JNTUK R20 1-2 Mathematics – III Material/Notes PDF Download

Students those who are studying JNTUK R20 EEE Branch, Can Download Unit wise R20 1-2 Mathematics – III (Vector Calculus, Transforms and PDE-M3) Material/Notes PDFs below.

JNTUK R20 1-2 Mathematics – III Material/Notes PDF Download

Course Objectives:

• To familiarize the techniques in partial differential equations
• To furnish the learners with basic concepts and techniques at plus two level to lead them into advanced level by handling various real world applications.

Course Outcomes: At the end of the course, the student will be able to

• interpret the physical meaning of different operators such as gradient, curl and divergence (L5)
• estimate the work done against a field, circulation and flux using vector calculus (L5)
• apply the Laplace transform for solving differential equations (L3)
• find or compute the Fourier series of periodic signals (L3)
• know and be able to apply integral expressions for the forwards and inverse Fourier transform to a range of non-periodic waveforms (L3)
• identify solution methods for partial differential equations that model physical processes (L3)

UNIT-1

Vector calculus:

Vector Differentiation: Gradient– Directional derivative – Divergence– Curl– Scalar Potential Vector Integration: Line integral – Work done – Area– Surface and volume integrals – Vector integral theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and problems on above theorems.

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UNIT-2

Laplace Transforms:

Laplace transforms – Definition and Laplace transforms of some certain functions– Shifting theorems – Transforms of derivatives and integrals – Unit step function –Dirac’s delta functionPeriodic function – Inverse Laplace transforms– Convolution theorem (without proof). Applications: Solving ordinary differential equations (initial value problems) using Laplace transforms.

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UNIT-3

Fourier series and Fourier Transforms:

Fourier Series: Introduction– Periodic functions – Fourier series of periodic function – Dirichlet’s conditions – Even and odd functions –Change of interval– Half-range sine and cosine series. Fourier Transforms: Fourier integral theorem (without proof) – Fourier sine and cosine integrals – Sine and cosine transforms – Properties (article-22.5 in text book-1)– inverse transforms – Convolution theorem (without proof) – Finite Fourier transforms.

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UNIT-4

PDE of first order:

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions – Solutions of first order linear (Lagrange) equation and nonlinear (standard types) equations.

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UNIT-5:

Second order PDE and Applications:

Second order PDE: Solutions of linear partial differential equations with constant coefficients –Nonhomogeneous term of the type ax by m n e ,sin( ax  by), cos(ax  by), x y . Applications of PDE: Method of separation of Variables– Solution of One dimensional Wave, Heat and two-dimensional Laplace equation

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TEXT BOOKS:

1. B. S. Grewal, Higher Engineering Mathematics, 44th Edition, Khanna Publishers, 2018.
2. B. V. Ramana,Higher Engineering Mathematics, 2007 Edition, Tata McGraw Hill Education.

REFERENCE BOOKS:

1. Erwin Kreyszig, Advanced Engineering Mathematics, 10th Edition, Wiley-India. 2015.
2. Dean. G. Duffy, Advanced Engineering Mathematics with MATLAB, 3rd Edition, CRC Press, 2010.
3. Peter O’ Neil, Advanced Engineering Mathematics, 7 th edition, Cengage, 2011..
4. Srimantha Pal, S C Bhunia, Engineering Mathematics, Oxford University Press, 2015.

JNTUK R20 1-2 Electrical Circuit Analysis-I Material PDF Download

Students those who are studying JNTUK R20 EEE Branch, Can Download Unit wise R20 1-2 Electrical Circuit Analysis-I (ECA-1) Material/Notes PDFs below.

JNTUK R20 1-2 Electrical Circuit Analysis-I Material PDF Download

Preamble: This course introduces the basic concepts of circuit analysis which is the foundation for all subjects of the Electrical Engineering discipline. The emphasis of this course is laid on the basic analysis of circuits which includes single phase circuits, magnetic circuits, network theorems, transient analysis and network topology.

Course Objectives:

• To study the concepts of passive elements, types of sources and various network reduction techniques.
• To understand the applications of network topology to electrical circuits.
• To study the concept of magnetic coupled circuit.
• To understand the behavior of RLC networks for sinusoidal excitations.
• To study the performance of R-L, R-C and R-L-C circuits with variation of one of the parameters and to understand the concept of resonance.
• To understand the applications of network theorems for analysis of electrical networks

UNIT-1

Introduction to Electrical Circuits

Basic Concepts of passive elements of R, L, C and their V-I relations, Sources (dependent and independent), Kirchhoff’s laws, Network reduction techniques (series, parallel, series – parallel, star-to-delta and delta-to-star transformation), source transformation technique, nodal analysis and mesh analysis to DC networks with dependent and independent voltage and current sources., node and mesh analysis.

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Unit-2

Magnetic Circuits

Basic definition of MMF, flux and reluctance, analogy between electrical and magnetic circuits, Faraday’s laws of electromagnetic induction – concept of self and mutual inductance, Dot convention – coefficient of coupling and composite magnetic circuit, analysis of series and parallel magnetic circuits.

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Unit-3

Single Phase A.C Systems

Periodic waveforms (determination of rms, average value and form factor), concept of phasor, phase angle and phase difference – waveforms and phasor diagrams for lagging, leading networks, complex and polar forms of representations. node and mesh analysis. Steady state analysis of R, L and C circuits, power factor and its significance, real, reactive and apparent power, waveform of instantaneous power and complex power .

