Physics Cycle

Engineering Mathematics I (21MAT11)

Question Papers

Notes

  • Differential Calculus:
    Partial Differentiation: Basics; Euler’s theorem of first kind (only problems); Total derivatives; Jacobian; Maclaurin’s series of one and two variable; Differentiation under Integral sign.

    Applications: Problems on evaluation of non-elementary integrals using Maclaurin’s series

    Module 1

  • Ordinary Differential Equations
    Linear Equations: Bernoulli’s equation; Exact Equations; Reducible to Exact (If of the form); Orthogonal Trajectory (Cartesian only); and Newton’s law of cooling.

    Non- Linear Equations: Solve for p, Clairaut’s form (singular, general solution).

    Applications: Problems on LR circuits leading to linear differential equations.

    Module 2

  • Integral Calculus:
    Multiple Integrals: Double integrals, changing the order of integration, changing Cartesian form to polar form. Special Functions- Beta and Gamma Functions, relation between beta and gamma function, properties, and its problems (related to reduction formula of definite integral).

    Applications: Problems on centre of gravity and moment of inertia which involve evaluation of multiple integrals.

    Module 3

  • Numerical methods and Infinite Series
    Numerical methods: Types of errors in numerical methods, Solution of Algebraic and Transcendental Equation: Newton Raphson. Finite Differences: Forward and Backward, Interpolation, Lagrange’s Interpolation. Numerical Integration- Simpson’s 1/3rdrule.

    Infinite Series: Convergence of infinite series: D-Alembert’s Ratio Test, Raabe's Test, Leibniz test, absolute and conditional convergent.

    Applications: Problems on application of Newton-Raphson method to some physical contexts

    Module 4

  • Linear Algebra
    Vectors, linearly dependent and independent vectors, Solution to systems of Linear Equation: Rank, Consistency, Gauss Elimination, LU decomposition. Eigen values- Eigen vectors, Diagonalization, Gauss–Seidel Method, Rayleigh Power method.

    Applications: Problems on Kirchhoff’s law leading to solving system of linear equations. Problems on computation of inverse matrix using LU decomposition.

    Module 5
Engineering Mathematics II (21MAT21)

Question Papers

Notes

  • Higher Order Differential Equations
    Inverse Differential Operator: Particular integral of the form eax, Sinax, polynomials and eaxV(x) (up to third order) and Variation of Parameters. Differential Equation with variable coefficient: Cauchy’s and Legendre differential equations.

    Applications: Problems on LRC circuit leading to higher order differential equation. Problems on forced oscillation leading to homogeneous linear ODE

    Module 1

  • Power Series Solutions: Frobenius method of Power Series (only second order), Bessel’s Differential Equation leading to Jn(x), J1/2(x), J-1/2(x), Legendre’s Differential Equations, Rodrigues formula(without proof)-Legendre’s Polynomial.

    Module 2

  • Vector Calculus:VPDO- Gradient of a scalar field (angle between two surfaces & Directional Derivatives),Divergence and Curl of Vector field and its properties (Solenoidal and Irrotational). Line integrals, Green’s theorem, Stroke’s theorem, and Gauss Divergence theorem.

    Applications: Problems on calculating work done using line integrals. Problems on finding the outward flux of a filed using Green’s theorem

    Module 3

  • Laplace Transform
    Definition and Laplace transforms of elementary functions (statements only). Laplace transforms of Periodic functions and unit-step function (problems only). Inverse Laplace Transform: Inverse Laplace transforms by method of partial fractions, Convolution theorem to find the inverse Laplace transforms. Solution of linear differential equations using Laplace transforms.

    Applications: Problems on Laplace transforms related to electric circuits.

    Module 4

  • Advanced Linear Algebra: Vector Space, basis and span, subspace, linear Transformation (LT), Matrix representation of LT, Change of basis, Rank nullity theorem, inverse LT.

    Module 5
Engineering Physics (21PHY12/22)

Question Papers

Notes

  • Electrostatics, Magnetostatics and Elastic properties of materials:
    Electrostatics: Electrostatic field and potential of a dipole, dielectric constant, Bound charges due to electric polarization, electric displacement, dielectric slab in uniform electric field, relation between dielectric susceptibility (χ), dielectric constant and polarization density (P). Numerical problems.

    Magnetostatics: Biot Savart’s law, divergence and curl of static magnetic field, Gauss divergence theorem sand stokes’ theorem, Faraday’s law in terms of EMF produced by changing magnetic flux.

    Elastic properties of materials: concept of elasticity, stress, strain, tensile stress, shear stress, compressive stress. Hooke’s law, different elastic moduli: Poisson’s ratio, Expression for Young’s modulus (Y), Bulk modulus and Rigidity modulus (n) in terms of α and β. Relation between Y, n and K. Derivation of expression for bending moment of a beam with circular and rectangular cross section. Numerical problems.

