Courses

1. Mathematics

1. The IUT pre-university mathematics curriculum offers its students chances to study mathematics more thoroughly and systematically, supplementing their high school class work.

2. The pre-university courses in mathematics are designed to help students to understand fundamental concepts and work out more challenging problems.

3. The IUT pre-university mathematics program offers three levels of curriculum depending on the students’ mathematical knowledge and problem-solving abilities.

  •  Basic Level

- The basic level is designed for high school students with a working knowledge of about 1th or higher grade mathematics.

- In particular, students who register at this level should know in advance how to manipulate real numbers and polynomial expressions, draw graphs of linear, quadratic and trigonometric functions, understand geometry on Euclidean plane, solve quadratic equations, and prove mathematical statements from a given set of conditions, etc.

- The curriculum at this level provides the students with fundamental mathematical concepts including complex numbers, matrices, exponents, logarithms, sequence of numbers, and infinite series and basic techniques in calculus involving polynomial functions only

- The courses in the basic level will help students to progress to the intermediate or advanced level.

Subject

Contents

1

Complex numbers

Definition of complex numbers, their additions, multiplications, polar form r(cos a + i sin b)

2

Matrices and their operations

Definition of matrices, their additions and multiplications, multiplication of matrices with a real number, and other properties

3

Matrices and system of linear equations

Inverse matrix of matrix, formula of inverse matrix for a 2x2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables

4

Exponents

Manipulation of exponents and n-th root, how to define a real power of a positive real number

5

Exponential functions

Properties of exponential functions and their graphs

6

Logarithms

Definition of a logarithm, common logarithm, characteristic, mantissa

7

Logarithmic functions

Properties of logarithmic functions and their graphs

8

Arithmetic progressions

Definition of a sequence and arithmetic progressions

9

Geometric progressions

Definition of a geometric progressions

10

Other sequences

Progression of differences and other type of sequences

11

Mathematical induction, limits of Sequences

Mathematical induction, intuitive introduction to limit of a sequence

12

Infinite series

Partial sum and infinite series, geometric series

13

Mid-term examination

14

Solving equations

Solving rational and irrational equations

15

Solving inequalities

Solving cubic, quartic and rational inequalities

16

Trigonometric functions

Manipulation of trigonometric functions using various formulas

17

Limits of functions

Intuitive understading of limits of a function in terms of shape of the graph of a function

18

Continous functions

Definition of a continuous function, intermediate value theorem, extreme value theorem

19

Derivative and differentiation

Definition of a derivative, differentiation of polynomial functions, sum and product of two functions

20

Tangent lines to a curve

Application of derivative to find the tangent line to a curve, increasing and decreasing functions

21

Derivative and graph of a function

Many worked out examples of graph drawing of cubic or quartic polynomial functions using differentiation

22

Moving particle, velocity, acceleration

Application of derivative to physics of a moving particle.

23

Anti-derivative (Indefinite integral)

Definition of indefinite integrals and formulas for indefinite integral of polynomial functions

24

Definite integral

Definition of definite integral and fundamental theorem of calculus

25

Areas and other applications of integral

Computation of area enclosed by curves, how to find a position of a moving particle when its velocity is known

26

Term-end examination

  • Intermediate

- The intermediate level is designed for high school students with a working knowledge of 2nd or higher grade mathematics.

- The courses in this level provide students more advanced topics in high school and prepare them to go on to the advanced level seamlessly.

- The intermediate level differs from the basic level in that it deals with trigonometric, exponential, logarithmic functions and utilize chain rule in calculus contents whereas the basic level only deals with polynomial functions.

Subject

Contents

1

Complex numbers

Definition of complex numbers, their additions, multiplications, polar form r(cos a + i sin b)

2

Matrices and their operations

Definition of matrices, their additions and multiplications, multiplication of matrices with a real number, and other properties

3

Matrices and system of linear equations

Inverse matrix of matrix, formula of inverse matrix for a 2x2 matrix, Use of matrices to solve system of 2 linear equations with 2 variables

4

Exponents and exponential functions

Manipulation of exponents and n-th root, how to define a real power of a positive real number, graphs of exponential functions

5

Logarithms and logarithmic functions

Definition of a logarithm, common logarithm, characteristic, mantissa, graphs of logarithmic functions

6

Arithmetic and geometric progressions

Definition of a sequence, arithmetic progressions, and geometric progressions

7

Other sequences and mathematical induction

Progression of differences and other type of sequences, how to prove a theorem using a mathematical induction

8

Limits of Sequences and infinite series

Intuitive introduction to limit of a sequence, infinite series, geometric series

9

Solving equations

Solving rational and irrational equations

10

Solving inequalities

Solving cubic, quartic and rational inequalities

11

Trigonometric functions

Manipulation of trigonometric functions using various formulas

12

Trigonometric equations

Solving equations involving trigonometric functions

13

Mid-term examination

14

Limits of a function

Intuitive understading of limits of a function in terms of shape of the graph of a function, limits of sum, product, quotient of 2 functions

