This document provides an introduction to and overview of engineering mathematics concepts for GATE exam preparation. It was created by K. Manikantta Reddy for aspirants taking the GATE exam. The document covers topics like linear algebra, calculus, vector calculus, differential equations, and probability and statistics. It also contains notes on solving problems from previous GATE papers and advises students to review the syllabus and problems from their specific paper. The author notes that the book is a work in progress and requests feedback to improve it.
Mathematics and History of Complex VariablesSolo Hermelin
Mathematics of complex variables, plus history.
This presentation is at a Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com, thanks! For more presentations, please visit my website at http://www.solohermelin.com
Mathematics and History of Complex VariablesSolo Hermelin
Mathematics of complex variables, plus history.
This presentation is at a Undergraduate in Science (Math, Physics, Engineering) level.
Please send comments and suggestions to solo.hermelin@gmail.com, thanks! For more presentations, please visit my website at http://www.solohermelin.com
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
These slides contain information about Euler method,Improved Euler and Runge-kutta's method.How these methods are helpful and applied to our questions are detailed discussed in the slides.
quantitative aptitude for bank po (ibps)
Aptitude Engineering Handwritten classes Notes (Study Materials) for IES PSUs GATE
Aptitude Engineering Book (Study Materials) for IES PSUs GATE
Gate ME ,CE EE,CS ,EC Engineering Made Easy Handwritten coaching classes Notes (Study Materials) for IES PSUs GATE
Production Process 3 Mechanical Engineering Handwritten classes Notes (Study ...Khagendra Gautam
Production Process manufacturing technology
material science Mechanical Engineering Handwritten classes Notes (Study Materials) for IES PSUs GATE
Gate ME (Mechanical Engineering) Made Easy Handwritten coaching classes Notes (Study Materials) for IES PSUs GATE
CETPA INFOTECH PVT LTD is one of the IT education and training service provider brands of India that is preferably working in 3 most important domains. It includes IT Training services, software and embedded product development and consulting services.
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CETPA INFOTECH PVT LTD is one of the IT education and training service provider brands of India that is preferably working in 3 most important domains. It includes IT Training services, software and embedded product development and consulting services.
Candidates must be aware of the syllabus in order to prepare effectively. A thorough understanding of the syllabus will assist all candidates in developing an effective preparation strategy. Watch this PPT to know more about CSIR NET syllabus mathematics.
Production Process 2 Mechanical Engineering Handwritten classes Notes (Study ...Khagendra Gautam
Production Process manufacturing technology
material science Mechanical Engineering Handwritten classes Notes (Study Materials) for IES PSUs GATE
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Saudi Arabia stands as a titan in the global energy landscape, renowned for its abundant oil and gas resources. It's the largest exporter of petroleum and holds some of the world's most significant reserves. Let's delve into the top 10 oil and gas projects shaping Saudi Arabia's energy future in 2024.
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
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A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
2. This book is intended to provide basic knowledge on
Engineering Mathematics to the GATE aspirants. Even though
the syllabus is same, the questions appearing in different
papers follows different patterns. So the GATE aspirants are
advised to go through their respective paper syllabus
(available in official GATE website) and previous question
papers to understand the depth of the subject required to
prepare for GATE exam. Most of the solved problems in this
material are the questions appeared in EC/EE/ME/CE/IN/PI
papers. So the remaining branches students are advised to
solve the previous problems from their respective papers.
EE branch students are advised to prepare transform theory,
which is not available in this book.
This book is still under preparation. If you find any mistakes
in this, please inform me through an e-mail. Don’t share this
book without proper citation and credits.
Thank You
All The Best
3. SYLLABUS – GATE 2016
CIVIL ENGINEERING - CE
Linear Algebra: Matrix algebra; Systems of linear equations; Eigen values and Eigen vectors.
Calculus: Functions of single variable; Limit, continuity and differentiability; Mean value theorems,
local maxima and minima, Taylor and Maclaurin series; Evaluation of definite and indefinite
integrals, application of definite integral to obtain area and volume; Partial derivatives; Total
derivative; Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green’s theorems.
