Categories
Uncategorized

GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING Regulation 2021 Anna University

GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING Regulation 2021 Anna University free download. PROBLEM SOLVING AND PYTHON PROGRAMMING Important Questions GE3151 pdf download free.

UNIT I COMPUTATIONAL THINKING AND PROBLEM SOLVING 

Fundamentals of Computing – Identification of Computational Problems -Algorithms, building blocks of algorithms (statements, state, control flow, functions), notation (pseudo code, flow chart,
programming language), algorithmic problem solving, simple strategies for developing algorithms (iteration, recursion). Illustrative problems: find minimum in a list, insert a card in a list of sorted
cards, guess an integer number in a range, Towers of Hanoi.

UNIT II DATA TYPES, EXPRESSIONS, STATEMENTS

Python interpreter and interactive mode, debugging; values and types: int, float, boolean, string, and list; variables, expressions, statements, tuple assignment, precedence of operators, comments; Illustrative programs: exchange the values of two variables, circulate the values of n variables, distance between two points. GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING

UNIT III CONTROL FLOW, FUNCTIONS, STRINGS

Conditionals: Boolean values and operators, conditional (if), alternative (if-else), chained conditional (if-elif-else); Iteration: state, while, for, break, continue, pass; Fruitful functions: return values,
parameters, local and global scope, function composition, recursion; Strings: string slices, immutability, string functions and
methods, string module; Lists as arrays. Illustrative programs: square root, gcd, exponentiation, sum an array of numbers, linear search, binary search. GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING

UNIT IV LISTS, TUPLES, DICTIONARIES 

Lists: list operations, list slices, list methods, list loop, mutability, aliasing, cloning lists, list parameters; Tuples: tuple assignment, tuple as return value; Dictionaries: operations and methods;
advanced list processing – list comprehension; Illustrative programs: simple sorting, histogram, Students marks statement, Retail bill preparation.

UNIT V FILES, MODULES, PACKAGES 

Files and exception: text files, reading and writing files, format operator; command line arguments, errors and exceptions, handling exceptions, modules, packages; Illustrative programs: word count,
copy file, Voter’s age validation, Marks range validation (0-100).

GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING Click Here To Download

GE3151 Syllabus PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Question Bank PROBLEM SOLVING AND PYTHON PROGRAMMING

Categories
Uncategorized

GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING Regulation 2021 Anna University

GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING Regulation 2021 Anna University free download. PROBLEM SOLVING AND PYTHON PROGRAMMING Notes GE3151 pdf download free.

TEXT BOOKS: GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING

1. Allen B. Downey, “Think Python: How to Think like a Computer Scientist”, 2nd Edition, O’Reilly Publishers, 2016.
2. Karl Beecher, “Computational Thinking: A Beginner's Guide to Problem Solving and programming”, 1st Edition, BCS Learning & Development Limited, 2017.

REFERENCES: GE3151 Notes PSPP

1. Paul Deitel and Harvey Deitel, “Python for Programmers”, Pearson Education, 1st Edition, 2021.
2. G Venkatesh and Madhavan Mukund, “Computational Thinking: A Primer for Programmers and Data Scientists”, 1st Edition, Notion Press, 2021.
3. John V Guttag, "Introduction to Computation and Programming Using Python: With Applications to Computational Modeling and Understanding Data‘‘, Third Edition, MIT Press
2021 GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING
4. Eric Matthes, “Python Crash Course, A Hands – on Project Based Introduction to Programming”, 2nd Edition, No Starch Press, 2019.
5. https://www.python.org/
6. Martin C. Brown, “Python: The Complete Reference”, 4th Edition, Mc-Graw Hill, 2018.

COURSE OBJECTIVES:

􀁸 To understand the basics of algorithmic problem solving.
􀁸 To learn to solve problems using Python conditionals and loops.
􀁸 To define Python functions and use function calls to solve problems.
􀁸 To use Python data structures – lists, tuples, dictionaries to represent complex data. GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING
􀁸 To do input/output with files in Python.