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Unit-4

Resonance – Locus Diagrams

series and parallel resonance, selectively band width and Quality factor, locus diagram- RL, RC, RLC with R, L and C variables.

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Unit-5

Network theorems (DC & AC Excitations)

Superposition theorem, Thevenin’s theorem, Norton’s theorem, Maximum Power Transfer theorem, Reciprocity theorem, Millman’s theorem and compensation theorem.

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Credits: shaik.himam (Prakasam engineering college)

Text Books:

1. Engineering Circuit Analysis by William Hayt and Jack E. Kemmerley, 6 th edition McGraw Hill Company, 2012.
2. Network Analysis: Van Valkenburg; Prentice-3 rd edition, Hall of India Private Ltd, 2015.

Reference Books:

1. Fundamentals of Electrical Circuits by Charles K. Alexander and Mathew N.O.Sadiku, 5th edition, McGraw Hill Education (India), 2013.

2. Linear Circuit Analysis by De Carlo, Lin, 2 nd edition, Oxford publications, 2001.

3. Electric Circuits – (Schaum’s outlines) by Mahmood Nahvi & Joseph Edminister, Adapted by KumaRao, 5th Edition – McGraw Hill, 2017.

4. Electric Circuits by David A. Bell, 7 th edition, Oxford publications, 2009.

5. Introductory Circuit Analysis by Robert L Boylestad, 13th edition, Pearson, 2015

6. Circuit Theory (Analysis and Synthesis) by A. Chakrabarthi, 7th edition, DhanpatRai & Co., 2018.

Course Outcomes: After the completion of the course the student should be able to:

• Various electrical networks in presence of active and passive elements.
• Electrical networks with network topology concepts.
• Any magnetic circuit with various dot conventions.
• Any R, L, C network with sinusoidal excitation.
• Any R, L, network with variation of any one of the parameters i.e R, L, C and f.
• Electrical networks by using principles of network theorems.

JNTUK R20 1-2 Data Structures Through C Material/Notes PDF Download

Students those who are studying JNTUK R20 EEE Branches, Can Download Unit wise R20 1-2 Data Structures Through C Material/Notes PDFs below.

JNTUK R20 1-2 Data Structures Through C Material/Notes PDF Download

Preamble: This course is core subject developed to help the student understand the data structure principles used in power systems, machines and control systems. This subject covers linear data structures, linked lists, trees, graphs, searching and sorting.

Course Objectives:

• Operations on linear data structures and their applications.
• The various operations on linked lists.
• The basic concepts of Trees, Traversal methods and operations.
• Concepts of implementing graphs and its relevant algorithms.
• Sorting and searching algorithms.

UNIT-1

Linear Data Structures: Arrays, Stacks and Queues Data Structures -Operations-Abstract Data Types-Complexity of Algorithms-Time and SpaceArrays-Representation of Arrays-Linear Arrays-Insertion–Deletion and Traversal of a Linear Array-Array as an Abstract Data Type-Multi-Dimensional arrays-Strings-String OperationsStoring Strings-String as an Abstract Data Type

Stack -Array Representation of Stack-Stack Abstract Data Type-Applications of Stacks: PrefixInfix and Postfix Arithmetic Expressions-Conversion-Evaluation of Postfix ExpressionsRecursion-Towers of Hanoi-Queues-Definition-Array Representation of Queue-The Queue Abstract Data Type-Circular Queues-Dequeues-Priority Queues.

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Unit-2

Linked Lists

Pointers-Pointer Arrays-Linked Lists-Node Representation-Single Linked List-Traversing and Searching a Single Linked List-Insertion into and Deletion from a Single Linked List-Header Linked Lists-Circularly Linked Lists-Doubly Linked Lists-Linked Stacks and QueuesPolynomials-Polynomial Representation-Sparse Matrices.

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Unit-3

Trees

Terminology-Representation of Trees-Binary Trees-Properties of Binary Trees-Binary Tree Representations-Binary Tree Traversal-Preorder-Inorder and Postorder Traversal-ThreadsThread Binary Trees-Balanced Binary Trees-Heaps-Max Heap-Insertion into and Deletion from a Max Heap-Binary Search Trees-Searching-Insertion and Deletion from a Binary Search TreeHeight of Binary Search Tree, m-way Search Trees, B-Trees.

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Unit-4

Graphs

Graph Theory Terminology-Graph Representation-Graph Operations-Depth First Search-Breadth First Search-Connected Components-Spanning Trees-Biconnected Components-Minimum Cost Spanning Trees-Kruskal’s Algorithm-Prism’s Algorithm-Shortest Paths-Transitive Closure-AllPairs Shortest Path-Warshall’s Algorithm.

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Unit-5

Searching and Sorting

Searching -Linear Search-Binary Search-Fibonacci Search-Hashing-Sorting-Definition-Bubble Sort-Insertion sort-Selection Sort-Quick Sort-Merging-Merge Sort-Iterative and Recursive Merge Sort-Shell Sort-Radix Sort-Heap Sort.

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Course Outcomes: After the completion of the course the student should be able to:

• data structures concepts with arrays, stacks, queues.
• linked lists for stacks, queues and for other applications.
• traversal methods in the Trees.
• various algorithms available for the graphs.
• sorting and searching in the data ret retrival applications.

TEXT BOOKS:

1. Fundamentals of Data Structures in C, 2nd Edition, E.Horowitz, S.Sahni and Susan Anderson Freed, Universities Press Pvt. Ltd.
2. Data Structures with C, Seymour Lipschutz, Schaum’s Outlines, Tata McGraw Hill