Question 1c Math 1
•Download as DOCX, PDF•
0 likes•363 views
The document calculates the divergence and curl of the vector field 퐹 = (푧2푒−푥)푖 + (푦3푙푛푧)푗 + (푥푒−푦)푘. The divergence is calculated to be -푧2푒−푥 + 3푦2푙푛푧 + 0. The curl is calculated to be (-푦푥푒−푦 - 푦3/푧)푖 - (푒−
Report
Share
Report
Share
Recommended
Double Integrals
The double integral of a function f(x,y) over a bounded region R in the xy-plane is defined as the limit of Riemann sums that approximate the total value of f over R. This double integral is denoted by the integral of f(x,y) over R and its value is independent of the subdivision used in the Riemann sums. Properties and methods for evaluating double integrals are discussed, along with applications such as finding the area, volume, mass, and moments of inertia. Changes of variables in double integrals using the Jacobian are also covered.
multiple intrigral lit
This document contains information about a calculus project completed by students of the Mechanical Engineering department at Laxmi Institute of Technology in Sarigam. It includes the names and student IDs of 13 students who participated in the project. The document covers topics in multiple integrals, including double integrals, Fubini's theorem, double integrals in polar coordinates, and triple integrals. Formulas and examples are provided for each topic.
Sistemas Digitais Exercicios de fixacao 09-05-18
This document contains 3 logic expressions using variables A, B, C, and D along with the operators AND (⋅), OR (⊕), and NOT (̅). The first expression calculates S1 using A AND the complement of B OR C. The second expression calculates S2 using A OR B AND the complement of C OR B. The third expression calculates S3 using the sum of A OR B AND the complement of C OR the product of D OR the complement of A.
Volume of revolution
The document discusses calculating volumes of revolution by rotating an area about the x-axis or y-axis. It provides the formulas for finding these volumes using integration, with examples of setting up the integrals to calculate specific volumes. It also covers cases where the curve needs to be rearranged in order to substitute it into the integral when rotating about the y-axis.
Sol87
1) The document discusses the problem of a particle sliding off a moving hemisphere, using conservation of momentum and energy equations to derive an expression for the particle's horizontal velocity vx as a function of the angle θ.
2) Setting the derivative of vx equal to zero yields a cubic equation that determines the angle θ at which vx is maximized, corresponding to the particle losing contact with the hemisphere.
3) For the special case where the particle and hemisphere masses are equal (ratio r = 1), the cubic equation can be solved to find θ ≈ 42.9 degrees.
Integration Ppt
The document discusses using definite integration to find areas bounded by curves. Definite integration gives the area between the boundaries set by the limits of integration, provided the curve lies above the x-axis in that region. If part of the curve is below the x-axis, the definite integral will be negative and the absolute value must be taken to find the true area. The area can also be found by switching the x and y variables if bounded by a curve, the y-axis, and vertical lines.
Vertical tangents and cusps
The document discusses vertical tangents and cusps in graphs of functions. It provides examples and definitions of vertical tangents, vertical cusps, and corners. A vertical tangent occurs when the derivative of a function is undefined at a point, meaning the slope is infinite. A vertical cusp happens when the left and right derivatives are infinite. While vertical tangents and cusps have infinite slopes, a corner can occur when left and right derivatives are finite but unequal.
A proof of an equation containing improper gamma distribution
This document proves the equation exp(-∞∫a(1 - e-tz)z-1e-zdz) = (1 + t)-a by taking the logarithm of both sides and rewriting the integral using Taylor series expansions of the exponential and logarithm functions. The integral is expanded as the sum from 0 to infinity of tn/n!Γ(n), which is shown to equal the Taylor series expansion of ln(1 + t), proving the original equation.
Recommended
Double Integrals
The double integral of a function f(x,y) over a bounded region R in the xy-plane is defined as the limit of Riemann sums that approximate the total value of f over R. This double integral is denoted by the integral of f(x,y) over R and its value is independent of the subdivision used in the Riemann sums. Properties and methods for evaluating double integrals are discussed, along with applications such as finding the area, volume, mass, and moments of inertia. Changes of variables in double integrals using the Jacobian are also covered.
multiple intrigral lit
This document contains information about a calculus project completed by students of the Mechanical Engineering department at Laxmi Institute of Technology in Sarigam. It includes the names and student IDs of 13 students who participated in the project. The document covers topics in multiple integrals, including double integrals, Fubini's theorem, double integrals in polar coordinates, and triple integrals. Formulas and examples are provided for each topic.
Sistemas Digitais Exercicios de fixacao 09-05-18
This document contains 3 logic expressions using variables A, B, C, and D along with the operators AND (⋅), OR (⊕), and NOT (̅). The first expression calculates S1 using A AND the complement of B OR C. The second expression calculates S2 using A OR B AND the complement of C OR B. The third expression calculates S3 using the sum of A OR B AND the complement of C OR the product of D OR the complement of A.
Volume of revolution
The document discusses calculating volumes of revolution by rotating an area about the x-axis or y-axis. It provides the formulas for finding these volumes using integration, with examples of setting up the integrals to calculate specific volumes. It also covers cases where the curve needs to be rearranged in order to substitute it into the integral when rotating about the y-axis.
Sol87
1) The document discusses the problem of a particle sliding off a moving hemisphere, using conservation of momentum and energy equations to derive an expression for the particle's horizontal velocity vx as a function of the angle θ.
2) Setting the derivative of vx equal to zero yields a cubic equation that determines the angle θ at which vx is maximized, corresponding to the particle losing contact with the hemisphere.
