# ESO courses

IIT Kanpur offers a variety of **Elementary Science Options**( ESO ) courses to choose from to nurture science interest in students apart from core departmental and compulsory courses. As the name suggests, all of these courses (9-10) are there to lay the foundation stones for understanding the respective domains like thermodynamics, data structures, fluid mechanics etc. Every UG deparment has laid down some minimum credit requirements that are to be fulfilled by choosing 3-4 courses of your like to gain a substantial understanding in respective areas.

## Course Details

Currently available ESO courses with details are as follows:

### ESO201 (Thermodynamics)

3 lectures, 1 tutorial = 11 credits

**Syllabus:**

Definitions and concepts: System and CV, Macroscopic and microscopic view points;
Property, Thermodynamics Static and Equilibrium, Energy, Work interaction and various
modes of work, Heat: Zeroth Law of Thermodynamics, Temperature Scale.

Properties of Pure Substances, Phase, Simple compressible substance, Mathematical,
Tabular and Graphical representation of data; Ideal gas Van der Waals Equation of state;
Compressibility chart; Thermodynamic Diagrams including Mollier diagram and Steam
Tables.

First law of thermodynamics and its applications to non-flow processes, Applications of
first law of thermodynamics to flow processes; Steady flow and Transient flow processes.

Second Law of Thermodynamics and its Applications, Availability.

Applications of first law of thermodynamics to chemically reacting systems.

Gas power cycles, Vapor power cycles, Refrigeration cycles.

Thermodynamic potentials, Maxwell relations; Thermodynamic relations.
^{[1]}

### ESO202 (Mechanics of Solids)

3 lectures, 1 tutorial = 11 credits

**Syllabus:**

Free body diagram, Modelling of supports, Conditions for Equilibrium, Friction
Force-deformation relationship and geometric compatibility (for small deformations)
with illustrations through simple problems on axially loaded members and thinwalled
pressure vessels, Force analysis (axial force, shear force, bending
moment, and twisting moment diagrams) of slender members (singularity
functions not to be used), Concept of stress at a point, Transformation of
stresses at a point, Principal stresses, Mohr’s circle (only for plane stress case),
Displacement field, Concept of strain at a point, Transformation of strain at
a point, Principal strains, Mohr’s circle (only for plane strain case), Strain Rosette,
Modelling of problem as a plane stress or plane strain problem, Discussion of
experimental results on 1-D material behaviour, Concepts of elasticity, plasticity,
strain-hardening, failure (fracture/yielding), idealization of 1-D stress-strain
curve, Concepts of isotropy, orthotropy, anisotropy, Generalized Hooke’s law
(without and with thermal strains), Complete equations of elasticity, Torsion
of circular shafts and thin-walled tubes (plastic analysis and rectangular shafts
not to be discussed), Bending of beams with symmetric cross-section (normal
and shear stresses) (shear centre and plastic analysis not to be discussed),
Combined stresses, Yield criteria, Deflection due to bending, Integration of the
moment-curvature relationship for simple boundary conditions, Superposition
principle (singularity functions not to be used), Concepts of strain energy and
complementary strain energy for simple structural elements (those under axial
load, shear force, bending moment, and torsion), Castigliano’s theorems for
deflection analysis and indeterminate problems, Concept of elastic instability,
Introduction to column buckling, Euler’s formula (post-buckling behaviour not
to be covered)
^{[2]}

### ESO203(Introduction of Electrical Engineering)

3 lectures, 1 tutorial, 1 lab(2 hr) = 13 credits

**Syllabus:**

Introduction, Single-Phase Circuits, Power Calculations, Analysis of Three-Phase
Circuits, Mutually Coupled Circuits
Transformers: Magnetic Circuits, Equivalent Circuit and Performance
Direct-Current Machines: Construction, Equivalent Circuit, Torque-Speed
Characteristics, Applications
Induction Machines: Construction, Equivalent Circuit, Torque-speed characteristics,
Speed Control, Starting, Applications
Synchronous Machines: Construction, Equivalent Circuit, Generator & Motor
Operation, Power Angle Characteristics, Hunting, Pull-Out
Special Topics: Stepper Motors
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### ESO204(Fluid Mechanics and Rate Processes)

3 lectures, 1 tutorial = 11 credits

**Syllabus:**

FLUID MECHANICS: Introduction to fluids, Fluid static's; pressure as a scalar, manometer, forces on submerged
surfaces (NO moments NOR center of pressure), Description of flows; field approach, Euler acceleration
formula, streamlines, streak lines, etc., Reynolds transport theorem Conservation of mass; stream function,
Linear (NOT angular) Momentum balance, Navier Stokes (NS) equation; elementary derivation; application;
Poiseuille flow, Couette flow, Energy equation. Bernoulli equation, applications including flow measurement (Pitot
tube, Orifice meters); Pipe flows and losses in fittings; Similitude and modeling: using non dimensionalization of
NS equations and boundary conditions, simplifications for cases without free surfaces and without cavitations
(scale factor approach should NOT be done); High Re flow: Prandtis approximation; basic in viscid flow; need for
boundary layer; Magnus effect (mathematical derivations be avoided), Boundary layer selementary results for
flat plates. Separation, flow past immersed bodies (bluff, streamlined); physics of ballgames (qualitative) Heat
Transfer: Introduction, rate law and conservation law, Conduction equation; non dimensionalization, various
approximations, Steady state conduction concept of resistances in series and of critical thickness of insulation,
Unsteady conduction; significance of Biot and Fourier numbers, Heissler charts; Low Bi case.
^{[4]}

### ESO205(Nature and Properties of Materials)

3 lectures, 1 tutorial, 1 lab(3 hr) = 14 credits

**Syllabus:**

Examples of materials highlighting Structure-Processing-Property-performance
relations. 14 space lattices, unit cells, cubic and HCP structures, Miller indices,
Packing, interstitials, different ceramic structures; Non-crystalline/nanocrystalline
materials-definitions, concept of Tg, local order, different polymer
structures.