GE3151 Notes PROBLEM SOLVING AND PYTHON PROGRAMMING Click Here To Download

GE3151 Syllabus PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Important Questions PROBLEM SOLVING AND PYTHON PROGRAMMING

GE3151 Question Bank PROBLEM SOLVING AND PYTHON PROGRAMMING

Categories
Uncategorized

CY3151 Question Bank ENGINEERING CHEMISTRY Regulation 2021 Anna University

CY3151 Question Bank ENGINEERING CHEMISTRY

CY3151 Question Bank ENGINEERING CHEMISTRY Regulation 2021 Anna University free download. ENGINEERING CHEMISTRY Question Bank CY3151 pdf download free.

COURSE OUTCOMES CY3151 Syllabus ENGINEERING CHEMISTRY

At the end of the course, the students will be able:
􀁸 To infer the quality of water from quality parameter data and propose suitable treatment methodologies to treat water.
􀁸 To identify and apply basic concepts of nanoscience and nanotechnology in designing the synthesis of nanomaterials for engineering and technology applications.
􀁸 To apply the knowledge of phase rule and composites for material selection requirements.
􀁸 To recommend suitable fuels for engineering processes and applications.
􀁸 To recognize different forms of energy resources and apply them for suitable applications in energy sectors.

TEXT BOOKS: CY3151 Syllabus ENGINEERING CHEMISTRY

1. P. C. Jain and Monica Jain, “Engineering Chemistry”, 17th Edition, Dhanpat Rai Publishing Company (P) Ltd, New Delhi, 2018.
2. Sivasankar B., “Engineering Chemistry”, Tata McGraw-Hill Publishing Company Ltd, New Delhi, 2008.
3. S.S. Dara, “A Text book of Engineering Chemistry”, S. Chand Publishing, 12th Edition, 2018.

REFERENCES:
1. B. S. Murty, P. Shankar, Baldev Raj, B. B. Rath and James Murday, “Text book of nanoscience and nanotechnology”, Universities Press-IIM Series in Metallurgy and Materials Science, 2018.
2. O.G. Palanna, “Engineering Chemistry” McGraw Hill Education (India) Private Limited, 2nd Edition, 2017.
3. Friedrich Emich, “Engineering Chemistry”, Scientific International PVT, LTD, New Delhi, 2014.
4. ShikhaAgarwal, “Engineering Chemistry-Fundamentals and Applications”, Cambridge University Press, Delhi, Second Edition, 2019.
5. O.V. Roussak and H.D. Gesser, Applied Chemistry-A Text Book for Engineers and Technologists, Springer Science Business Media, New York, 2nd Edition, 2013.

CY3151 Question Bank ENGINEERING CHEMISTRY Click Here To Download

CY3151 Syllabus ENGINEERING CHEMISTRY 

CY3151 Notes ENGINEERING CHEMISTRY 

CY3151 Important Questions ENGINEERING CHEMISTRY

 

Categories
Uncategorized

CY3151 Important Questions ENGINEERING CHEMISTRY Regulation 2021 Anna University

CY3151 Important Questions ENGINEERING CHEMISTRY

CY3151 Important Questions ENGINEERING CHEMISTRY Regulation 2021 Anna University free download. ENGINEERING CHEMISTRY Important Questions CY3151 pdf download free.

UNIT I WATER AND ITS TREATMENT 

Water: Sources and impurities, Water quality parameters: Definition and significance of-color, odour, turbidity, pH, hardness, alkalinity, TDS, COD and BOD, flouride and arsenic. Municipal water
treatment: primary treatment and disinfection (UV, Ozonation, break-point chlorination). Desalination of brackish water: Reverse Osmosis. Boiler troubles: Scale and sludge, Boiler corrosion, Caustic embrittlement, Priming &foaming. Treatment of boiler feed water: Internal treatment (phosphate, colloidal, sodium aluminate and calgon conditioning) and External treatment – Ion exchange demineralization and zeolite process.