3) For the special case where the particle and hemisphere masses are equal (ratio r = 1), the cubic equation can be solved to find θ ≈ 42.9 degrees.
Integration Ppt
The document discusses using definite integration to find areas bounded by curves. Definite integration gives the area between the boundaries set by the limits of integration, provided the curve lies above the x-axis in that region. If part of the curve is below the x-axis, the definite integral will be negative and the absolute value must be taken to find the true area. The area can also be found by switching the x and y variables if bounded by a curve, the y-axis, and vertical lines.
Vertical tangents and cusps
The document discusses vertical tangents and cusps in graphs of functions. It provides examples and definitions of vertical tangents, vertical cusps, and corners. A vertical tangent occurs when the derivative of a function is undefined at a point, meaning the slope is infinite. A vertical cusp happens when the left and right derivatives are infinite. While vertical tangents and cusps have infinite slopes, a corner can occur when left and right derivatives are finite but unequal.
A proof of an equation containing improper gamma distribution
This document proves the equation exp(-∞∫a(1 - e-tz)z-1e-zdz) = (1 + t)-a by taking the logarithm of both sides and rewriting the integral using Taylor series expansions of the exponential and logarithm functions. The integral is expanded as the sum from 0 to infinity of tn/n!Γ(n), which is shown to equal the Taylor series expansion of ln(1 + t), proving the original equation.
2 d transformations
The document discusses 2D transformations in computer graphics, including translation, rotation, scaling, and shearing. Translation moves an object by adding offsets to x and y coordinates. Rotation rotates objects around the origin by applying trigonometric functions to x and y. Scaling enlarges or shrinks objects along the x- and y-axes. Shearing distorts objects along an axis based on their position on the other axis. Homogeneous coordinates allow transformations like translation, rotation, and scaling to be expressed using matrix multiplication.
Topological Strings Invariants
This document discusses topological string theory and Gromov-Witten invariants. It begins by introducing supersymmetric sigma models on Kähler manifolds with N=2 supersymmetry. These lead to a topological twist known as the A-model, which is independent of the target space metric. Gromov-Witten invariants count rational curves in an algebraic variety X and are unchanged by complex structure deformations of X, making them a manifestation of the A-model's independence of complex structure. The Gromov-Witten invariants are also directly related to Donaldson-Thomas invariants.
Math12 lesson5
The document summarizes the key properties and graphs of six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. For each function, it discusses amplitude, period, zeros or asymptotes, and shows an example graph over one period. It also covers transformations of trig functions that change amplitude, period, phase and vertical shifts.
Trapezoidal Method IN Numerical Analysis
The document defines the trapezoidal rule for approximating definite integrals. It provides the trapezoidal formula, explains the geometric interpretation of dividing the region into trapezoids, and outlines an algorithm and flowchart for implementing the trapezoidal rule in Python. Sample problems applying the trapezoidal rule are included to evaluate definite integrals numerically.
Kinetic line plane
This document discusses mathematical relationships between planes, lines, areas, and gravitational fields. It establishes that the area (a) of a plane is equal to the gravitational field (z) of that plane, and represents this as the equation z = a. It also references line infinity planes and compares offering a line infinity plane versus a half cube plane.
curve two
The document discusses several types of parametric surfaces used to represent 3D objects:
- Parametric bi-cubic surfaces include Hermite surfaces, Bezier surfaces, and B-spline surfaces which are represented using control points and parameters.
- Quadric surfaces are described by second-degree equations and include common shapes like spheres, ellipsoids, and cylinders.
- Surface of revolution objects are generated by rotating a 2D shape like a line or curve around an axis, producing shapes like cylinders and tori.
- Sweep representation involves sweeping a 2D shape through a region using transformations like translation, scaling, or rotation.
Multiple integral(tripple integral)
This document discusses triple integrals and their evaluation in different coordinate systems. It begins by defining a triple integral as the generalization of a double integral to three dimensions. It then discusses evaluating triple integrals in rectangular, cylindrical, and spherical coordinate systems. For each system it provides the coordinate transformations between rectangular and the other system and the formula for the volume element used in the triple integral.
Geophysical prospecting
This document discusses different methods for calculating seismic velocity and summarizing seismic data. It describes:
1) Average velocity, which is used to convert reflection time to depth by dividing depth by one-way travel time.
2) Interval velocity, which is the velocity between two reflectors and is calculated by dividing the depth difference by the time difference.
3) Instantaneous velocity, which is the derivative of depth with respect to time for a continuously varying velocity.
4) Methods have evolved from manual graphical techniques to digital methods like wave equation migration to properly position seismic reflectors.
Cluster abundances and clustering Can theory step up to precision cosmology?
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
Computer graphics
The document discusses 2D and 3D transformations used in computer graphics. It covers topics like scaling, rotation, translation and how they can be represented using matrices. Matrix representations allow multiple transformations to be combined through matrix multiplication. Both linear transformations like scaling and rotation, as well as affine transformations like translation, can be captured with matrices. The order of matrix multiplications is important, as transformations are not commutative. These concepts extend from 2D to 3D graphics using homogeneous coordinates.
divergence of vector and divergence theorem
This document discusses the divergence of a vector field and the divergence theorem. It begins by defining the divergence of a vector field as a measure of how much that field diverges from a given point. It then illustrates the divergence of a vector field can be positive, negative, or zero at a point. The document expresses the divergence in Cartesian, cylindrical, and spherical coordinate systems. It proves the divergence theorem, which states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the enclosed volume. The document provides two examples applying the divergence theorem to calculate outward fluxes.
