced Exercises (part3).

16. Innovation, new projects and development of alternatives (part 3)

17. Preliminaries on Micro- and Macroeconomics. Real vs nominal prices. Consumer and producer price indexes.
Supply and Demand curves. The Reserve Price.

18. Limits of the GDP. Shifting of Supply and Demand curves. The Market Mechanism. Market Clearing Price.
Price Elasticity of Demand.

19. No Class - National Holiday

20. Elasticities of Supply and Demand. Point, arc and cross-price elasticities. Other elasticities.

21. World oil market example. Exercises.

22. Long-run and Short-run elasticities. Exercises. Consumer behaviour and preferences.

23. Indifference curves. Perfect complements and substitutes. Marginal rate of substitution. Regular preferences. Exercises.

24. Utility and utility functions. Exercises. Marginal Utility. Utility functions (also for perfect complements and substitutes).

25. Almost linear preferences. Exercises. Budget line. Changes in income and prices. Consumer choice and maximization of consumer satisfaction.

26. Consumer choice in the case of perfect complements and substitutes. Exercises.

27. Production. The production function. Average and marginal products. Isoquants. Production in the short and long run. Marginal rate of technical substitution.

28. Costs of production in the long and short run. Shapes of the cost curves. Isocost curves. Choice of optimum inputs. Exercises.

29. Advanced exercises.

Pindyck, R., & Rubinfeld, D. Microeconomics (7th ed. or newer). Prentice Hall International.
Thuesen, G. J., & Fabrycky, W. J. Engineering Economy (9th ed.). Prentice Hall International.

Structure of the Atom, Schrödinger wave equation, Hydrogen atom, Atomic orbitals, Electron Configuration, Periodic Properties and the Periodic table of Elements. Chemical bond: Octet rule, Ionic bond, Covalent bond, Multiple bonds, Lewis electron dot formula, Polar covalent bond, Electronegativity, Valence bond theory, Hybridization, VSEPR theory, Molecular orbital theory, Application of MO theory for diatomic molecules, Forces of attraction between molecules.
Law of chemical combination, Law of combining volumes, Mole concept, Formula. Stoichiometric Calculations. Gases: Gas Laws, Ideal gas law, Dalton's law of partial pressure, van der Waals equation. Thermochemistry, Heat, Work, First law of thermodynamics, Enthalpy, Entropy, Free energy. Solid and Liquid States, Types of solids, Phase change: vapor pressure. Non-Electrolytic Solutions, Raoult's law, Deviation from Raoult's law, Henry's law, Colligative properties. Chemical equilibrium. Le Chatelier’s principle. Equilibrium constants. Law of mass action. Volume dependency, Temperature dependency, Equilibria in aqueous solutions, Electrolytic dissociation. Colligative properties of electrolyte solutions. Acids and bases, Bronsted-Lowry concept, Lewis concept, Ionization of Water, Acid-base equilibria and pH. Buffers, Solubility product. Oxidation numbers. Redox reactions. Electrochemical cells.

Reference book: Raymond Chang, “General Chemistry: The Essential Concepts”, McGraw-Hill.
Teaching activities: Lessons. Collective tutorial by correcting written exercises.

Differential and integral calculus for real functions: real and complex numbers; elementary real functions and their inverse: polynomial, exponential, logarithm, trigonometric etc.; concept of limit, limits of indefinite forms; continuity, properties of continuous functions, uniform continuity; derivatives, maxima and minima, the graph of a function; De L 'Hopital's Rule; Taylor expansions; antiderivatives, integrals; improper integrals; series; elementary differential equations of first and second order. Introduction to multivariable calculus: continuity; differentiation, directional derivatives, gradient; higher order differentiations, Hessian matrix.

Tom M. Apostol: Calculus Vol.1, second edition; John Wiley & Sons, (1974).
Claudio Canuto, Anita Tabacco: Mathematical Analysis I-Springer International Publishing, UNITEXT 84, (2015).