Ordinary Differential Equation (ODE): First order (linear and non-linear) equations; higher order
linear equations with constant coefficients; Euler-Cauchy equations; Laplace transform and its
application in solving linear ODEs; initial and boundary value problems.
Partial Differential Equation (PDE): Fourier series; separation of variables; solutions of
onedimensional diffusion equation; first and second order one-dimensional wave equation and two-
dimensional Laplace equation.
Probability and Statistics: Definitions of probability and sampling theorems; Conditional
probability; Discrete Random variables: Poisson and Binomial distributions; Continuous random
variables: normal and exponential distributions; Descriptive statistics - Mean, median, mode and
standard deviation; Hypothesis testing.
Numerical Methods: Accuracy and precision; error analysis. Numerical solutions of linear and non-
linear algebraic equations; Least square approximation, Newton’s and Lagrange polynomials,
numerical differentiation, Integration by trapezoidal and Simpson’s rule, single and multi-step
methods for first order differential equations.
1. MECHANICAL ENGINEERING – ME
2. METALLURGICAL ENGINEERING - MT
3. PRODUCTION AND INDUSTRIAL ENGINEERING - PI
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
Calculus: Functions of single variable, limit, continuity and differentiability, mean value theorems,
indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial
derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier
series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and
volume integrals, applications of Gauss, Stokes and Green’s theorems.
Differential equations: First order equations (linear and nonlinear); higher order linear differential
equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems;
Laplace transforms; solutions of heat, wave and Laplace's equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem
and integral formula; Taylor and Laurent series. (Except for MT paper)
Probability and Statistics: Definitions of probability, sampling theorems, conditional probability;
mean, median, mode and standard deviation; random variables, binomial, Poisson and normal
distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration
by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.
4. ELECTRONICS AND COMMUNICATION ENGINEERING – EC
Linear Algebra: Vector space, basis, linear dependence and independence, matrix algebra, eigen
values and eigen vectors, rank, solution of linear equations – existence and uniqueness.
Calculus: Mean value theorems, theorems of integral calculus, evaluation of definite and improper
integrals, partial derivatives, maxima and minima, multiple integrals, line, surface and volume
integrals, Taylor series.
Differential equations: First order equations (linear and nonlinear), higher order linear differential
equations, Cauchy's and Euler's equations, methods of solution using variation of parameters,
complementary function and particular integral, partial differential equations, variable separable
method, initial and boundary value problems.
Vector Analysis: Vectors in plane and space, vector operations, gradient, divergence and curl,
Gauss's, Green's and Stoke's theorems.
Complex Analysis: Analytic functions, Cauchy's integral theorem, Cauchy's integral formula;
Taylor's and Laurent's series, residue theorem.
Probability and Statistics: Mean, median, mode and standard deviation; combinatorial probability,
probability distribution functions - binomial, Poisson, exponential and normal; Joint and conditional
probability; Correlation and regression analysis.
Numerical Methods: Solutions of non-linear algebraic equations, single and multi-step methods for
differential equations, convergence criteria.
ELECTRICAL ENGINEERING - EE
Linear Algebra: Matrix Algebra, Systems of linear equations, Eigenvalues, Eigenvectors.
Calculus: Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper
integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities,
Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s
theorem, Green’s theorem.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential
equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s
equation, Initial and boundary value problems, Partial Differential Equations, Method of separation of
variables.
Complex variables: Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor
series, Laurent series, Residue theorem, Solution integrals.
Probability and Statistics: Sampling theorems, Conditional probability, Mean, Median, Mode,
Standard Deviation, Random variables, Discrete and Continuous distributions, Poisson distribution,
Normal distribution, Binomial distribution, Correlation analysis, Regression analysis.
Numerical Methods: Solutions of nonlinear algebraic equations, Single and Multi‐step methods for
differential equations.
Transform Theory: Fourier Transform, Laplace Transform, z‐Transform.