Convolution sum and block diagram representation
The document discusses convolution sums and provides examples of calculating convolution sums for different signals. It also includes block diagram representations of direct form I and direct form II structures. Specifically:
1. It gives the mathematical expression for a convolution sum and calculates the convolution sum of two signals x[n]=anu[n] and h[n]=bnu[n].
2. It calculates the convolution sum of x[n]=r[n] and h[n]=u[n], where r[n]=n and u[n]=1, showing the overlapping interval is from 0 to n.
3. It briefly mentions block diagram representations of direct form I and direct form II structures at the end
Convolution sum using graphical and matrix method
The document describes two methods for computing the convolution sum of two sequences: the graphical method and the matrix method.
The graphical method involves plotting the two sequences and calculating their point-wise multiplication at each instance of overlap as one sequence is shifted across the other.
The matrix method forms a Toeplitz matrix from one sequence and a vector from the other. The convolution sum is then computed as the matrix-vector product of these two representations.
Examples are provided to demonstrate computing the convolution sum of sample sequences using both methods.
Mahaviracharya (hindi)
The document discusses different mathematical concepts including operations, formulas, shapes, and calculations. It covers topics such as permutations, combinations, fractions, areas, volumes, squares, ellipses, and cyclic quadrilaterals. Formulas are provided for combinations, areas, perimeters, and the sums of sides and diagonals of cyclic quadrilaterals. A variety of mathematical terms and concepts are defined.
Centroid
this is a ppt on centroid,covering centroid of regular figures and there is a example of a composite figure,it has applications,uses of centroid,it is use ful for engineering students,it has 15 slides.
by -nishant kumar.
nk18052001@gmail.com
Pres_Zurich14
This document discusses the Hofstadter butterfly model for the honeycomb lattice structure of graphene. It shows that the Hall conductivity σH in an energy gap must satisfy a Diophantine equation relating σH, the magnetic flux per unit cell p/q, and an integer s. For the honeycomb lattice, the conjecture is that σH lies in the window (-q,q) rather than the typical (-q/2,q/2). The bulk-edge correspondence relates σH to the number of edge state crossings in the Brillouin zone. Numerical results for σH calculated from the edge state spectrum agree with the Diophantine equation in 99.8% of cases.
Spatial Transformation
This document discusses different types of geometric transformations including linear transformations, affine transformations, and projective transformations. Linear transformations allow for scaling, rotation, reflection, and shearing using a 2x2 matrix. Affine transformations preserve parallel lines and proportional distances but not lengths and angles. Projective transformations describe how objects appear rather than how they are, distorting lengths, angles, and parallelism. Both affine and projective transformations are important applications in computer graphics and robot recognition.
Geometric transformation cg
This document discusses 2D and 3D transformations. It begins with an overview of basic 2D transformations like translation, scaling, rotation, and shearing. It then covers representing transformations with matrices and combining transformations through matrix multiplication. Homogeneous coordinates are introduced as a way to represent translations with matrices. The key transformations can all be represented as 3x3 matrices using homogeneous coordinates.
Trigonometric functions
This document discusses trigonometric functions and their properties. It defines periodic functions and their periods. It describes the amplitude of sine and cosine functions as half the difference between the maximum and minimum values. It discusses how transformations of a, b, h, and k values can stretch, compress, reflect, translate and shift the graphs of sine and cosine functions and how these affect their amplitudes and periods. Examples are provided to demonstrate identifying amplitudes, periods, phase shifts from transformed trigonometric functions.
Solid Waste & Hazardous Waste
The document discusses solid and hazardous waste classification and management. It outlines different types of wastes and how they are regulated. Hazardous wastes are defined as those exhibiting ignitable, corrosive, reactive or toxic properties above certain thresholds. The document also discusses various waste treatment and disposal methods like incineration, landfilling and the use of geosynthetics in landfill design.
Question 5 Math 1
The document evaluates a surface integral over a portion of a cone bounded by z=0, z=1, and inside a cylinder of radius 1.
The surface is parametrically represented by a cone with parameters r and θ.
The surface normal is calculated to be [-r cosθ, r sinθ, r].
The integral is evaluated to be 3π.
More Related Content
What's hot
2 d transformations
The document discusses 2D transformations in computer graphics, including translation, rotation, scaling, and shearing. Translation moves an object by adding offsets to x and y coordinates. Rotation rotates objects around the origin by applying trigonometric functions to x and y. Scaling enlarges or shrinks objects along the x- and y-axes. Shearing distorts objects along an axis based on their position on the other axis. Homogeneous coordinates allow transformations like translation, rotation, and scaling to be expressed using matrix multiplication.
Topological Strings Invariants
This document discusses topological string theory and Gromov-Witten invariants. It begins by introducing supersymmetric sigma models on Kähler manifolds with N=2 supersymmetry. These lead to a topological twist known as the A-model, which is independent of the target space metric. Gromov-Witten invariants count rational curves in an algebraic variety X and are unchanged by complex structure deformations of X, making them a manifestation of the A-model's independence of complex structure. The Gromov-Witten invariants are also directly related to Donaldson-Thomas invariants.
Math12 lesson5
The document summarizes the key properties and graphs of six trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. For each function, it discusses amplitude, period, zeros or asymptotes, and shows an example graph over one period. It also covers transformations of trig functions that change amplitude, period, phase and vertical shifts.
Trapezoidal Method IN Numerical Analysis
The document defines the trapezoidal rule for approximating definite integrals. It provides the trapezoidal formula, explains the geometric interpretation of dividing the region into trapezoids, and outlines an algorithm and flowchart for implementing the trapezoidal rule in Python. Sample problems applying the trapezoidal rule are included to evaluate definite integrals numerically.