Basic elements. Real and complex numbers. Topologi of the rial line and the n-dimensional real space.

Differential calculus for real functions.
Elementary real functions and their inverse: polynomial, exponential, logarithm, trigonometric function. Concept of limit, limits of indefinite forms; continuity, properties of continuous functions, uniform continuity; derivatives, maxima and minima, the graph of a function; De L’Hopital’s Rule; Taylor expansions.

Introduction to multivariable calculus: continuity, differentiation, directional derivatives, gradient; higher order differentiations, Hessian matrix.

Integral calculus for real functions: antiderivatives, Riemann integrals; improper integrals.

Numerical series.

Introduction to ordinary differential equations of first and second order.

Textbooks

Apostol, T. M., Calculus Vol.1, second edition; John Wiley & Sons, (1974).

Canuto C., Tabacco A., Mathematical Analysis I & II; Springer International Publishing, UNITEXT 84, (2015).

Trench, William F., Introduction to Real Analysis (2013). Faculty Authored Books. Book 7. http://digitalcommons.trinity.edu/mono/7 .

Introduction to Computer Science; Von Neumann architecture; Programming Paradigms; Functional and Object Oriented Approaches; Principles of Software Engineering and Modeling; Basic concepts and comparison of Programming Languages; Variables; Control structures (Loops, Conditional Selection), Data structures and algorithms; Computational Complexity; Functions and parameters; Recursion; Sorting algorithms; Input/Output; Concurrency and Parallelism; Networking and Distributed Applications; Version Control; The Art of Documentation; Introduction to Security and Reliability concepts.

1. Course Slides
2. http://cslibrary.stanford.edu/101/EssentialC.pdf
3. RUST Programming Language Book
https://doc.rust-lang.org/book/
4. Thinking in Java
http://www.mindview.net/Books/TIJ/

In the lectures and in the exercises the student will be introduced into the main principles of Linear
Algebra, Euclidean Geometry and their interplay. They include vector algebra, matrices and
determinants, linear transformations, differentiable curves, inner product spaces, eigenvalues and
eigenvectors, spectral theorem for symmetric and hermitian operators.
Each topic is illustrated by examples and exercises. Additionally the student receives additional
example problems for home-studies.

Learning Outcomes:
A working knowledge of the basic elements of Linear Algebra and Euclidean Geometry.
Getting the ability to apply the basic linear algebra techniques both to linear algebra problems and
to geometric problems.
Getting the competence to apply the principles of Linear Algebra and Geometry to problems in the
various branches of Engineering Sciences.


Further Information:
http://www.mat.uniroma2.it/~pareschi/didattica/AA1314/LAG2014home.html

T. Apostol, Calculus, Vol. I (Chapters 12-16), Vol. II (Chapters 3-5), Second edition, Wiley

Electrical Quantities and SI Units. Force, Work and Power. Electric Charge and Current. Electric Potential. Energy and Electrical Power. Constant and Variable Functions. Circuit Concepts. Passive and Active Elements. Sign Conventions. Voltage-Current Relations. Resistance, Inductance, Capacitance. Circuit Laws: Kirchhoff’s Voltage Law, Kirchhoff’s Current Law, Series and Parallel. Branch Current Method, Mesh Current Method, Node Voltage Method, Superposition, Sinusoidal Functions, Average and Effective (RMS) Values. Series and Parallel RLC Circuit, Sinusoidal Steady-State Circuit Analysis. Phasors. Impedance and Admittance. Thevenin’s and Norton’s Theorems, Superposition of AC Sources, Power in the Time Domain, Power in Sinusoi dal Steady State, Active Power, Reactive Power, Complex Power. Maximum Power Transfer. Thevenin’s and Norton’s Theorems, Maximum Power Transfer Theorem. Three-Phase Systems, Frequency Response and Network Functions, RLC Parallel Circuit; Parallel Resonance, Mutual Inductance, Ideal Transformer, AC Steady State and Frequency Response, Time Response and Transient Analysis, The Unit Step Function, Unit Impulse Function, Exponential Function, First-Order Circuits, Laplace Transform Method, Selected Laplace Transforms, Initial-Value and Final-Value Theorems, Partial-Fractions Expansions, Circuits in the s-Domain.