15

Continuous function

Definition of a continuous function, intermediate value theorem, extreme value theorem

16

Derivative and differentiation

Definition of a derivative, differentiation of polynomial functions, sum and product of two functions

17

Differentiation techniques

Differentiation of trigonometric functions, exponential functions

18

More differentiation techniques

Chain rule, differentiation of inverse functions

19

Application of derivative

Concavity, many worked out examples of graph drawing of various functions using its first and second derivative

20

Anti-derivative (Indefinite integral)

Definition of indefinite integrals and formulas for indefinite integral, integration by parts, integration by substition

21

Definite integral

Definition of definite integral and fundamental theorem of calculus

22

Areas and other applications of integral

Computation of area enclosed by curves, motion of a particle (position, velocity, acceleration)

23

Basic combinatorics and binomial theorem

Permutations, combinations, binomial theorem

24

Probability, conditional probability

Probability, conditional probability

25

Probability distribution

Discrete and continuous probability distribution, expected value, variance, standard deviation

26

Term-end examination

  • Advanced

- The advanced level is designed to provide students with enough mathematical knowledge and maturity to study the IUT mathematics courses.

- In an early stage of the advanced level, the students will go over matrices which are also treated in the intermediate level but their relation with linear transformations are emphasized.

- Then, the program introduces single variable calculus involving more complicated functions than the previous levels.

- This level also provides vector treatment of space geometry. Note also that the language of instruction in the advanced level is English.

Subject

Contents

1

Matrices and linear equations

Matrix, sum and product of matrices, determinant, inverse matrix, use of matrices to solve system of 2 linear equations with 2 variables

2

Matrices and linear transformation

Linear transformation and its associated matrices, rotation, reflection about x and y axis

3

Composition of linear transformations and inverse transformation

Composition of linear transformations and inverse transformation and their associated matrices

4

Mathematical induction and sequence of numbers

How to prove a theorem using a mathematical induction, sequences, arithmetic and geometric progressions

5

Limits of sequences and infinite series

Intuitive introduction to limit of a sequence, infinite series, geometric series

6

Trigonometric functions and equations

Manipulation of trigonometric functions using various formulas, inverse trigonometric functions, equations involving trigonometric functions

7

Limits of a function

Intuitive understading of limits of a function in terms of shape of the graph of a function, limits of sum, product, quotient of 2 functions

8

Continuous function

Definition of a continuous function, intermediate value theorem, extreme value theorem

9

Derivative and differentiation

Definition of a derivative, differentiation of polynomial functions, sum and product of two functions

10

Differentiation techniques

Differentiation of trigonometric functions, exponential functions

11

More differentiation techniques

Chain rule, differentiation of inverse functions, related rate real-life problems

12

Application of derivative

Concavity, many worked out examples of graph drawing of various functions using its first and second derivative

13

Mid-term examination

14

Anti-derivative (Indefinite integral)

Definition of indefinite integrals and formulas for indefinite integral, integration by parts, integration by substitution

15

Definite integral

Definition of definite integral and fundamental theorem of calculus

16

Integration techniques

Partial fractions, trigonometric substitutions, many worked out examples of integrations

17

Area on a plane and volume of a rotated solid

Computation of area enclosed by curves, volume of a rotated solid

18

Arc length and other applications of integral

Arc length, motion of a particle (position, velocity, acceleration)

19

Some basic differential equations

Introduction to differential equations and how to solve first order ordinary differential equations

20

Basic combinatorics and binomial theorem

Permutations, combinations, binomial theorem

21

Probability, conditional probability

probability, conditional probability

22

Probability distribution

discrete and continuous probability distribution, expected value, variance, standard deviation

23

Euclidean coordinates in 3 dimensional space

Equation of lines, planes and spheres, angle between 2 planes, orthogonal projection onto a plane,

24

Vectors, inner and cross product of two vectors

Vectors, sum of 2 vectors, a scalar product of a vector, angle between 2 vectors, inner and cross product of 2 vectors

25

Equations of lines and planes in 3 dimensional space

Vector equation of lines, planes and spheres, solving 3 dimensional geometry problems

26

Term-end examination

 

2. Physics

1. The IUT pre-university curriculum in Physics includes all of the high-school physics courses and some basic university physics courses.

2. The pre-university courses in physics intend to help students well prepare to learn and understand university physics at IUT.

3. There are three kinds of curriculum according to the level of courses: Basic, Intermediate, and Advanced Level.

4. The scope of each level is described as in the following.

  • Basic Level

- The basic level is an introduction to physical worlds for high school students who have learned the physics subject for less than 1 year or even haven't learned physics at all.