Kinetic line plane
This document discusses mathematical relationships between planes, lines, areas, and gravitational fields. It establishes that the area (a) of a plane is equal to the gravitational field (z) of that plane, and represents this as the equation z = a. It also references line infinity planes and compares offering a line infinity plane versus a half cube plane.
curve two
The document discusses several types of parametric surfaces used to represent 3D objects:
- Parametric bi-cubic surfaces include Hermite surfaces, Bezier surfaces, and B-spline surfaces which are represented using control points and parameters.
- Quadric surfaces are described by second-degree equations and include common shapes like spheres, ellipsoids, and cylinders.
- Surface of revolution objects are generated by rotating a 2D shape like a line or curve around an axis, producing shapes like cylinders and tori.
- Sweep representation involves sweeping a 2D shape through a region using transformations like translation, scaling, or rotation.
Multiple integral(tripple integral)
This document discusses triple integrals and their evaluation in different coordinate systems. It begins by defining a triple integral as the generalization of a double integral to three dimensions. It then discusses evaluating triple integrals in rectangular, cylindrical, and spherical coordinate systems. For each system it provides the coordinate transformations between rectangular and the other system and the formula for the volume element used in the triple integral.
Geophysical prospecting
This document discusses different methods for calculating seismic velocity and summarizing seismic data. It describes:
1) Average velocity, which is used to convert reflection time to depth by dividing depth by one-way travel time.
2) Interval velocity, which is the velocity between two reflectors and is calculated by dividing the depth difference by the time difference.
3) Instantaneous velocity, which is the derivative of depth with respect to time for a continuously varying velocity.
4) Methods have evolved from manual graphical techniques to digital methods like wave equation migration to properly position seismic reflectors.
Cluster abundances and clustering Can theory step up to precision cosmology?
This document discusses improvements to the Press-Schechter theory for modeling the abundances and clustering of dark matter halos. It proposes that modeling halo collapse as requiring the density to "step up" above a critical density threshold at progressively larger spatial scales provides a better approximation than assuming fully correlated or uncorrelated densities. This "stepping up" approach requires only 2-point statistics and can be applied to non-Gaussian fields. The document also suggests that modeling the distribution of density slopes at peak positions provides a way to match halo counts through an Excursion Set Peaks model.
Computer graphics
The document discusses 2D and 3D transformations used in computer graphics. It covers topics like scaling, rotation, translation and how they can be represented using matrices. Matrix representations allow multiple transformations to be combined through matrix multiplication. Both linear transformations like scaling and rotation, as well as affine transformations like translation, can be captured with matrices. The order of matrix multiplications is important, as transformations are not commutative. These concepts extend from 2D to 3D graphics using homogeneous coordinates.
divergence of vector and divergence theorem
This document discusses the divergence of a vector field and the divergence theorem. It begins by defining the divergence of a vector field as a measure of how much that field diverges from a given point. It then illustrates the divergence of a vector field can be positive, negative, or zero at a point. The document expresses the divergence in Cartesian, cylindrical, and spherical coordinate systems. It proves the divergence theorem, which states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence of the field over the enclosed volume. The document provides two examples applying the divergence theorem to calculate outward fluxes.
Convolution sum and block diagram representation
The document discusses convolution sums and provides examples of calculating convolution sums for different signals. It also includes block diagram representations of direct form I and direct form II structures. Specifically:
1. It gives the mathematical expression for a convolution sum and calculates the convolution sum of two signals x[n]=anu[n] and h[n]=bnu[n].
2. It calculates the convolution sum of x[n]=r[n] and h[n]=u[n], where r[n]=n and u[n]=1, showing the overlapping interval is from 0 to n.
3. It briefly mentions block diagram representations of direct form I and direct form II structures at the end
Convolution sum using graphical and matrix method
The document describes two methods for computing the convolution sum of two sequences: the graphical method and the matrix method.
The graphical method involves plotting the two sequences and calculating their point-wise multiplication at each instance of overlap as one sequence is shifted across the other.
The matrix method forms a Toeplitz matrix from one sequence and a vector from the other. The convolution sum is then computed as the matrix-vector product of these two representations.
Examples are provided to demonstrate computing the convolution sum of sample sequences using both methods.
Mahaviracharya (hindi)
The document discusses different mathematical concepts including operations, formulas, shapes, and calculations. It covers topics such as permutations, combinations, fractions, areas, volumes, squares, ellipses, and cyclic quadrilaterals. Formulas are provided for combinations, areas, perimeters, and the sums of sides and diagonals of cyclic quadrilaterals. A variety of mathematical terms and concepts are defined.
Centroid
this is a ppt on centroid,covering centroid of regular figures and there is a example of a composite figure,it has applications,uses of centroid,it is use ful for engineering students,it has 15 slides.
by -nishant kumar.
nk18052001@gmail.com
Pres_Zurich14
This document discusses the Hofstadter butterfly model for the honeycomb lattice structure of graphene. It shows that the Hall conductivity σH in an energy gap must satisfy a Diophantine equation relating σH, the magnetic flux per unit cell p/q, and an integer s. For the honeycomb lattice, the conjecture is that σH lies in the window (-q,q) rather than the typical (-q/2,q/2). The bulk-edge correspondence relates σH to the number of edge state crossings in the Brillouin zone. Numerical results for σH calculated from the edge state spectrum agree with the Diophantine equation in 99.8% of cases.