Reference book: Il testo consigliato è M. Nahvi, J. A. Edminister "Electric Circuits" Schaum's Outlines Series, Mc Graw Hill

Apostol Volume 1:
1 Sequences, infinite series, improper integrals, Ch. 10
2 Sequences and series of functions, Ch. 11
Apostol Volume 2:
3 Differential calculus of scalar and vector fields, Ch. 8
4 Applications of differential calculus, Ch. 9
5 Line integrals, Ch. 10
6 Multiple integrals, Ch. 11
7 Surface integrals, Ch. 12
8 Applications to Maxwell's equations

Tom M. Apostol, Calculus, Volumes 1 and 2

Electric charges, Coulomb’s law, continuous charge distribution, the electric field, the electric field o point charges, electric field of continuous charge distributions, electric field lines, the dipole, field generated by a dipole, the flux of the electric field, Gauss law, applications of the gauss law, electric potential energy, electric potential, calculating field and potential, electrical properties of materials, Ohm’s law: a microscopic view, capacitance, calculating the capacitance, capacitors in series and parallel, capacitors with dielectric, electric current, resistance, resistors in series and parallel, charge and discharge of a capacitor, the magnetic field, the magnetic force on a moving charge, the Hall effect, magnetic force on a current carrying wire, the torque on current loop, the magnetic field due to a moving charge, the magnetic field of a current, the solenoid, Ampere’s law, faraday’s law of induction, Lenz’ law, motional emf, inductance, magnetic properties of materials, magnetization, paramagnetism, diamagnetism, ferromagnetism, Maxwell’s equations, electromagnetic waves, energy transport and the Poynting vector, the electromagnetic spectrum, introducing the photon concept, photoelectric effect. Particles as waves: the de Broglie relation. The Schrödinger equation: time dependent and time independent. The free particle. Quantum well and tunnel effect. The Fermi gas. Origin of bands in metals.

Physics, Volume 2 (fifth edition)

Halliday, Resnick, Krane (Wiley)

Classification of electrical systems and requirements. Analysis of transitory and frequency behavior. Distortion in electronic systems and Bode diagrams. Diode semiconductor devices and circuit applications: clipper, clamper, peak detector, etc. Bipolar Junction and Field Effect Transistors. Biasing techniques for Transistors. Amplifiers classification, analysis and circuit design. Frequency response of single and cascaded amplifiers. Differential amplifiers and Cascode. Current mirrors. Feedback amplifiers and stability issues. Power amplifiers. Operational amplifiers and related applications. Oscillator circuits. Integrated circuits and voltage waveform generators.

“Electronics: a systems approach”, Neil Storey, Prentice Hall
“Elettronica di Millman”, J. Millman, A. Grabel, P. Terreni, McGraw-Hill
Course material (slides) provided through Didattica WEB

Elements of electrical engineering, Thevenin, Norton and Superposition theorems.
Analysis and synthesis of circuits based on diodes with both Turning Point and State methods.
Analysis and Synthesis of amplifiers based on both BJT and FET devices in common emitter (source), collector (drain) and base (gate) configurations.
Analysis and synthesis of circuits with operational amplifiers.