UNIT II NANOCHEMISTRY CY3151 Important Questions ENGINEERING CHEMISTRY

Basics: Distinction between molecules, nanomaterials and bulk materials; Size-dependent properties (optical, electrical, mechanical and magnetic); Types of nanomaterials: Definition, properties and uses of – nanoparticle, nanocluster, nanorod, nanowire and nanotube. Preparation of nanomaterials: sol-gel, solvothermal, laser ablation, chemical vapour deposition, electrochemical deposition and electro spinning. Applications of nanomaterials in medicine, agriculture, energy, electronics and catalysis.

UNIT III PHASE RULE AND COMPOSITES

Phase rule: Introduction, definition of terms with examples. One component system – water system; Reduced phase rule; Construction of a simple eutectic phase diagram – Thermal analysis; Two component system: lead-silver system – Pattinson process.
Composites: Introduction: Definition & Need for composites; Constitution: Matrix materials (Polymer matrix, metal matrix and ceramic matrix) and Reinforcement (fiber, particulates, flakes and
whiskers). Properties and applications of: Metal matrix composites (MMC), Ceramic matrix composites and Polymer matrix composites. Hybrid composites – definition and examples.

UNIT IV FUELS AND COMBUSTION CY3151 Important Questions ENGINEERING CHEMISTRY

Fuels: Introduction: Classification of fuels; Coal and coke: Analysis of coal (proximate and ultimate), Carbonization, Manufacture of metallurgical coke (Otto Hoffmann method). Petroleum and Diesel:
Manufacture of synthetic petrol (Bergius process), Knocking – octane number, diesel oil – cetane number; Power alcohol and biodiesel. Combustion of fuels: Introduction: Calorific value – higher and lower calorific values, Theoretical calculation of calorific value; Ignition temperature: spontaneous ignition temperature, Explosive
range; Flue gas analysis – ORSAT Method. CO2 emission and carbon foot print.

UNIT V ENERGY SOURCES AND STORAGE DEVICES

Stability of nucleus: mass defect (problems), binding energy; Nuclear energy: light water nuclear power plant, breeder reactor. Solar energy conversion: Principle, working and applications of solar cells; Recent developments in solar cell materials. Wind energy; Geothermal energy; Batteries: Types of batteries, Primary battery – dry cell, Secondary battery – lead acid battery and lithium-ionbattery; Electric vehicles – working principles; Fuel cells: H2-O2 fuel cell, microbial fuel cell; Supercapacitors: Storage principle, types and examples.

CY3151 Important Questions ENGINEERING CHEMISTRY Click Here To Download

CY3151 Syllabus ENGINEERING CHEMISTRY

CY3151 Notes ENGINEERING CHEMISTRY 

CY3151 Question Bank ENGINEERING CHEMISTRY

Categories
Uncategorized

CY3151 Notes ENGINEERING CHEMISTRY Regulation 2021 Anna University

CY3151 Notes ENGINEERING CHEMISTRY

CY3151 Notes ENGINEERING CHEMISTRY Regulation 2021 Anna University free download. ENGINEERING CHEMISTRY Notes CY3151 pdf download free.

TEXT BOOKS: CY3151 Notes ENGINEERING CHEMISTRY

1. P. C. Jain and Monica Jain, “Engineering Chemistry”, 17th Edition, Dhanpat Rai Publishing Company (P) Ltd, New Delhi, 2018.
2. Sivasankar B., “Engineering Chemistry”, Tata McGraw-Hill Publishing Company Ltd, New Delhi, 2008.
3. S.S. Dara, “A Text book of Engineering Chemistry”, S. Chand Publishing, 12th Edition, 2018.

REFERENCES:
1. B. S. Murty, P. Shankar, Baldev Raj, B. B. Rath and James Murday, “Text book of nanoscience and nanotechnology”, Universities Press-IIM Series in Metallurgy and Materials Science, 2018.
2. O.G. Palanna, “Engineering Chemistry” McGraw Hill Education (India) Private Limited, 2nd Edition, 2017.
3. Friedrich Emich, “Engineering Chemistry”, Scientific International PVT, LTD, New Delhi, 2014.
4. ShikhaAgarwal, “Engineering Chemistry-Fundamentals and Applications”, Cambridge University Press, Delhi, Second Edition, 2019.
5. O.V. Roussak and H.D. Gesser, Applied Chemistry-A Text Book for Engineers and Technologists, Springer Science Business Media, New York, 2nd Edition, 2013.