Spatial Transformation
This document discusses different types of geometric transformations including linear transformations, affine transformations, and projective transformations. Linear transformations allow for scaling, rotation, reflection, and shearing using a 2x2 matrix. Affine transformations preserve parallel lines and proportional distances but not lengths and angles. Projective transformations describe how objects appear rather than how they are, distorting lengths, angles, and parallelism. Both affine and projective transformations are important applications in computer graphics and robot recognition.
Geometric transformation cg
This document discusses 2D and 3D transformations. It begins with an overview of basic 2D transformations like translation, scaling, rotation, and shearing. It then covers representing transformations with matrices and combining transformations through matrix multiplication. Homogeneous coordinates are introduced as a way to represent translations with matrices. The key transformations can all be represented as 3x3 matrices using homogeneous coordinates.
Trigonometric functions
This document discusses trigonometric functions and their properties. It defines periodic functions and their periods. It describes the amplitude of sine and cosine functions as half the difference between the maximum and minimum values. It discusses how transformations of a, b, h, and k values can stretch, compress, reflect, translate and shift the graphs of sine and cosine functions and how these affect their amplitudes and periods. Examples are provided to demonstrate identifying amplitudes, periods, phase shifts from transformed trigonometric functions.
What's hot (19)
Cluster abundances and clustering Can theory step up to precision cosmology?
Cluster abundances and clustering Can theory step up to precision cosmology?
Viewers also liked
Solid Waste & Hazardous Waste
The document discusses solid and hazardous waste classification and management. It outlines different types of wastes and how they are regulated. Hazardous wastes are defined as those exhibiting ignitable, corrosive, reactive or toxic properties above certain thresholds. The document also discusses various waste treatment and disposal methods like incineration, landfilling and the use of geosynthetics in landfill design.
Question 5 Math 1
The document evaluates a surface integral over a portion of a cone bounded by z=0, z=1, and inside a cylinder of radius 1.
The surface is parametrically represented by a cone with parameters r and θ.
The surface normal is calculated to be [-r cosθ, r sinθ, r].
The integral is evaluated to be 3π.
Letter Format
The document discusses the format and structure of a business letter, including:
- The main parts of a letter are the heading, inside address, salutation, subject line, body, complimentary close, and signature.
- The body includes an introduction paragraph, main discussion in the middle paragraphs, and a concluding paragraph.
- Additional notations may include identification of the typist, word processing file name, enclosures, and distribution list.
- Proper formatting includes margins and spacing between paragraphs. Sample letters are provided to illustrate the discussed structures and conventions.
Directional Drilling
This document discusses directional drilling techniques and their applications. It begins by defining directional drilling as deflecting a wellbore in a specified direction to reach a target below the surface. It then lists several applications of directional drilling including drilling multiple wells from a single location, drilling in inaccessible locations, avoiding geological problems, sidetracking, relief well drilling, and horizontal drilling. The document also discusses directional drilling applications in mining, construction, and geothermal engineering. It provides details on well profiles, azimuth and quadrants, horizontal well types, and directional drilling assemblies for building angle and holding angle.
Drilling Engineering - Directional Drilling
This document provides definitions and information about directional drilling. It discusses the applications of directional drilling including its history and typical uses. It describes the main deflection tools used like whipstocks, jetting bits, and bent subs with mud motors. It also explains the two main types of mud motors - turbines and positive displacement motors. Finally, it outlines the three main types of well profiles: Type I or "build and hold", Type II "build, hold, and drop", and Type III "continuous build".
Viewers also liked (6)
More from M.T.H Group
Engineering Internship in Yemen.pptx
This document outlines an internship at Dome Yemen, an engineering and construction company with offices in the Middle East. It provides an overview of the company, which aims to be a leading regional company through consistently offering superior and timely products and services. The intern completed tasks such as analyzing plot plans for various projects, using simulation software, calculating heat and material balances, designing and installing wellheads, and learning about process and instrumentation diagrams and valve/flange types. Safety was the top priority. The last tasks involved drilling, cementing, shutdown and maintenance work alongside other oilfield service companies.
License to operate a forklift truck 2
This document provides information and guidance for obtaining a licence to operate a forklift truck. It outlines two modules that licence applicants must complete: 1) planning work which involves risk management procedures like identifying hazards, assessing risks, and implementing controls; and 2) carrying out forklift operations like routine checks, load shifting, and shutdown. The document provides details on the licence application process and requirements under relevant work health and safety legislation to obtain a forklift operating licence.
License to operate a forklift truck 1
This document is a student workbook for a forklift licence training course. It contains questions to assess the student's knowledge of forklift safety and operation. The workbook covers topics like hazards and risk management, pre-start checks of the forklift, operating procedures, and parking and shutting down procedures. The student must complete the workbook before their scheduled training session. It will be used by the trainer to identify any gaps in the student's knowledge and tailor the training accordingly.
Forklift Study Guide
The document provides information and guidelines for operating a forklift safely, including:
- A forklift license is required to operate a forklift as it is considered high risk work.
- Proper inspections of the forklift, load, and work area must be conducted before operation to identify any hazards.
- Loads must be checked to ensure they are within the forklift's lifting capacity specifications and are secured properly.
- Driving procedures like maintaining stability, giving way to emergencies, and parking safely must be followed.