Jimmie J. Cathey, “Theory and Problems of Elctronic Devices and Circuits” Schaum’s Outlines Series McGRAW-HILL

The theory of differential equations can be successfully used to gain profound insight into the fundamental mathematical control design techniques for linear and nonlinear dynamical systems. Tutor-guided individual projects (including computer simulations and lab experiments) invite an intensive participation.
- Linear systems
The matrix exponential; the variation of constants formula. Computation of the matrix exponential via eigenvalues and eigenvectors and via residual matrices. Necessary and sufficient conditions for exponential stability: Routh-Hurwitz criterion. Invariant subspaces. Impulse responses, step responses and steady state responses to sinusoidal inputs. Transient behaviors. Modal analysis: mode excitation by initial conditions and by impulsive inputs; modal observability from output measurements; modes which are both excitable and observable. Popov conditions for modal excitability and observability. Autoregressive moving average (ARMA) models and transfer functions.
Kalman reachability conditions, gramian reachability matrices and the computation of input signals to drive the system between two given states. Kalman observability conditions, gramian observability matrices and the computation of initial conditions given input and output signals. Equivalence between Kalman and Popov conditions. Kalman decomposition for non reachable and non observable systems.
Eigenvalues assignment by state feedback for reachable systems. Design of asymptotic observers and Kalman filters for state estimation of observable systems. Design of dynamic compensators to stabilize any reachable and observable system. Design of regulators to reject disturbances generated by linear exosystems.
Introduction to adaptive control. Introduction to tracking control. Minimum phase systems and proportional Integral Derivative (PID) control.
Bode plots. Static gain, system gain and high frequency gain. Zero-pole cancellation. Nyquist plot and Nyquist criterion. Root locus analysis. Stability margins. Frequency domain design. Realization theory.
- Introduction to nonlinear systems
Nonlinear models and nonlinear phenomena. Fundamental properties. Lyapunov stability. Linear systems and linearization. Center manifold theorem. Stabilization by linearization. Control mechanisms, bifurcation phenomena, complexities and subtleties in biology and physiological processes.
Books.
C.M.Verrelli. La matematica elementare del feedback, III Edizione. Esculapio, 2015.
H. Klee, R. Allen. Simulation of Dynamic Systems with MATLAB and Simulink, Second Edition, CRC Press, 2011.
G.F. Franklin, J.D. Powell, A. Emami-Naeini, Feedback control of dynamic systems, VI Edizione. Pearson.
Michael E. Taylor. Introduction to Differential Equations. American Mathematical Society, 2011.
M.W. Hirsch, S. Smale, R.L. Devaney. Differential equations, dynamical systems & an introduction to chaos. Elsevier, Academic Press, 2004.
Richard C. Dorf, Robert H. Bishop. Modern Control Systems. Prentice Hall, 2011.
K.J.Astrom, R. Murray. Feedback systems. An introduction for scientists and engineers. Princeton University Press, 2008.
L.A. Segel, L. Edelstein-Keshet, A Primer on Mathematical Models in Biology, Cambridge University Press, 2013.
Tutor-guided individual projects (including computer simulations) are involved and may concern one of the following topics.

Population dynamics

- L. Edelstein-Keshet, Mathematical models in biology, Siam, 2005.
- J. D. Murray, Mathematical biology I, Springer, 2003.
- D. S. Jones, M. J. Plank, B. D. Sleeman, Differential equations and mathematical biology, CRC press, 2010.

Mathematics of heart physiology and control

- D. S. Jones, M. J. Plank, B. D. Sleeman, Differential equations and mathematical biology, CRC press, 2010.
- J. Keener, J. Sneyd, Mathematical physiology, Springer, 2004.
- M. C. K. Khoo, Physiological control systems, IEEE press, 2000.

Mathematics for glucose regulation control

- J. Keener, J. Sneyd, Mathematical physiology, Springer, 2004.
- M. C. K. Khoo, Physiological control systems, IEEE press, 2000.

Course contents:
- Free and constrained systems, constraints and their classification, possible and virtual displacements,
ideal constraints, D'Alembert's Principle.
- Truss structures, beams and frames, the force method, the deformation method, stability of beams and
frames.
- The geometry of deformation, transmission of force, elastic constitutive theory, boundary-value
problems in Elasticity, yield conditions.
- Extension, bending, torsion, and shear of prismatic bars; thin-walled beams.
- Energetic principles, the Ritz method, the Galerkin method, the Finite Element Method.