COURSE OBJECTIVES:
􀁸 To inculcate sound understanding of water quality parameters and water treatment techniques.
􀁸 To impart knowledge on the basic principles and preparatory methods of nanomaterials.
􀁸 To introduce the basic concepts and applications of phase rule and composites.
􀁸 To facilitate the understanding of different types of fuels, their preparation, properties and
combustion characteristics.
􀁸 To familiarize the students with the operating principles, working processes and applications
of energy conversion and storage devices.

CY3151 Notes ENGINEERING CHEMISTRY Click Here To Download

CY3151 Syllabus ENGINEERING CHEMISTRY 

CY3151 Important Questions ENGINEERING CHEMISTRY

CY3151 Question Bank ENGINEERING CHEMISTRY

Categories
Uncategorized

PH3151 Question Bank ENGINEERING PHYSICS Regulation 2021 Anna University

PH3151 Question Bank ENGINEERING PHYSICS

PH3151 Question Bank ENGINEERING PHYSICS Regulation 2021 Anna University free download. ENGINEERING PHYSICS Important Questions PH3151 pdf download free.

REFERENCES:
1. R.Wolfson. Essential University Physics. Volume 1 & 2. Pearson Education (Indian Edition),
2009.􀍒
2. Paul A. Tipler, Physic – Volume 1 & 2, CBS, (Indian Edition), 2004.
3. K.Thyagarajan and A.Ghatak. Lasers: Fundamentals and Applications, Laxmi Publications,
(Indian Edition), 2019.
4. D.Halliday, R.Resnick and J.Walker. Principles of Physics, Wiley (Indian Edition), 2015.
5. N.Garcia, A.Damask and S.Schwarz. Physics for Computer Science Students. Springer-
Verlag, 2012.

COURSE OUTCOMES
After completion of this course, the students should be able to
􀁸 Understand the importance of mechanics.
􀁸 Express their knowledge in electromagnetic waves.
􀁸 Demonstrate a strong foundational knowledge in oscillations, optics and lasers.
􀁸 Understand the importance of quantum physics.
􀁸 Comprehend and apply quantum mechanical principles towards the formation of energy
bands.

COURSE OBJECTIVES
􀁸 To make the students effectively to achieve an understanding of mechanics.
􀁸 To enable the students to gain knowledge of electromagnetic waves and its applications.
􀁸 To introduce the basics of oscillations, optics and lasers.
􀁸 Equipping the students to be successfully understand the importance of quantum physics.
􀁸 To motivate the students towards the applications of quantum mechanics.

PH3151 Question Bank ENGINEERING PHYSICS Click Here To Download

PH3151 Syllabus ENGINEERING PHYSICS

PH3151 Notes ENGINEERING PHYSICS

PH3151 Important Question ENGINEERING PHYSICS

 

Categories
Uncategorized

PH3151 Important Questions ENGINEERING PHYSICS Regulation 2021 Anna University

PH3151 Important Questions ENGINEERING PHYSICS

PH3151 Important Questions ENGINEERING PHYSICS Regulation 2021 Anna University free download. ENGINEERING PHYSICS Important Questions PH3151 pdf download free.

UNIT I MECHANICS
Multi-particle dynamics: Center of mass (CM) – CM of continuous bodies – motion of the CM – kinetic energy of system of particles. Rotation of rigid bodies: Rotational kinematics – rotational kinetic energy and moment of inertia – theorems of M .I –moment of inertia of continuous bodies –
M.I of a diatomic molecule – torque – rotational dynamics of rigid bodies – conservation of angular momentum – rotational energy state of a rigid diatomic molecule – gyroscope – torsional pendulum – double pendulum –Introduction to nonlinear oscillations.