- This level provides basic concept on physical phenomena with only a little mathematical treatment.

Subject

Contents

1

Measurement

Measuring things, Standards and units, International system of units

2

Straight line motion 1

Position and speed, Motion with constant velocity

3

Straight line motion 2

Acceleration, Motion with constant acceleration, Freely-falling bodies

4

Newton's laws of motion 1

Newton's first law, Force, Newton's second law, Mass and weight

5

Newton's laws of motion 2

Newton's third law, Applying Newton's laws in straight line motion

6

Work and Energy 1

Work, Work done by the gravitational force and a spring force

7

Work and Energy 2

Kinetic energy, Work-energy theorem, Power

8

Momentum and Impulse

Linear momentum, Collision and impulse, Momentum-impulse theorem

9

Conservation of momentum

Conservation of momentum in collision along a straight line

10

Periodic motion

Describing oscillation, Simple harmonic motion, Energy in simple harmonic motion

11

Temperature and Heat

Measuring temperature, Kelvin scale, Quantity of heat, Heat and energy

12

Thermal expansion and Heat transfer

Thermal expansion, Heat transfer (Conduction, Convection, Radiation)

13

Midterm examination

14

Electric charge and Coulomb's law

Electric charge, Conductors and insulators, Electric force and Coulomb's law

15

Electric field

Electric field by a point charge, Electric field lines

16

Ohm's law

Electric current, Voltage, Resistance, Ohm's law

17

Electric circuit 1

Resistors in series and parallel, Single-loop circuit

18

Electric circuit 2

Multi-loop circuits, Kirchhoff's rules, Energy and power in electric circuits

19

Capacitor 1

Parallel-plate capacitor, Capacitance, Capacitors in series and parallel

20

Capacitor 2

Electric-field energy, Energy storage in capacitors, Dielectrics

21

Waves

Periodic waves, Wavelength and frequency, Types of waves

22

Propagation of light 1

Electromagnetic wave spectrum and light, Reflection and refraction, Index of refraction, Snell's law

23

Propagation of light 2

Total internal refraction, polarization

24

Geometric optics 1

Two types of images, Plane mirrors, Spherical mirrors

25

Geometric optics 2

Thin lenses, Optical instruments (eye, camera, magnifier)

26

Term-end examination

  • Intermediate

- The purpose of the intermediate level is to help students develop and understand the physical world at a deep and fundamental level.

- This level is appropriate for those high school students who have learned the physics subject for about 1 year and equipped themselves with some mathematical skills.

Subject

Contents

1

Vector quantities

Vectors and scalars, Components of vectors, Products of vectors

2

Motion in two or three dimensions

Displacement, velocity, and acceleration vectors in a plane, Relative velocity

3

Projectile and Circular motion

Projectile motion, Uniform circular motion

4

Newton's laws of motion

Applying Newton's laws of motion in two dimensions

5

Friction and Centripetal force

Properties of friction, Drag force and terminal speed, Circular motion and centripetal force

6

Conservation of energy

Work and potential energy, Conservation of mechanical energy

7

Momentum and Collision 1

Momentum and kinetic energy in collision, Elastic and inelastic collision

8

Momentum and Collision 2

Collision and momentum conservation in two-dimensions

9

Gravitation 1

Newton's law of gravitation, Gravitation near Earth's surface

10

Gravitation 2

Gravitational potential energy, Kepler's laws and motion of planets

11

First law of thermodynamics

Thermodynamic systems, Heat, work, and internal energy in thermodynamic systems, The first law of thermodynamics

12

Thermodymic processes

Kinds of thermodynamic processes, Some special cases of the first low of thermodynamics

13

Mid-term examination

14

Electric field and Potential

Electric field by electric charges, Electric potential and Emf, Dielectrics and conductors

15

RC circuit

Electric circuits with resistors and capacitors, The RC circuit

16

Magnetic field

Magnetic field, Motion of charged particles in a magnetic field

17

Magnetic field and Current 1

Magnetic field of a moving charge and current, Law of Biot and Savart

18

Magnetic field and Current 2

Ampere's law, Force between parallel currents, Magnetic field in solenoids and toroids

19

Electromagnetic induction

Faraday's law of induction, Lenz's law, Induced electric field

20

Transverse waves

Mathematical description of waves, Principle of superposition, interference of waves, standing waves

21

Longitudinal waves and Sound

Sound waves, Musical sound, Interference and beat, Decibel level, Doppler effect

22

Interference of light

Light as a wave, Young's double-slit experiment, Interference in thin films, Michelson interferometer

23

Diffraction of light

Huygens's principle, Diffraction by a slit, Diffraction grating and a spectrometer

24

Particle nature of light

Blackbody radiation, Photoelectric effect, Compton's experiment

25

Light quanta and Matter waves

The duality of light, Light as a probability wave, Electrons and matter waves, Heisenberg's uncertainty principle

26

Term-end examination

  • Advanced

- The advanced level includes some topics in the university physics along with advanced topics in high school physics.