Learning outcomes:
This course is designed to introduce basic principles of statics for rigid and deformable bodies. The
main objective is to help the students develop an intuition for equilibrium, properly constrained
systems, and deformation under external loadings. Students will also know how to program the Finite
Element Method.

Textbooks:
S. Krenk and J. Høgsberg: Statics and Mechanics of Structures, Springer 2013

Other reference books:
K. D. Hjelmstad: Fundamentals of Structural Mechanics, Springer 2005
A. Jhennane: Introduction to Finite Element Analysis Using MATLAB and Abaqus, CRC Press 2013
F. Gantmacher: Lectures in Analytical Mechanics, MIR Publishers 1975
T.J. Oden and E.A. Ripperger: Mechanics of Elastic Structures – Second Edition, McGraw-Hill 1981
M.S. Gockenbach: Understanding and Implementing the Finite Element Method, SIAM 2006

Contents:
In the lectures and the exercises, the student will be introduced into the main principles of
Engineering Thermodynamics, Thermo Fluid Dynamics and Heat Transfer. They include: - Fundamental laws of thermodynamics
- Thermodynamic diagrams
- Thermodynamic cycles for close and open systems
- Air and steam mixtures
- Basic laws of fluid dynamics
- Heat transfer mechanisms: conduction, convection, and radiation heat transfer. Heat

Each topic goes with an exercise, which will be solved as an example in the exercise. Additionally
the student receives additional example problems for home studies.

Learning Outcomes:
K1: Learning the basic elements of Engineering Thermodynamics, Fluid Dynamics and Heat
transfer, including introduction to fundamental physical and analytical principles and their
application. K2: Giving students an understanding of the basic problems and concepts in Thermodynamics,
Fluid Dynamics and Heat Transfer and developing the competence to analyze problems regarding
thermal plants and components and to solve them mathematically.
K3: Getting the competence to apply the principles of Thermodynamics, Fluid Dynamics and Heat
Transfer to affords practical problems in thermal plant and component design

Reading Resources: - M.W.Zemanski, M.M. Abbott, H.C. Van Ness, Basic Engineering Thermodynamics, Mc-Graw
Hill Inc. 1975
- I.P.Holman, Heat Transfer, Mc. Graw Hill Int. 1981
- Any other equivalent book

KINEMATICS
Rigid body motion and Rivals theorems. Relative motion and Coriolis theorem. Instant center of rotation and Chasles theorem. Velocity vector field. Fixed and moving centrodes. Application: Cardan mechanism. Curvature analysis and Euler-Savary equation. Inflection circle and return circle. Aronhold theorems. Acceleration pole and Bresse circle. Acceleration vector field.
Lower and higher kinematic pairs. Kinematic chains and derived mechanisms. Grübler’s formula. Kinematic inversion. Four-bar linkages and Grashof law. Slider-crank/rocker mechanisms. Double sliders mechanisms. Aronhold-Kennedy theorem. Collineation axis and Bobillier theorem. Loop closure equation method: four-bar and slider-crank analysis. Kinematic analysis of planar mechanisms. Introduction to the kinematic synthesis of planar mechanisms (graphical methods): rigid body guidance (two and three positions), straight path generators, function generators.
Conjugate profiles and Euler-Savary equation. Gear transmissions. Transmission ratio, interference, minimum number of teeth, continuity of motion, contact ratio, sliding velocity. Kinematic analysis of epicyclic gear trains based on graph theory. Cardan joint.

MECHANICAL VIBRATIONS
Free and forced response of one degree-of-freedom mass spring-damper model. Amplification factor. Vibration of 1 d.o.f. system with moving base. Coefficients of transmissibility of forces and displacements. Logarithmic decrement. Average dissipated power. Two degrees-of-freedom systems: Equations of motion. Dynamic dampers. Fourier series. Free response of n degrees of freedom undamped system. Natural frequencies and vibration modes. Orthogonality of vibration modes. Decoupling of equations. Critical speed of shafts. Frequency equation. Dunkerley equation. Rayleigh method.