5. INSTRUMENTATION ENGINEERING - IN
Linear Algebra: Matrix algebra, systems of linear equations, Eigen values and Eigen vectors.
Calculus: Mean value theorems, theorems of integral calculus, partial derivatives, maxima and
minima, multiple integrals, Fourier series, vector identities, line, surface and volume integrals, Stokes,
Gauss and Green’s theorems.
Differential equations: First order equation (linear and nonlinear), higher order linear differential
equations with constant coefficients, method of variation of parameters, Cauchy’s and Euler’s
equations, initial and boundary value problems, solution of partial differential equations: variable
separable method.
Analysis of complex variables: Analytic functions, Cauchy’s integral theorem and integral formula,
Taylor’s and Laurent’s series, residue theorem, solution of integrals.
Probability and Statistics: Sampling theorems, conditional probability, mean, median, mode and
standard deviation, random variables, discrete and continuous distributions: normal, Poisson and
binomial distributions.
Numerical Methods: Matrix inversion, solutions of non-linear algebraic equations, iterative methods
for solving differential equations, numerical integration, regression and correlation analysis.
1. PETROLEUM ENGINEERING – PE
2. CHEMICAL ENGINEERING - CH
Linear Algebra: Matrix algebra, Systems of linear equations, Eigen values and eigenvectors.
Calculus: Functions of single variable, Limit, continuity and differentiability, Taylor series, Mean value
theorems, Evaluation of definite and improper integrals, Partial derivatives, Total derivative, Maxima
and minima, Gradient, Divergence and Curl, Vector identities, Directional derivatives, Line, Surface
and Volume integrals, Stokes, Gauss and Green’s theorems.
Differential equations: First order equations (linear and nonlinear), Higher order linear differential
equations with constant coefficients, Cauchy’s and Euler’s equations, Initial and boundary value
problems, Laplace transforms, Solutions of one dimensional heat and wave equations and Laplace
equation.
Complex variables: Complex number, polar form of complex number, triangle inequality.
Probability and Statistics: Definitions of probability and sampling theorems, Conditional probability,
Mean, median, mode and standard deviation, Random variables, Poisson, Normal and Binomial
distributions, Linear regression analysis.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations. Integration by
trapezoidal and Simpson’s rule. Single and multi-step methods for numerical solution of differential
equations.
6. 1. AGRICULTURE ENGINEERING – AG
2. BIOTECHNOLOGY – BT
3. MINING ENGINEERING - MN
Linear Algebra: Matrices and determinants, systems of linear equations, Eigen values and eigen
vectors.
Calculus: Limit, continuity and differentiability; partial derivatives; maxima and minima; sequences
and series; tests for convergence; Fourier series, Taylor series.
Vector Calculus: Gradient; divergence and curl; line; surface and volume integrals; Stokes, Gauss
and Green’s theorems. (Except for BT paper)
Differential Equations: Linear and non-linear first order Ordinary Differential Equations (ODE);
Higher order linear ODEs with constant coefficients; Cauchy’s and Euler’s equations; Laplace
transforms; Partial Differential Equations - Laplace, heat and wave equations.
Probability and Statistics: Mean, median, mode and standard deviation; random variables; Poisson,
normal and binomial distributions; correlation and regression analysis; tests of significance, analysis of
variance (ANOVA).
Numerical Methods: Solutions of linear and non-linear algebraic equations; numerical integration -
trapezoidal and Simpson’s rule; numerical solutions of ODE.
AEROSPACE ENGINEERING - AE
Linear Algebra: Vector algebra, Matrix algebra, systems of linear equations, rank of a matrix,
eigenvalues and eigenvectors.
Calculus: Functions of single variable, limits, continuity and differentiability, mean value theorem,
chain rule, partial derivatives, maxima and minima, gradient, divergence and curl, directional
derivatives. Integration, Line, surface and volume integrals. Theorems of Stokes, Gauss and Green.
Differential Equations: First order linear and nonlinear differential equations, higher order linear
ODEs with constant coefficients. Partial differential equations and separation of variables methods.