UNIT II ELECTROMAGNETIC WAVES PH3151 Important Questions ENGINEERING PHYSICS
The Maxwell’s equations – wave equation; Plane electromagnetic waves in vacuum, Conditions on the wave field – properties of electromagnetic waves: speed, amplitude, phase, orientation and waves in matter – polarization – Producing electromagnetic waves – Energy and momentum in EM
waves: Intensity, waves from localized sources, momentum and radiation pressure – Cell-phone reception. Reflection and transmission of electromagnetic waves from a non-conducting mediumvacuum
interface for normal incidence.

UNIT III OSCILLATIONS, OPTICS AND LASERS
Simple harmonic motion – resonance –analogy between electrical and mechanical oscillating systems – waves on a string – standing waves – traveling waves – Energy transfer of a wave – sound waves – Doppler effect. Reflection and refraction of light waves – total internal reflection – interference –Michelson interferometer –Theory of air wedge and experiment.􀍒Theory of laser – characteristics – Spontaneous and stimulated emission – Einstein’s coefficients – population inversion – Nd-YAG laser, PH3151 Important Questions ENGINEERING PHYSICS
CO2 laser, semiconductor laser –Basic applications of lasers in industry.

UNIT IV BASIC QUANTUM MECHANICS
Photons and light waves – Electrons and matter waves –Compton effect – The Schrodinger equation (Time dependent and time independent forms) – meaning of wave function – Normalization –Free particle – particle in a infinite potential well: 1D,2D and 3D Boxes- Normalization, probabilities and the correspondence principle.

UNIT V APPLIED QUANTUM MECHANICS PH3151 Important Questions ENGINEERING PHYSICS
The harmonic oscillator(qualitative)- Barrier penetration and quantum tunneling(qualitative)- Tunneling microscope – Resonant diode – Finite potential wells (qualitative)- Bloch’s theorem for particles in a periodic potential –Basics of Kronig-Penney model and origin of energy bands.

PH3151 Important Questions ENGINEERING PHYSICS Click Here To Download

PH3151 Syllabus ENGINEERING PHYSICS

PH3151 Notes ENGINEERING PHYSICS

PH3151 Question Bank ENGINEERING PHYSICS

Categories
Uncategorized

PH3151 Notes ENGINEERING PHYSICS Regulation 2021 Anna University

PH3151 Notes ENGINEERING PHYSICS

PH3151 Notes ENGINEERING PHYSICS Regulation 2021 Anna University free download. ENGINEERING PHYSICS Notes PH3151 pdf download free.

COURSE OUTCOMES
After completion of this course, the students should be able to
􀁸 Understand the importance of mechanics.
􀁸 Express their knowledge in electromagnetic waves.
􀁸 Demonstrate a strong foundational knowledge in oscillations, optics and lasers.
􀁸 Understand the importance of quantum physics.
􀁸 Comprehend and apply quantum mechanical principles towards the formation of energy
bands.

TEXT BOOKS: PH3151 Notes ENGINEERING PHYSICS

1. D.Kleppner and R.Kolenkow. An Introduction to Mechanics. McGraw Hill Education (Indian
Edition), 2017. 􀍒
2. E.M.Purcell and D.J.Morin, Electricity and Magnetism, Cambridge Univ.Press, 2013.
3. Arthur Beiser, Shobhit Mahajan, S. Rai Choudhury, Concepts of Modern Physics, McGraw-Hill
(Indian Edition), 2017.

REFERENCES:
1. R.Wolfson. Essential University Physics. Volume 1 & 2. Pearson Education (Indian Edition),
2009.􀍒
2. Paul A. Tipler, Physic – Volume 1 & 2, CBS, (Indian Edition), 2004.
3. K.Thyagarajan and A.Ghatak. Lasers: Fundamentals and Applications, Laxmi Publications,
(Indian Edition), 2019.
4. D.Halliday, R.Resnick and J.Walker. Principles of Physics, Wiley (Indian Edition), 2015.
5. N.Garcia, A.Damask and S.Schwarz. Physics for Computer Science Students. Springer-
Verlag, 2012.

COURSE OBJECTIVES
􀁸 To make the students effectively to achieve an understanding of mechanics.
􀁸 To enable the students to gain knowledge of electromagnetic waves and its applications.
􀁸 To introduce the basics of oscillations, optics and lasers.
􀁸 Equipping the students to be successfully understand the importance of quantum physics.
􀁸 To motivate the students towards the applications of quantum mechanics.