DYNAMICS
Equivalent systems of forces. The equations of Statics. Static analysis of a slider-crank. The Principle of Virtual Work and its application to statics.
Resultant of inertia forces. The Lagrange-d'Alembert principle. Application of virtual work principle to the solution of dynamics problems. Energy balance equation. Mechanical efficiency. Static and dynamics analysis of slider-crank and four-bar linkages. Applications of the Principle of Virtual Work. Numerical integrations of equations of motion: methods of Euler, Heun, Runge.

1. R. Norton, Design of Machinery: An Introduction To The Synthesis and Analysis of Mechanisms and Machines,.
2. J. Denavit, R.S. Hartenberg, Kinematic Synthesis of Linkages (pdf available online)
3. Rao, S.S, Mechanical Vibrations, Wiley & Sons

KINEMATICS
Rigid body motion and Rivals theorems. Relative motion and Coriolis theorem. Instant center of rotation and Chasles theorem. Velocity vector field. Fixed and moving centrodes. Application: Cardan mechanism. Curvature analysis and Euler-Savary equation. Inflection circle and return circle. Aronhold theorems. Acceleration pole and Bresse circle. Acceleration vector field.
Lower and higher kinematic pairs. Kinematic chains and derived mechanisms. Grübler’s formula. Kinematic inversion. Four-bar linkages and Grashof law. Slider-crank/rocker mechanisms. Double sliders mechanisms. Aronhold-Kennedy theorem. Collineation axis and Bobillier theorem. Loop closure equation method: four-bar and slider-crank analysis. Kinematic analysis of planar mechanisms. Introduction to the kinematic synthesis of planar mechanisms (graphical methods): rigid body guidance (two and three positions), straight path generators, function generators.
Conjugate profiles and Euler-Savary equation. Gear transmissions. Transmission ratio, interference, minimum number of teeth, continuity of motion, contact ratio, sliding velocity. Kinematic analysis of epicyclic gear trains based on graph theory. Cardan joint.

MECHANICAL VIBRATIONS
Free and forced response of one degree-of-freedom mass spring-damper model. Amplification factor. Vibration of 1 d.o.f. system with moving base. Coefficients of transmissibility of forces and displacements. Logarithmic decrement. Average dissipated power. Two degrees-of-freedom systems: Equations of motion. Dynamic dampers. Fourier series. Free response of n degrees of freedom undamped system. Natural frequencies and vibration modes. Orthogonality of vibration modes. Decoupling of equations. Critical speed of shafts. Frequency equation. Dunkerley equation. Rayleigh method.

DYNAMICS
Equivalent systems of forces. The equations of Statics. Static analysis of a slider-crank. The Principle of Virtual Work and its application to statics.
Resultant of inertia forces. The Lagrange-d'Alembert principle. Application of virtual work principle to the solution of dynamics problems. Energy balance equation. Mechanical efficiency. Static and dynamics analysis of slider-crank and four-bar linkages. Applications of the Principle of Virtual Work. Numerical integrations of equations of motion: methods of Euler, Heun, Runge.

1. R. Norton, Design of Machinery: An Introduction To The Synthesis and Analysis of Mechanisms and Machines,.
2. J. Denavit, R.S. Hartenberg, Kinematic Synthesis of Linkages (pdf available online)
3. Rao, S.S, Mechanical Vibrations, Wiley & Sons