Structure determination using X-ray diffraction (Bragg’s diffraction and structure
factor for cubic lattices); Point defects, edge and screw dislocations-their
notation and concepts, energy of a dislocation, stacking fault, grains and grain
boundaries, bulk defects;

PHASE EVOLUTION: Definition of diffusivity, concept of activation energy,
examples of diffusion process; Definition of a phase, phase rule, unary and
binary (eutectic, eutectic with terminal solid solutions) systems and examples,
phase diagrams of important metal and ceramic systems, Nucleation and growth
(homogeneous and heterogeneous), Introduction to TTT curves, examples of
various transformations;

MECHANICAL BEHAVIOUR: Measures of mechanical response (fundamental
measurable mechanical properties), engineering and true stress-true strain
response, concept of yield point and Elastic modulus (composite materials)
viscoelesticity, fracture toughness, stress intensity factor, fracture energy,
comparison of these properties for different engineering materials.
Deformation of single and polycrystalline materials, slip systems, critical resolved
shear stress, mechanisms of slip and twinning; Fatigue and creep properties
of materials with suitable examples, Strengthening mechanisms, Fracture in
ductile and brittle (Griffith’s Theory) solids, ductile to brittle transition,
ELECTRONIC PROPERTIES: Drude theory of metals, free electron theory (density
of states, Fermi energy, Fermi-Dirac statistics, band theory of solids, existence
of metals and insulators, Brillouin zones), Semiconductors (structures of elements
and compounds), equilibrium properties of semiconductors, conductivity as a
function of temperature, measurement of band gap, doping, law of mass action,
Hall effect, carrier concentration of mobility of non-generate semiconductors,
Excess carrier generation, optical properties of semiconductors, concept of
lifetime, I-V characteristics of p-n junction and their applications as LEDs, lasers
and solar cells, Introduction to semiconductor crystal growth and processing
modern methods of expitaxy (brief introduction to quantum wells and superlattices,
if time permits), Dia-, para-ferro- and ferri magnetism; soft/hard magnetic
materials.

Dielectric and ferroelectric materials (BaTiO3 as an example); linear and nonlinear
behaviour.
^{[5]}

### ESO206(Biotechnology)

3 lectures, 1 tutorial = 11 credits

**Information:** The course is offered by BSBE department, IIT Kanpur. The course lies at the intersection of Biology and technology. Further information is unavailable at this stage.

### ESO207(Data Structures)

3 lectures = 9 credits

**Information:** This course is by far and large, the most popular course taught at IIT Kanpur.

**Syllabus:**

Data Types and ADTs: Modular, Reusable and Safer computing

Generic Data Types, Stack, Expression Evaluator

Recursion, Loop Invariant, Induction, Proof of correctness

Order Analysis: Big-oh, Theta and Omega Notations

Algo. Design Tech.: D-n-C (Binary Search, Max. Element, Merge Sort), Dynamic Prog. (Fibonacci Nos, Knapsack), Greedy

Linear Data Structures: Stack, Queue and List; Sparse Polynomial and Matrix

Tree: Properties, Representation and Traversal, Expression Tree, Binary Search Tree

Priority Queue, Partial Order, Heap and Heap Sort

Sorting: Review of quadratic complexity sorts; Shell and Quick Sort; Order Statistics

Hashing; Bin, Counting, Radix and Bucket Sorting

Balanced Search Trees: Nearly Balanced Trees, Red-Black Tree

Graph: Definitions and Properties, Representation, DFS and BFS Traversals, Topological Sorting, MST, Shortest Path

P and NP (if time permits).

### ESO208(Numerical Methods)

3 lectures, 1 tutorial = 11 credits

**Syllabus:**

Introduction,Engineering Systems,Physical and Mathematical Modeling
• Error Analysis: Approximations and round off and Truncation errors
• Roots of Equations: Method of Bisection, Method of Interpolation, Secant Method, Netiton
Raphson method, Secant Method, Multiple roots
• Solution of Linear Simultaneous Equations: Direct Methods9Gauss Elimination, Gauss9Jordan, LU
decomposition; lterative Methods9Gauss9Seidel, Conjugate Gradient, Banded and Sparse systems
• Solution of Nonlinear Simultaneous Equations
• Curve Ficng9Least Square regression, Interpolation including splines
• Fast Fourier Transforms, Regression Analysis for Multivariable
• Eigen Values and Eigen Vectors9 Potier method, Relaxation Method, Diagonalization method.
• Numerical Differentiation and Integration9High9Accuracy Differentiation Formulas, Derivatives of
Unequal Spaced Data. The trapezoidal Rule, Simpson’s rule, Integration tiith unequal segments,
Open Integration Formulas
• Ordinary Differential Equations9 Finite Difference method, Method of weighted Residuals
• Analytical versus Numerical Methods, Initial Value and Boundary Value Problems Euler’s method,
Improvement of Euler’s method, Runge9Ku>a Method, Multiple Steps Method
• Partial Differential Equations Elliptic and parabolic Equations, Explicit and Implicit Methods, Crank
Nicholson Method, ADI method
• Introduction to Finite Element Method, Applications.
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### ESO209(Dynamics)

2 lectures, 1 tutorial = 8 credits

**Information:**

This course deals with an advanced study of Mechanics. It is considered to be one of the toughest courses at IIT Kanpur.