Key aspects of reservoir evaluation for deep water reservoirs
The document summarizes key aspects of reservoir evaluation for deep water projects. It discusses challenges including geomechanics, reservoir characterization of thin beds and compartmentalization, and flow assurance requiring accurate fluid characterization. Reservoir characterization is identified as the biggest risk due to complex lithology, thin beds, and low contrast pay. Accurate fluid analysis and asphaltene characterization can help determine reservoir connectivity. Operator priorities include minimizing operational risk through rig efficiency and completion/production reliability. Reservoir evaluation is critical for deep water projects due to significant costs.
Preparing & Delivering Oral Presentations
The document provides 10 guidelines for preparing and delivering effective oral presentations: 1) Define objectives and understand audience and context. 2) Select an appropriate delivery style based on purpose and audience. 3) Focus on a few main points given audience attention span. 4) Use clear structure and signaling. 5) Employ a conversational style. 6) Maintain eye contact with audience. 7) Exhibit enthusiasm and interest. 8) Prepare for questions. 9) Accept and work with nervousness. 10) Rehearse extensively. It also provides tips for preparing informative and persuasive speeches, including outlining, anticipating questions, and concluding powerfully.
Communication & Your Career
This document discusses the importance of communication skills for careers and provides strategies for writing with readers in mind. It notes that writing at work differs from school in purpose, audience, and types. The main advice is to think constantly about readers by using a reader-centered writing process and talking with readers. Some strategies discussed are stating main points upfront, using headings and lists, explaining relevance, and writing in an easy to read style.
Technical Communication
This document outlines the technical communication semester that began on January 2nd, 2008. It introduces the fundamentals of various forms of technical writing and presentation required in engineering. Students will learn to take a reader-centered approach and work as a team on projects. Over the course of the semester, topics like reports, proposals, presentations, and other technical documents will be covered. Students will complete assignments biweekly to develop their technical communication skills.
Technical Communication
The document provides guidelines for effective team projects, including defining objectives, involving the whole team, making a project schedule, sharing leadership responsibilities, encouraging debate and diversity, being sensitive to cultural and gender differences, and using computer support. It discusses defining objectives and planning as a team to generate better results. It also describes task roles like initiators and opinion givers, and group maintenance roles to assure good working relationships.
Technical Communication
The document summarizes key points about effective communication at work from a textbook. It discusses how writing at work differs from academics in purpose, audience, and types of documents. The main advice is to think constantly about readers by using a reader-centered writing process and getting feedback from readers. This helps writers understand how to effectively convey information to meet readers' needs.
Technical Communication
The document discusses guidelines for defining objectives when writing a communication. It recommends starting by describing the desired final result and identifying the tasks readers will perform. Writers should also consider how to change readers' attitudes, learn important reader characteristics like job role and familiarity, identify all potential readers, and consider any special circumstances. Defining objectives in a reader-centered way by addressing readers' needs and characteristics can help make communications more effective.
Physics 19
This document provides an overview of key concepts related to sound:
- Sound waves are longitudinal waves that travel through solids, liquids, and gases by transmitting compressions and rarefactions.
- The speed of sound depends on properties of the medium like temperature, density, and elastic modulus. In air at 0°C, the speed is 331 m/s.
- Sound intensity refers to the amount of sound energy passing through a unit area per second. The decibel scale is used to quantify loudness levels that correspond to different sound intensities perceived by humans.
Physics 18
This document provides an overview of key concepts related to sound:
- Sound waves are longitudinal waves that travel through solids, liquids, and gases by transmitting compressions and rarefactions.
- The speed of sound depends on properties of the medium like temperature, density, and elastic modulus. In air at 0°C, the speed is 331 m/s.
- Sound intensity refers to the amount of sound energy passing through a unit area per second. The decibel scale is used to quantify loudness levels that correspond to different sound intensities perceived by humans.
Physics 17
This chapter discusses various aspects of waves including the period of a wave, the equation of a wave, reflection of waves, superposition of waves, and stationary waves. It examines waves using a liquid such as mercury or alcohol sealed in a glass capillary tube with a bulb. The chapter covers key wave concepts such as nodes, fixed ends, free ends, phase angle, elasticity, and the analogy of superimposing multiple waves.
Physics 17-2
This document provides an overview of wave motion concepts including wave propagation, types of waves, wave terminology, speed of transverse waves, standing waves, and resonance. Key points covered include:
- Transverse waves have vibration perpendicular to propagation direction, while longitudinal waves have parallel vibration.
- Period, frequency, wavelength, speed, and phase are defined for waves.
- The speed of a transverse wave depends on the tension and linear mass density of the string.
- Standing waves occur at resonant frequencies when the string length is an integer multiple of half wavelengths.
Physics 16
This document covers the topics of simple harmonic motion and springs. It defines key terms like period, frequency, amplitude, and restoring force. It describes how vibrating systems like springs and pendulums undergo simple harmonic motion where the restoring force is proportional to displacement via Hooke's law. Examples are provided to show how to calculate values like spring constant, maximum speed and acceleration, and the speed at a given displacement during vibration. Worked problems demonstrate applying these concepts.
Physics 15
This document discusses thermal properties of matter, including calorimetry concepts like heat changes during temperature changes, phase changes, and mixing substances. It also covers thermal expansion, defining linear, area, and volume coefficients of expansion. Worked examples show how to calculate temperature changes during mixing/phase changes, length changes due to thermal expansion, and volume changes using the coefficient of volume expansion.
Physics 13
This document discusses mechanical properties of matter such as density, elasticity, and fluid pressure. It defines key terms like density, specific gravity, stress, strain, and Hooke's law. Hooke's law states that the deformation of a material is proportional to the force applied. Young's modulus is introduced as a measure of a material's elasticity, relating stress to strain. Examples are worked through to demonstrate calculating density, specific gravity, stress, strain, and deformation based on given values and materials.
