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Here, we have provided the links which contains the study materials which will help you in studying and preparing for your examinations of the B.Tech 1st Year Mathematics. Referring to the links we’ve provided below and the links which contains the study materials in PDF Format along with the list of recommended books which we’ve provided below, you will be able to ace your examinations. We have also provided you the further details which will allow you to do well in your exams and learn more. These study materials help you understand the concepts and everything easily and creates a better space for you to work on. These study materials give you the best resources to study from.

Engineering Mathematics

This subject helps a student gain analytical ability in solving mathematics problems by applying them in respective branches of engineering. This is about applying advanced matrix knowledge in engineering problems.

Download B.Tech 1st Year Maths PDF

Engineering mathematics  textbook pdf free download Download
first-year engineering  mathematics notesDownload
Engineering mathematics 1 notes free download  Download
Engineering mathematics 2 pdf  Download
Engineering mathematics 3 question papers pdfDownload
Engineering mathematics 1 question papers pdfDownload
Engineering mathematics 2 Question paper  Download

Recommended Books

  •  Ramana B.V., Higher Engineering Mathematics, TMH, Ist edition
  •  J.Sinha Roy and S Padhy, A course on ordinary and partial differential Equation, Kalyani Publication, 3rd edition
  •  Kreyszig E., Advanced Engineering Mathematics, Wiley, 9th edition.
  •  Shanti Narayan and P.K.Mittal, Differential Calculus, S. Chand, reprint 2009
  •  Grewal B.S., Higher Engineering Mathematics, Khanna Publishers,36th edition
  •  Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition
  • Ramana B.V., Higher Engineering Mathematics, TMH, 1st edition
  • J.Sinha Roy and S Padhy, A course on ordinary and partial differential Equation, Kalyani Publication, 3rd edition
  • Chakraborty and Das; Principles of transportation engineering; pHI
  • Rangwala SC; Railway Engineering; charotar Publication House, Anand
  •  Rangwala sc; Bridge Engineering; charotar Publication House, Anand
  •  Ponnuswamy; Bridge Engineering; TMH
  • Kreyszig E., Advanced Engineering Mathematics, Wiley, 9th edition.
  • Grewal B.S., Higher Engineering Mathematics, Khanna Publishers, 36th edition
  •  Dass H.K., Introduction to engineering Mathematics, S.Chand & Co Ltd, 11th edition

Syllabus

Mathematics I:

I: Ordinary Differential Equations :

Basic concepts and definitions of 1st order differential equations; Formation of differential equations; solution of
differential equations: variable separable, homogeneous, equations reducible to homogeneous form, exact differential equation, equations reducible to exact form, linear differential equation, equations reducible to linear form (Bernoulli’s equation); orthogonal trajectories, applications of differential equations.

II: Linear Differential equations of 2nd and higher-order 

Second-order linear homogeneous equations with constant coefficients; differential operators; solution of homogeneous equations; Euler-Cauchy equation; linear dependence and independence; Wronskian; Solution of nonhomogeneous equations: general solution, complementary function, particular integral; solution by variation of parameters; undetermined coefficients; higher order linear homogeneous equations; applications.

III: Differential Calculus(Two and Three variables)

Taylor’s Theorem, Maxima, and Minima, Lagrange’s multipliers

IV: Matrices, determinants, linear system of equations

Basic concepts of algebra of matrices; types of matrices; Vector Space, Sub-space, Basis and dimension, linear the system of equations; consistency of linear systems; rank of matrix; Gauss elimination; inverse of a matrix by Gauss Jordan method; linear dependence and independence, linear transformation; inverse transformation ; applications of matrices; determinants; Cramer’s rule.

V: Matrix-Eigen value problems

Eigen values, Eigen vectors, Cayley Hamilton theorem, basis, complex matrices; quadratic form; Hermitian, SkewHermitian forms; similar matrices; diagonalization of matrices; transformation of forms to principal axis (conic section).