SYLLABUS
Lesson 1 - 13th October 2016
• Entry Test to evaluate students’ current level of English.
Lesson 2 - 20th October 2016
Contents and aims of the lesson:
• To revise the form and general use of verb tenses for further development in the following lessons of the course. Tenses revised include: present simple, present continuous, past simple, past simple continuous, present perfect simple, present perfect continuous, future forms, present simple passive and past simple passive in the context of three short texts about French people living in London.
• To illustrate the differences in use of the auxiliary verbs ‘to be’, ‘to have’ and ‘to do’.
• To test students’ current knowledge in question formation, negative statements formation and in active and passive forms.
• To give students initial practice in recognising the differences in meaning between present simple and present continuous, past simple, present perfect simple and future forms.
• To help students develop a cooperative attitude towards language learning by encouraging pair work and group work.
By the end of the lesson, students should be able to:
• Recognise different tenses and name them.
• Understand which auxiliary verb needs to be used for each tense.
• Make questions, use negative forms and convert active statements into passive ones.
• Have an initial understanding of the potential difficulties in the use of the present perfect simple and continuous.
Lesson 3 - 26th October 2016
Contents and aims of the lesson:
• To illustrate the meaning and use of the present perfect to express 1) an unfinished past, 2) a present result and 3) an indefinite past in the context of an article about Bob Dylan.
• To compare and contrast the differences in meaning between the simple and continuous aspects of the present perfect.
• To enable students to start developing the ability of noticing language in authentic texts.
• To raise students’ awareness of target language by facilitating students peer check and feedback.
By the end of the lesson, students should be able to:
• Identify present perfect verbs in authentic texts.
• Notice the differences in meaning among the three uses of the present perfect listed in the above section.
• Recognise the differences in meaning between simple and continuous aspects.
• Explain to other students the meanings and use of the present perfect.
Lesson 4 - 3rd November 2017
Contents and aims of the lesson:
• To consolidate the meaning and use of the present perfect to describe: 1) an unfinished past, 2) a present result and 3) an indefinite past in the context of three short readings about travel guides, travellers and about people living in hotels.
• To give students practice through three different types of exercise: 1) gapped text with graded difficulty, 2) question formation and 3) error correction.
• To give students the opportunity to practice their speaking skills during pair/group work.
• To give students control over their own learning by facilitating controlled peer correction during pair/group work.
By the end of the lesson, students should be able to:
• Understand the differences in meaning and use of the present perfect.
• Use the present perfect simple and continuous contrastively with the past simple, past continuous, present simple and present continuous.
• Identify, correct and explain misuses of the present perfect.
• Use the present perfect in controlled practice environments.
Lesson 5 - 10th November 2016
Contents and aims of the lesson:
• To illustrate the meaning, use and form of the modal verbs ‘must’, ‘mustn’t, ‘have to’, ‘don’t have to’ and ‘should’ to express advice and obligation.
• To give students the opportunity to develop the ability of deducing grammar rules from context.
• To give students controlled practice through different types of exercises: options, gapped text, error correction, sentence formation.
• To give students freer speaking practice in a role play activity.
By the end of the lesson, students should be able to:
• Understand the differences in meaning and use of the modal verbs mentioned in the section above.
• Deduce grammar patterns from context.
• Explain to their peers the meaning and uses of the modal verbs.
• Identify and correct misuses of the modal verbs.
• Use modal verbs in controlled and freer practice environments.
Lesson 6 - 17th November 2016
Contents and aims of the lesson:
• To give students freer speaking practice in the use of the modal verbs ‘must’, ‘mustn’t, ‘have to’, ‘don’t have to’ and ‘should’ to express advice and obligation in a role play activity.
• To enable students to develop their ability to negotiate and to express agreement and disagreement.
• To give students the opportunity to practice their writing skills in the context of a news channel.
By the end of the lesson, students should be able to:
• Express advice and obligation properly.
• Express agreement and disagreement as well as developing negotiation skills.
• Have an initial understanding of the main linguistic features of news articles.
• Write an article of approximately 150 words.