Physics 12
This document summarizes lessons on rigid body rotation, including the parallel-axis theorem, combined translation and rotation, and angular momentum. Key concepts are the moment of inertia of objects about different axes using the parallel-axis theorem, and that the kinetic energy of a rolling object equals the sum of its rotational kinetic energy and translational kinetic energy. Several examples are worked through, such as finding the acceleration of a rotating wheel and the angular speed when disks with different moments of inertia combine rotation.
Physics 11
1) This document discusses rotational motion and inertia. It defines rotational kinetic energy as KEr = 1⁄2 Iω2, where I is the object's moment of inertia.
2) The moment of inertia I depends on how mass is distributed about the axis of rotation. I is calculated by I = Σmiri2, where mi is the mass of each tiny part and ri is its distance from the axis.
3) A torque applied to a rotating object will cause it to accelerate according to τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.
More from M.T.H Group (20)
Key aspects of reservoir evaluation for deep water reservoirs
Key aspects of reservoir evaluation for deep water reservoirs
Recently uploaded
22CYT12-Unit-V-E Waste and its Management.ppt
Introduction- e - waste – definition - sources of e-waste– hazardous substances in e-waste - effects of e-waste on environment and human health- need for e-waste management– e-waste handling rules - waste minimization techniques for managing e-waste – recycling of e-waste - disposal treatment methods of e- waste – mechanism of extraction of precious metal from leaching solution-global Scenario of E-waste – E-waste in India- case studies.
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
The rivalry between prominent international actors for dominance over Central Asia's hydrocarbon
reserves and the ancient silk trade route, along with China's diplomatic endeavours in the area, has been
referred to as the "New Great Game." This research centres on the power struggle, considering
geopolitical, geostrategic, and geoeconomic variables. Topics including trade, political hegemony, oil
politics, and conventional and nontraditional security are all explored and explained by the researcher.
Using Mackinder's Heartland, Spykman Rimland, and Hegemonic Stability theories, examines China's role
in Central Asia. This study adheres to the empirical epistemological method and has taken care of
objectivity. This study analyze primary and secondary research documents critically to elaborate role of
china’s geo economic outreach in central Asian countries and its future prospect. China is thriving in trade,
pipeline politics, and winning states, according to this study, thanks to important instruments like the
Shanghai Cooperation Organisation and the Belt and Road Economic Initiative. According to this study,
China is seeing significant success in commerce, pipeline politics, and gaining influence on other
governments. This success may be attributed to the effective utilisation of key tools such as the Shanghai
Cooperation Organisation and the Belt and Road Economic Initiative.
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Sinan from the Delivery Hero mobile infrastructure engineering team shares a deep dive into performance acceleration with Gradle build cache optimizations. Sinan shares their journey into solving complex build-cache problems that affect Gradle builds. By understanding the challenges and solutions found in our journey, we aim to demonstrate the possibilities for faster builds. The case study reveals how overlapping outputs and cache misconfigurations led to significant increases in build times, especially as the project scaled up with numerous modules using Paparazzi tests. The journey from diagnosing to defeating cache issues offers invaluable lessons on maintaining cache integrity without sacrificing functionality.
Understanding Inductive Bias in Machine Learning
This presentation explores the concept of inductive bias in machine learning. It explains how algorithms come with built-in assumptions and preferences that guide the learning process. You'll learn about the different types of inductive bias and how they can impact the performance and generalizability of machine learning models.
The presentation also covers the positive and negative aspects of inductive bias, along with strategies for mitigating potential drawbacks. We'll explore examples of how bias manifests in algorithms like neural networks and decision trees.
By understanding inductive bias, you can gain valuable insights into how machine learning models work and make informed decisions when building and deploying them.
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Climate change's impact on the planet forced the United Nations and governments to promote green energies and electric transportation. The deployments of photovoltaic (PV) and electric vehicle (EV) systems gained stronger momentum due to their numerous advantages over fossil fuel types. The advantages go beyond sustainability to reach financial support and stability. The work in this paper introduces the hybrid system between PV and EV to support industrial and commercial plants. This paper covers the theoretical framework of the proposed hybrid system including the required equation to complete the cost analysis when PV and EV are present. In addition, the proposed design diagram which sets the priorities and requirements of the system is presented. The proposed approach allows setup to advance their power stability, especially during power outages. The presented information supports researchers and plant owners to complete the necessary analysis while promoting the deployment of clean energy. The result of a case study that represents a dairy milk farmer supports the theoretical works and highlights its advanced benefits to existing plants. The short return on investment of the proposed approach supports the paper's novelty approach for the sustainable electrical system. In addition, the proposed system allows for an isolated power setup without the need for a transmission line which enhances the safety of the electrical network
Literature Review Basics and Understanding Reference Management.pptx
Three-day training on academic research focuses on analytical tools at United Technical College, supported by the University Grant Commission, Nepal. 24-26 May 2024
Comparative analysis between traditional aquaponics and reconstructed aquapon...
The aquaponic system of planting is a method that does not require soil usage. It is a method that only needs water, fish, lava rocks (a substitute for soil), and plants. Aquaponic systems are sustainable and environmentally friendly. Its use not only helps to plant in small spaces but also helps reduce artificial chemical use and minimizes excess water use, as aquaponics consumes 90% less water than soil-based gardening. The study applied a descriptive and experimental design to assess and compare conventional and reconstructed aquaponic methods for reproducing tomatoes. The researchers created an observation checklist to determine the significant factors of the study. The study aims to determine the significant difference between traditional aquaponics and reconstructed aquaponics systems propagating tomatoes in terms of height, weight, girth, and number of fruits. The reconstructed aquaponics system’s higher growth yield results in a much more nourished crop than the traditional aquaponics system. It is superior in its number of fruits, height, weight, and girth measurement. Moreover, the reconstructed aquaponics system is proven to eliminate all the hindrances present in the traditional aquaponics system, which are overcrowding of fish, algae growth, pest problems, contaminated water, and dead fish.