MATHEMATICS-II

I: Laplace Transforms

Laplace Transform, Inverse Laplace Transform, Linearity, transform of derivatives and Integrals, Unit Step function, Dirac delta function, Second Shifting theorem, Differentiation and Integration of Transforms, Convolution, Integral Equation, Application to solve differential and integral equations, Systems of differential equations.

II: Series Solution of Differential Equations

Power series; the radius of convergence, power series method, Frobenius method; Special functions: Gamma function,
Beta function; Legendre’s and Bessel’s equations; Legendre’s function, Bessel’s function, orthogonal functions;
generating functions.

III: Fourier series, Integrals and Transforms

Periodic functions, Even and Odd functions, Fourier series, Half Range Expansion, Fourier Integrals, Fourier sine, and cosine transforms, Fourier Transform

IV: Vector Differential Calculus

Vector and Scalar functions and fields, Derivatives, Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field.

V: Vector Integral Calculus

Line integral, Double Integral, Green’s theorem, Surface Integral, Triple Integral, Divergence Theorem for Gauss, Stoke’s Theorem

Engineering Mathematics III:

UNIT I: Linear systems of equations:

Rank-Echelon form-Normal form – Solution of linear systems – Gauss elimination – Gauss Jordon- Gauss Jacobi and Gauss Seidel methods. Applications: Finding the current in electrical circuits.

UNIT II: Eigenvalues – Eigenvectors and Quadratic forms: 

Eigen values – Eigen vectors– Properties – Cayley-Hamilton theorem Inverse and powers of a matrix by using Cayley-Hamilton theorem- Diagonalization- Quadratic forms- Reduction of quadratic form to canonical form – Rank – Positive, negative and semi definite – Index – Signature. Applications: Free vibration of a two-mass system.

UNIT III: Multiple integrals:

Curve tracing: Cartesian, Polar and Parametric forms. Multiple integrals: Double and triple integrals – Change of variables –Change of order of integration. Applications: Finding Areas and Volumes.

UNIT IV: Special functions:

Beta and Gamma functions- Properties – Relation between Beta and Gamma functions- Evaluation of improper integrals.
Applications: Evaluation of integrals.

UNIT V: Vector Differentiation:

Gradient- Divergence- Curl – Laplacian and second-order operators -Vector identities. Applications: Equation of continuity, potential surfaces

UNIT VI: Vector Integration:

Line integral – Work is done – Potential function – Area- Surface and volume integrals Vector integral theorems: Greens, Stokes and Gauss Divergence theorems (without proof) and related problems.
Applications: Work is done, Force.

Important Questions

  • Give examples of Hermitian, skew-Hermitian and unitary matrices that have entries with non-zero imaginary parts.
  • Restate the results on transpose in terms of the conjugate transpose.
  • Show that for any square matrix A, S = A+A* 2 is Hermitian, T = A−A ∗ 2 is skew-Hermitian, and A = S + T.
  • Show that if A is a complex triangular matrix and AA∗ = A∗A then A is a diagonal matrix

Here, we have provided the links which contains the study materials which will help you in studying and preparing for your examinations of the GATE Mathematics. Referring to the links we’ve provided below and the links which contains the study materials in PDF Format along with the list of recommended books which we’ve provided below, you will be able to ace your examinations. We have also provided you the further details which will allow you to do well in your exams and learn more. These study materials help you understand the concepts and everything easily and creates a better space for you to work on. These study materials give you the best resources to study from.

More About GATE 2020

Graduate Aptitude Test in Engineering in a National Level Examination which is used to test a candidate’s performing skills along with their understanding capability. Acing this test will provide the students an easier path to admissions in M.M/M.MTech and other NITs which is throughout India. The GATE exam provides easier access to the seven IITs (Indian Institute of Technology) and IISc (Indian Institute of Science) which is done on behalf of National Coordination Board – GATE. Department of Higher Education, Ministry of HR Development (MHRD), Government of India.