Lesson 7 - 24th November 2016
Contents and aims of the lesson:
• To illustrate the meaning, use and form of the past perfect to describe an action that happened in the past before another action in the past.
• To illustrate the meaning, use and form of ‘used to’ to describe a habit or state in the past that is finished now.
• To compare the differences in meaning among the uses of the past simple, past continuous and past perfect.
By the end of the lesson, students should be able to:
• Define the rules of use of the past perfect and of ‘used to’.
• Use the past perfect contrastively with the past simple and past simple continuous.
• Identify incorrect uses of the past perfect and correct them.
• Explain to their peers the meaning and use of the past perfect and ‘used to’.
Lesson 8 - 1st December 2016
Contents and aims of the lesson:
• To give students the opportunity to practice expressions of predictions and guessing.
• To illustrate the meaning, use and form of different verb patterns: 1) verb + to 2) verb + -ing 3) verb + sb + to 4) verb + sb + -ing 5) verb + sb + infinitive (without to)
• To give students practice in the use of informal language in the context of email and dialogue writing.
By the end of the lesson, students should be able to:
• Recognise different verb patterns and use them accordingly.
• Convert a written text into a spoken dialogue.
• Use dictionary entries to correct mistakes.
• Identify and correct misuses of the target grammar item.
Lesson 9 - 15th December 2016
Contents and aims of the lesson:
• To illustrate the differences between formal language and informal language.
• To enable students to notice the structure and contents of formal and informal emails.
• To give students practice in writing a formal email to a professor.
• To give students the opportunity to develop the ability of learning new language by correcting sample tests.
By the end of the lesson, students should be able to:
• Recognise and use appropriately formal and informal language.
• To use different registers and expressions according to the context.
• Noticing and correcting formal emails.
• Plan the structure and write a formal email to a professor.
Lesson 10 - 22nd December 2016
Contents and aims of the lesson:
• To give students the opportunity to test their current knowledge of compound nouns.
• To illustrate the meaning, use and form of prefixes and suffixes.
• To give students pronunciation practice in words using prefixes and suffixes.
By the end of the lesson, students should be able to:
• Form compound nouns and be aware of different spelling conventions.
• Have a wider knowledge of prefixes and suffixes to form new words.
• Identify different stress patterns involving words using prefixes and suffixes.
• Adapt correctly the spelling of the base word when adding a prefix or a suffix.
Lesson 11 - 12th January 2017
Contents and aims of the lesson:
• To illustrate the meaning, use and form of definite and indefinite articles and of the zero article.
• To enable students to deduce rules of use from context.
• To give students practice in correcting misuses of the definite/indefinite article and zero article.
• To give students the opportunity to explore the subtleties of the language in two vocabulary exercises.
By the end of the lesson, students should be able to:
• Recognise and correct misuses in the use of the articles.
• Identify recurrent patterns in language and summarise them in rules of use.
• Consolidate and expand their current vocabulary knowledge.
Lesson 12 - 19th January 2017
Contents and aims of the lesson:
• To raise students’ awareness in the use of linking words to express attitude in the context of a short dialogue between two students.
• To give students controlled practice in the use of linking words in the context of an informal email.
• To give students the opportunity to practice their creative writing skills in the context of a short story.
By the end of the lesson, students should be able to:
• Recognise the importance of linking words to express attitude and to add emphasis.
• Adapt the intonation of the sentence accordingly if linking words are being used.
• Select the correct linking word in the context of informal writing.
• Use linking words when writing their own piece of work.
Lesson 13 - 26th January 2017
Contents and aims of the lesson:
• To raise students’ awareness of the differences in meaning in countable and uncountable nouns.
• To illustrate the meaning, use and form of the quantifiers: ‘some’, ‘any’, ‘much’, many’, ‘a lot of’, ‘lots of’.
• To give students the opportunity to practice the ability of noticing and deducing language rules from context.
By the end of the lesson, students should be able to:
• Recognise countable and uncountable nouns and specify any differences in meaning.
• Use a variety of quantifiers in affirmative, negative and interrogative sentences.
• Rephrase sentences using different words.
• Compare and contrast recurrent patterns in language in order to identify rules of use.

All materials provided during the lessons