5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...
Bigdata of technology
TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEM
Time Division Multiplexing (TDM) is a method of transmitting multiple signals over a single communication channel by dividing the signal into many segments, each having a very short duration of time. These time slots are then allocated to different data streams, allowing multiple signals to share the same transmission medium efficiently. TDM is widely used in telecommunications and data communication systems.
### How TDM Works
1. **Time Slots Allocation**: The core principle of TDM is to assign distinct time slots to each signal. During each time slot, the respective signal is transmitted, and then the process repeats cyclically. For example, if there are four signals to be transmitted, the TDM cycle will divide time into four slots, each assigned to one signal.
2. **Synchronization**: Synchronization is crucial in TDM systems to ensure that the signals are correctly aligned with their respective time slots. Both the transmitter and receiver must be synchronized to avoid any overlap or loss of data. This synchronization is typically maintained by a clock signal that ensures time slots are accurately aligned.
3. **Frame Structure**: TDM data is organized into frames, where each frame consists of a set of time slots. Each frame is repeated at regular intervals, ensuring continuous transmission of data streams. The frame structure helps in managing the data streams and maintaining the synchronization between the transmitter and receiver.
4. **Multiplexer and Demultiplexer**: At the transmitting end, a multiplexer combines multiple input signals into a single composite signal by assigning each signal to a specific time slot. At the receiving end, a demultiplexer separates the composite signal back into individual signals based on their respective time slots.
### Types of TDM
1. **Synchronous TDM**: In synchronous TDM, time slots are pre-assigned to each signal, regardless of whether the signal has data to transmit or not. This can lead to inefficiencies if some time slots remain empty due to the absence of data.
2. **Asynchronous TDM (or Statistical TDM)**: Asynchronous TDM addresses the inefficiencies of synchronous TDM by allocating time slots dynamically based on the presence of data. Time slots are assigned only when there is data to transmit, which optimizes the use of the communication channel.
### Applications of TDM
- **Telecommunications**: TDM is extensively used in telecommunication systems, such as in T1 and E1 lines, where multiple telephone calls are transmitted over a single line by assigning each call to a specific time slot.
- **Digital Audio and Video Broadcasting**: TDM is used in broadcasting systems to transmit multiple audio or video streams over a single channel, ensuring efficient use of bandwidth.
- **Computer Networks**: TDM is used in network protocols and systems to manage the transmission of data from multiple sources over a single network medium.
### Advantages of TDM
- **Efficient Use of Bandwidth**: TDM all
Recently uploaded (20)
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
CHINA’S GEO-ECONOMIC OUTREACH IN CENTRAL ASIAN COUNTRIES AND FUTURE PROSPECT
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
Optimizing Gradle Builds - Gradle DPE Tour Berlin 2024
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
2008 BUILDING CONSTRUCTION Illustrated - Ching Chapter 02 The Building.pdf
basic-wireline-operations-course-mahmoud-f-radwan.pdf
basic-wireline-operations-course-mahmoud-f-radwan.pdf
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Electric vehicle and photovoltaic advanced roles in enhancing the financial p...
Generative AI leverages algorithms to create various forms of content
Generative AI leverages algorithms to create various forms of content
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
BPV-GUI-01-Guide-for-ASME-Review-Teams-(General)-10-10-2023.pdf
Literature Review Basics and Understanding Reference Management.pptx
Literature Review Basics and Understanding Reference Management.pptx
Comparative analysis between traditional aquaponics and reconstructed aquapon...
Comparative analysis between traditional aquaponics and reconstructed aquapon...
5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...
5214-1693458878915-Unit 6 2023 to 2024 academic year assignment (AutoRecovere...
TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEM
TIME DIVISION MULTIPLEXING TECHNIQUE FOR COMMUNICATION SYSTEM
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
ML Based Model for NIDS MSc Updated Presentation.v2.pptx
Question 1c Math 1
- 1. 1) c) Find the divergence and the curl of the vector field. 퐹 = (푧2푒−푥 )푖 + (푦3푙푛푧)푗 + (푥푒−푦 )푘 ∇. 푉 = 푑푉1 푑푥 + 푑푉2 푑푦 + 푑푉3 푑푧 = −푧2푒−푥 + 3푦2푙푛푧 + 0 퐶푢푟푙 푉 = ∇ × 푣 = || 푖 푗 푘 푑푉1 푑푉2 푑푥 푑푦 푑푉3 푑푧 푧2푒−푥 푦3푙푛푧 푥푒−푦 || = ( 푑푥푒−푦 푑푦 − 푑푦3푙푛푧 푑푧 푑푥푒−푦 푑푥 ) 푖 − ( − 푑푧2푒−푥 푑푧 ) 푗 + ( 푑푦3푙푛푧 푑푥 − 푑푧2푒−푥 푑푦 ) 푘 = (−푦푥푒−푦 − 푦3 1 푧 ) 푖 − (푒−푦 − 2푧푒−푥 )푗 + (0) = (−푦푥푒−푦 − 푦3 푧 ) 푖 − (푒−푦 − 2푧푒−푥 )푗