    Module 1

  • Crystal physics: Space lattice, Basis vectors, Unit cell, lattice parameters. Bravais lattice and crystal systems, Estimation of directions and planes in a crystal lattice, Miller indices and expression for interplanar spacing in terms of Miller indices. Expression for lattice constant for a cubic lattice, Co ordination number, Atomic packing factor-Atomic packing factor for sc, bcc and fcc structures. Crystal structures of NaCl and diamond, Diffraction of X-rays –derivation of Bragg’s law, X-ray spectrometer, –problems on Bragg’s law.

    Module 2

  • Introduction to solids: Review of classical free electron theory, Quantum free electron theory, Fermi energy and Fermi factor in metals, Variation of Fermi factor with energy and temperature, Fermi-Dirac statistics, Derivation of density of states, Band theory of solids (qualitative approach) Intrinsic semiconductors, concept of effective mass (qualitative) Intrinsic carrier density, Fermi level in intrinsic semiconductors, Extrinsic semiconductors- types, variation of carrier concentration with temperature, variation of Fermi level with temperature, numerical problems.

    Module 3

  • Modern Physics
    Dual nature of matter: Wave particle dualism, de-Broglie hypothesis, Davisson and Germer experiment, Matter waves and their characteristic properties. Phase velocity and group velocity, Relation between phase velocity and group velocity. Relation between group velocity and particle velocity. Problems on de-Broglie’s wavelength.

    Wave mechanics; Heisenberg’s uncertainty principle, significance and its applications: non-existence of electron inside the nucleus. Properties of wave function and physical significance. Probability density and Normalization of wave function, Schrodinger time independent wave equation in one dimension, Eigen values and Eigen functions. Particle in one dimensional infinite potential well. Numerical problems.

    Module 4

  • Lasers, optical fibers and nanomaterials:
    Lasers: Laser Characteristics, Spatial and Temporal Coherence, Einstein Coefficient and its significance, Population inversion, Two, three and four level systems, Pumping schemes, Threshold gain coefficient, Components of laser, Nd-YAG, He-Ne, and Dye laser and their engineering applications. Numerical problems.

    Optical fibers- Construction and light propagation mechanism in optical fibers (total internal reflection and its importance), Propagation mechanism in optical fibers. Angle of acceptance. Numerical aperture. Types of optical fibers and modes of propagation. Attenuation, Pulse dispersion (qualitative only). Nanomaterials- Effect of nano-scale dimension, Classification of nano materials, Properties and applications of nano systems, Carbon nanotubes (CNTs).

    Module 5
Basic Electronics Engineering (21ELN13/23)

Question Papers

Notes

  • Semiconductor Diode and its Applications: Construction, working, and characteristics of PN-junction Diode, Diode approximations, Shockley’s Equation, Half-wave, Full-wave, and Bridge Rectifiers, Mention of expression for average, RMS, and Peak Inverse Voltage, and Ripple Factor to each configuration, Zener Diode and its Characteristics,

    Transistor: Construction and working of Bipolar Junction Transistor, Transistor voltages and currents, mention of CB, CE and CC configurations, Input and Output characteristics of CE configuration, Circuit diagram and working of Transistor as Switch and Amplifier.

    Amplifiers: Need for transistor biasing, Voltage-Divider Bias Circuit, Classification of amplifiers.

    Module 1

  • Field Effect Transistors: Construction and working of JFET, Common Drain and Transfer Characteristics of JFET.

    MOSFET: Construction, working and Characteristics of Depletion and Enhancement mode MOSFETs.

    CMOS: Construction, Working and Characteristics of CMOS transistors.

    Module 2

  • Basics of Digital Electronics: Analog verses Digital Signals, Decimal, Binary, Octal and Hexadecimal Numbers and interconversion among them, 2’s complement Arithmetic, Addition and Subtraction of Binary Numbers, Basic and Universal Gates.

    Combinational Logic Circuits: Boolean Algebra and Theorems, Simplification of Logic Circuits, SoP and PoS forms, 2 and 3 variable K-Maps.

    Sequential Logic Circuits: Basics of Flip-flops, SR and JK Flip-flops.

    Module 3

  • Operational Amplifiers and its Applications: Basics of Differential Ampler, Block diagram of Op-amp and its modes, Ideal verses Practical Op-amps, Open and Closed Loop Op amp configurations.

    Op-amp Parameters: Definition and expression for Voltage gain, CMRR, Input Offset Voltage and Current, Input Bias Current, Virtual Ground, Input and Output impedance, Slew Rate.

    Module 4

  • Basics of Electronic Communication: Definition of Modulation and Demodulation, Need for Modulation, Electromagnetic Frequency Spectrum.