GATE 2020 Exam DatesTo be Declared
Organizing Institution of GATEIIT Guwahati
GATE Official Websitehttp://www.gate.iitg.ac.in/
GATE Syllabus 2020Check Here
GATE 2020 Online ApplicationClick Here
GATE Previous Question PapersDownload Here
GATE Candidates LoginLink
GATE 2020 Cut OffCheck here

About Mathematics GATE 2020

The Engineering Mathematics is a combination of mathematical theory, practical engineering and scientific computing. This subject is a creative and exciting discipline, with spanning traditional boundaries. In order to prepare for GATE exam, the recommended books mentioned below along with the links provided below which allows you to download the study materials which will help you ace the exams.

Recommended books for GATE MA – Mathematics

Verbal and numerical ability:

  • General Aptitude: Quantitative Aptitude & Reasoning – G.K Publications
  • Objective English for Competitive Examination 5th Ed – Hari Mohan Prasad
  • Solved papers on verbal and numerical ability – Made Easy Team

Engineering Mathematics books for GATE

  1. Advanced Engineering Mathematics – RK Jain, SRK Iyengar
  2. Advanced Engineering Mathematics – HK Dass
  3. Advanced Engineering Mathematics – Erwin Kreyszig
  4. Engineering Mathematics solved papers – Made easy publications
  5. Engineering and Mathematics general aptitude – G.K Publications
  6. GATE Engineering and Mathematics – Nodia and company
  7. Higher Engineering Mathematics – Bandaru Ramana
  8. Higher Engineering Mathematics – B.S. Grewal

Mathematics GATE Reference Books 2020

SubjectBook TitleAuthor
Linear AlgebraLinear AlgebraSeymour Lipschutz, Marc Lipson
Linear Algebra and its applicationsGilbert Strang
Complex AnalysisComplex AnalysisGamelin
Complex analysis for mathematics and engineeringJ. H. Mathews
Foundations of complex analysisS. Ponnusamy
Real AnalysisReal AnalysisRoyden H.L., Fitzpatrick P. M
Introduction to Real analysisDonald R. Sherbert Robert G. Bartle
Elements of Real AnalysisShanti Narayan, M D Raisinghania
Ordinary Differential EquationsOrdinary Differential EquationsPurna Chandra Biswal
An introduction to Ordinary Differential EquationsEarl A. Coddington
Ordinary and Partial Differential EquationsM. D. Raisinghania
Partial Differential EquationsOrdinary and Partial Differential EquationsM. D. Raisinghania
Elements of Partial Differential EquationsIan N. Sneddon
Introduction to Partial Differential EquationsSankara Rao
 AlgebraTopics in AlgebraI. N. Herstein
Linear AlgebraIan N. Sneddon, Seymour Lipschutz, Marc Lipson
Functional AnalysisFunctional AnalysisRudin
Introductory Functional Analysis with ApplicationsErwin Kreyszig
Numerical AnalysisNumerical AnalysisFrancis Scheid
Introductory Methods of Numerical AnalysisSastry S. S.
Numerical Methods-Principles, Analysis & AlgorithmsSrimanta Pal
MechanicsClassical MechJohn Safko, Charles P. Poole Herbert Goldstein,
Engineering MechanicsS S Bhavikatti
TopologyTopologyJames R. Munkres
Introduction to Topology and Modern AnalysisS S Bhavikatti
Probability and StatisticsProbability and StatisticsJohn J. Schiller
Introduction to probability and statistics for engineers and scientistsSheldon M. Ross
Probability, Random Variables and Stochastic ProcessesS Pillai, Athanasios Papoullis
Linear ProgrammingLinear ProgrammingG. Hadley, J.G Chakraborty & P. R. Ghosh
Linear Programming And Network FlowsMokhtar S. Bazaraa John J. Jarvis Hanif D. Sherali
Calculus of Variation And Integral EquationsAn Introduction to the Calculus of VariationsPars
Calculus of VariationsGelfand, I. M. Gelfand, Wendy Ed. Silverman
Integral Transforms, Integral Equations, and Calculus Of VariationsP. C. Bhakta