- This level is appropriate for those high school students who have learned the physics subject for about 2 years and have good ability of mathematical skills.

Subject

Contents

1

Conservation of energy

Conservative forces and path independence, Conservation of mechanical energy and total energy

2

Momentum and Collision

Center of mass, Momentum of a system of particles, Momentum conservation in rocket propulsion

3

Gravitation

Motion of Satellites, Escape velocity, Black holes

4

Rotational motion

Rigid body, Angular velocity and acceleration, Moment of inertia

5

Rotational motion and Angular momentum

Kinetic energy of rotation, Torque, angular momentum, Conservation of angular momentum

6

Equilibrium and Elasticity

Equilibrium, Conditions for equilibrium, Elasticity, Stress and strain

7

Fluid mechanics 1

Density and pressure in a fluid, Pascal's principle

8

Fluid mechanics 2

Buoyancy, Fluid flow and Bernoulli's equation

9

Simple harmonic motion

Simple harmonic motion in a simple pendulum, The physical pendulum

10

Kinetic theory of ideal gases

Equation of state, Kinetic energy of ideal gases, Distribution of moelcular speeds, Degree of freedom

11

Second law of thermodynamics

Irreversible processes and entropy, Change in entropy, The second law of thermodynamics

12

Heat engines

Heat engines and refrigerators, Efficiency of real engines, The Carnot cycle

13

Mid-term examination

14

Gauss' law and electric field 1

Flux of electric field, Gauss' law, Gauss' law and Coulomb's law

15

Gauss' law and electric field 2

Application of Gauss' law in symmetric systems, Gauss' law in capacitors

16

Inductors and Inductance

Self-inductance and inductors, Magnetic-field energy in inductors, Mutual inductance

17

RL circuit

Electric circuit with resistors and inductors, The RL circuit

18

Alternating current

Alternating current, RLC series circuit, Reactance and impedance

19

Power in AC circuits and Transformers

Power in AC circuits, Transformers, Electric power transmission

20

Maxwell's equation and Electromagnetic waves

Gauss's law for magnetic field, Displacement current, Maxwell's equations, Electromagnetic waves and speed of light

21

Relativity 1

Einstein's postulates, Special theory of relativity, The relativity of simultaneity, time, and lentgth

22

Relativity 2

Relativistic momentum and kinetic energy, The general theory of relativity

23

The model of an atom

Rutherford's model of an atom, Hydrogen spectrum, The Bohr model of Hydrogen

24

Nuclear physics

Nucleon, Isotope, Radioactivity, Radioactive decay, Half-life, Nuclear reaction, Nuclear fission and fusion

25

Fundamental particles and Cosmology

Leptons and hadrons, The Quark model, The basic forces, The big bang and cosmic background radiation, Dark matter

26

Term-end examination

 

3. English

There are two programs at English: General English and IELTS.

        The program of General English is below:

  • Speaking and Listening: Help prospective students develop English skills needed to be communicatively competent in the era of globalization.
  • Grammar and Reading: Encourage prospective students to be academically well prepared for study in college or university.

                     Note: This program is for Basic Level Group.

         The program of IELTS is below:

  • Listening Test
  • Academic Reading Test
  • General Training Reading Test
  • Academic Writing Test
  • General Training Writing Test
  • Speaking Test

       Note: This program is for Advanced and Intermediate Level Group.

Additional information: English native speaker teaches pronunciation and English conversation at all groups 3 hours per a week

  • Basic Level
  • Helping students in improving English ability
  • Intermediate Level
  • Helping students in receiving 5 degree of IELTS
  • Advanced Level
  • Helping students in receiving 5 more degree of IELTS

 

IN FOCUS

IUT begins to accept applications for Pre-University Course

We are happy to announce that the Admissions process to IUT Pre-University Course is now open. We have two good news for our new generation of applicants.

Number one - from this year we are launching a two-year preparatory program. This was a long waited event since many parents have been requesting to provide this type of study program. From now on 1st and 2nd year students of academic lyceums and professional colleges have a great chance to study at Inha University preparatory courses for two years. This will enable them to improve their Math, Physics and English language skills further and be ready for an academic life at our University.

Number two – second-year lyceum and college students will have three opportunities to take entrance examination to IUT within a two year program.

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Why IUT?

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Why should I study at IUT?

The following article is available in Russian and Uzbek languages. 

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Why should I choose IUT?

It has been over 60 years since Inha University was established upon the ideals of leadership and expertise and service to the country.  

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Mission and objectives of the Inha University in Tashkent (IUT)

The central mission of Inha University in Tashkent is to achieve excellence in the undergraduate and graduate education.

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