    Analog Communication: Block Diagram of Analog Communication System, Principles of AM and FM Modulation Schemes and their Comparison.

    Digital Communication: Block Diagram of Digital Modulation System, Advantages of Digital Communication over Analog Communication.

    Module 5
Elements of Civil Engineering (21CIV14/24)

Question Papers

Notes

  • Introduction: Definition of Civil Engineering, Scope of different fields of Civil Engineering; Building Materials, Surveying, Geotechnical Engineering, Structural Engineering, Construction Technology, Hydraulics, Water Resources & Irrigation Engineering, Transportation Engineering and Environmental Engineering. Role of Civil Engineers in the Infrastructural development, effect of infrastructural facilities on social- economic development of a country.

    Bridges: Types of Bridges and Culverts, RCC, Steel and Composite Bridges Dams: Different types of Dams based on Material, Structural behaviour and functionality with simple sketches.

    Module 1

  • Virtual Work and Energy Method-Virtual displacements, principle of virtual work for particle and ideal system of rigid bodies, degrees of freedom. Active force diagram, systems with friction, mechanical efficiency. Conservative forces and potential energy (elastic and gravitational), energy equation for equilibrium. Applications of energy method for equilibrium. Stability of equilibrium.

    Module 2

  • Review of particle dynamics-Rectilinear motion; Plane curvilinear motion(rectangular, path, and polar coordinates). 3-D curvilinear motion; Relative and constrained motion; Newton’s 2nd law (rectangular, path, and polar coordinates). Work-kinetic energy, power, potential energy. Impulse-momentum (linear, angular).

    Module 3

  • Introduction to Kinetics of Rigid Bodies covering, Basic terms, general principles in dynamics; Types of motion, Instantaneous centre of rotation in plane motion and simple problems; D’Alembert’s principle and its applications in plane motion and connected bodies; Work energy principle and its application in plane motion of connected bodies; Kinetics of rigid body rotation.

    Module 4

  • Mechanical Vibrations covering, Basic terminology, free and forced vibrations, resonance and its effects; Degree of freedom; Derivation for frequency and amplitude of free vibrations without damping and single degree of freedom system, simple problems, types of pendulum, use of simple,compound and torsion pendulums.

    Module 5
Biology for Engineers (21BIE15/25)

Question Papers

Notes

  • Need to study Biology: – Life Science Studies Significance - Bio Inspired Inventions - Role of Biology in Next Generation Technology Development – Cell Structure – Cell Potential - Action Potential – ECG and other common signals – Sodium

    Module 1

  • Potassium channels – Neuron function – Central Nervous Systems – Discussion Topics: Evolution of Artificial Neural Networks, Machine Learning techniques.

    Module 2

  • Genetics: Basic Principles of Mendel, molecular genetics, Structure and function of genes and chromosomes, Transcription and Translation, Gene expression and regulation

    Module 3

  • Sensing Techniques: - Understanding of Sense organs working – Sensing mechanisms - Sensor Development issues – Discussion Topics: Digital Camera – Eye Comparison, electronic nose, electronic tongue, electronic skin.

    Module 4

  • Physiological Assist Device: Artificial Organ Development: Kidney, Liver, Pancreas, heart valves – Design Challenges and Technological Developments

    Module 5
Technical English (21EGH19)

Question Papers

  • Module 1

    1.1 Word Formation 1.2 Etymology, origin of foreign words and their use in English Language 1.3 Familiarizing with prefixes and suffixes from foreign languages in English to form derivatives. 1.4 Synonyms, Antonyms and Standard Abbreviations. Basic Writing Skills



    Module 2

    2.1 Structure of Sentences 2.2 Use of Idioms and phrases in sentences 2.3 Punctuation of Sentences 2.4 Syntax and Creating coherence 2.5 Organizing principles of paragraphs in documents



    Module 3

    Identifying Common Errors in Writing 3.1 Subject-verb agreement 3.2 Noun-pronoun agreement 3.3 Misplaced modifiers 3.4 Articles 3.5 Prepositions 3.6 Redundancies 3.7 Clichés



    Module 4

    Nature and Style of Proper Writing 4.1 Defining 4.2 Describing and Classifying 4.3 Illustrations with suitable examples 4.4 Formulating Introduction and Conclusion Honing Writing Skills



    Module 5

    5.1 Report Writing/Comprehension 5.2 Précis Writing 5.3 Essay Writing 5.4 Critical analysis of unknown Prose Pieces/Poems.
    Oral Communication (This unit involves interactive practice sessions in Language Lab) Listening Comprehension- Active Listening, Feedback and Response, Pronunciation, Intonation and Accent, Common Everyday Situations: Conversations and Dialogues, Communication at Workplace, Interviews, Formal and PPT Presentations

Technical Kannada (21KAN29)