PH3151 Notes ENGINEERING PHYSICS Click Here To Download

PH3151 Syllabus ENGINEERING PHYSICS

PH3151 Important Question ENGINEERING PHYSICS

PH3151 Question Bank ENGINEERING PHYSICS

Categories
Uncategorized

MA3151 Question Bank Matrix and Calculus Regulation 2021 Anna University

MA3151 Question Bank Matrix and Calculus

MA3151 Question Bank Matrix and Calculus Regulation 2021 Anna University free download. Matrix and Calculus Question Bank MA3151 pdf download free.

UNIT – I MATRICES 
Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal
transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane.

UNIT – II DIFFERENTIAL CALCULUS  MA3151 Question Bank Matrix and Calculus
Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules (sum, product, quotient, chain rules) – Implicit differentiation – Logarithmic differentiation – Applications :
Maxima and Minima of functions of one variable.

UNIT – III FUNCTIONS OF SEVERAL VARIABLES MA3151 Question Bank Matrix and Calculus

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of
two variables – Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.

UNIT – IV INTEGRAL CALCULUS MA3151 Question Bank Matrix and Calculus

Definite and Indefinite integrals – Substitution rule – Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial
fraction, Integration of irrational functions – Improper integrals – Applications : Hydrostatic force and pressure, moments and centres of mass.

UNIT – V MULTIPLE INTEGRALS 

Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals – Applications : Moments and centres of mass, moment of inertia.

MA3151 Question Bank Matrix and Calculus Click Here To Download

MA3151 Syllabus Matrix and Calculus

MA3151 Notes Matrix and Calculus 

MA3151 Important Questions Matrix and Calculus

 

Categories
Uncategorized

MA3151 Important Questions Matrix and Calculus Regulation 2021 Anna University

MA3151 Important Questions Matrix and Calculus

MA3151 Important Questions Matrix and Calculus Regulation 2021 Anna University free download. Matrix and Calculus Important Questions MA3151 pdf download free.

UNIT – I MATRICES 
Eigenvalues and Eigenvectors of a real matrix – Characteristic equation – Properties of Eigenvalues and Eigenvectors – Cayley – Hamilton theorem – Diagonalization of matrices by orthogonal
transformation – Reduction of a quadratic form to canonical form by orthogonal transformation – Nature of quadratic forms – Applications: Stretching of an elastic membrane.

UNIT – II DIFFERENTIAL CALCULUS  MA3151 Important Questions Matrix and Calculus
Representation of functions – Limit of a function – Continuity – Derivatives – Differentiation rules (sum, product, quotient, chain rules) – Implicit differentiation – Logarithmic differentiation – Applications :
Maxima and Minima of functions of one variable.

UNIT – III FUNCTIONS OF SEVERAL VARIABLES MA3151 Important Questions Matrix and Calculus

Partial differentiation – Homogeneous functions and Euler’s theorem – Total derivative – Change of variables – Jacobians – Partial differentiation of implicit functions – Taylor’s series for functions of
two variables – Applications : Maxima and minima of functions of two variables and Lagrange’s method of undetermined multipliers.

UNIT – IV INTEGRAL CALCULUS MA3151 Important Questions Matrix and Calculus

Definite and Indefinite integrals – Substitution rule – Techniques of Integration: Integration by parts, Trigonometric integrals, Trigonometric substitutions, Integration of rational functions by partial
fraction, Integration of irrational functions – Improper integrals – Applications : Hydrostatic force and pressure, moments and centres of mass.

UNIT – V MULTIPLE INTEGRALS 

Double integrals – Change of order of integration – Double integrals in polar coordinates – Area enclosed by plane curves – Triple integrals – Volume of solids – Change of variables in double and triple integrals – Applications : Moments and centres of mass, moment of inertia.

MA3151 Important Questions Matrix and Calculus Click Here To Download

MA3151 Syllabus Matrix and Calculus

MA3151 Notes Matrix and Calculus 

MA3151 Question Bank Matrix and Calculus