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1) The document discusses finding the maximum and minimum values of functions with constrained variables. It provides definitions and a working rule for determining extreme values in multiple steps. 2) Examples are provided to demonstrate the process of finding the minimum/maximum value and stationary points of functions subject to constraints. 3) The final example solves for the points on a surface nearest to the origin and the minimum distance.

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Partial differentiation B tech

A partial differential equation contains one dependent variable and more than one independent variable. The partial derivatives of a function f(x,y) with respect to x and y at a point (x,y) are represented as ∂f/∂x and ∂f/∂y. Higher order partial derivatives can be found by taking partial derivatives multiple times with respect to the independent variables. The chain rule can be used to find partial derivatives when the dependent variable is a function of other variables that are themselves functions of the independent variables.

Derivation of Simpson's 1/3 rule

This document explains Simpson's 1/3rd rule for numerical integration. Simpson's 1/3rd rule approximates the integral of a function over an interval by breaking the interval into equal subintervals and approximating the function within each subinterval as a quadratic polynomial. The approximation takes the function values at the endpoints and midpoint of each subinterval. The approximations over all subintervals are then summed to give an approximation of the full integral. Important considerations for applying Simpson's 1/3rd rule include using an even number of equal subintervals and having a minimum of 3 points defined in each subinterval.

Newton's forward & backward interpolation

Newton's forward and backward interpolation are methods for estimating the value of a function between known data points. Newton's forward interpolation uses a formula to calculate successive differences between the y-values of known x-values to estimate y-values for unknown x-values greater than the last known x-value. Newton's backward interpolation similarly uses differences but to estimate y-values for unknown x-values less than the first known x-value. The document provides an example of using Newton's forward formula to find the estimated y-value of 0.5 given a table of x and y pairs, calculating the differences and plugging into the formula. It also works through an example of Newton's backward interpolation to estimate the y-value at

DIFFERENTIAL EQUATIONS

- A differential equation involves an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the exponent of the highest order derivative.
- Linear differential equations involve the dependent variable and its derivatives only to the first power. Non-linear equations do not meet this criterion.
- The general solution of a differential equation contains as many arbitrary constants as the order of the equation. A particular solution results from assigning values to the arbitrary constants.
- Differential equations can be solved through methods like variable separation, inspection of reducible forms, and finding homogeneous or linear representations.

Limits And Derivative

The document discusses key concepts in calculus including functions, limits, derivatives, and derivatives of trigonometric functions. It provides examples of calculating derivatives from first principles using the definition of the derivative and common derivative rules like the product rule and quotient rule. Formulas are also derived for the derivatives of the sine, cosine, and tangent functions.

Rolles theorem

This ppt covers following topics of Unit - 2 of B.Sc. 2 Mathematics Rolle's Theorem , Lagrange's mean value theorem , Mean value theorem & its example .

Partial Differentiation & Application

The document discusses partial differentiation and its applications. It covers functions of two variables, first and second partial derivatives, and applications including the Cobb-Douglas production function and finding marginal productivity from a production function. Examples are provided to demonstrate calculating partial derivatives of various functions and applying partial derivatives in contexts like production analysis.

Applications of maxima and minima

This document discusses finding the maximum and minimum values of functions, as well as points of inflection. It provides instructions on how to find the coordinates of turning points by setting the derivative of the function equal to zero and solving. It also discusses how to determine if a turning point is a maximum or minimum by taking the second derivative and checking if it is positive or negative. The document concludes by giving examples of how to apply these concepts to optimization word problems involving areas, volumes, or other quantities that need to be maximized or minimized under certain constraints.

Real life Application of maximum and minimum

The document discusses uses of maximum and minimum values in various fields. It begins with definitions of maximum and minimum values in mathematics. It then lists several fields where maximum and minimum values are used, including physics, chemistry, space stations, architecture, economics, and aircraft. For example, it notes that maximum values of wave functions are used in physics to determine where electrons are likely to be found, and that maximum pressures help design space shuttles. Minimum and maximum values also have applications in high-speed architecture, price controls, and aircraft design.

Double Integral Powerpoint

Double integrals are used to calculate properties of planar laminas such as mass, center of mass, and moments of inertia by integrating a density function over a region. The inner integral is evaluated first, treating the other variable as a constant. Properties include:
1) Total mass by double integrating the density function over the region.
2) Center of mass coordinates by taking moments about axes and dividing by total mass.
3) Moments of inertia by double integrating the distance squared from an axis times the density.

Applications of partial differentiation

In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant (as opposed to the total derivative, in which all variables are allowed to vary). Partial derivatives are used in vector calculus and differential geometry.

1st order differential equations

1) First order ordinary linear differential equations can be expressed in the form dy/dx = p(x)y + q(x), where p and q are functions of x.
2) There are several types of first order linear differential equations, including separable, homogeneous, exact, and linear equations.
3) Separable equations can be solved by separating the variables and integrating both sides. Homogeneous equations involve functions that are homogeneous of the same degree in x and y.

Application of derivative

Additional Applications of the Derivative related to engineering maths
this presentation is only for the knowledge...............

Continuity and differentiability

The document discusses key concepts in calculus including continuity, differentiation, integration, and their applications. It defines continuity as being able to draw a function's graph without lifting the pen, and differentiation as computing the rate of change of a dependent variable with respect to changes in the independent variable. The document also covers differentiation rules and techniques for implicit, inverse, exponential, logarithmic, and parametric functions.

Complex number

This document contains information about Md. Arifuzzaman, a lecturer in the Department of Natural Sciences at the Faculty of Science and Information Technology, Daffodil International University. It includes his employee ID, designation, department, faculty, personal webpage, email, and phone number. The document also provides an overview of complex numbers, including their history, the number system, definitions of complex numbers, operations like addition and multiplication of complex numbers, and applications of complex numbers.

Differential calculus maxima minima

critical points/ stationary points , turning points,Increasing, decreasing functions, absolute maxima & Minima, Local Maxima & Minima , convex upward & convex downward - first & second derivative tests.

Maxima & Minima for IIT JEE | askIITians

Buckle up your IIT JEE preparation by exploring the world of maxima & minima with the help of various tips offered by askIITians. Read to know more….

Differential equations

- A differential equation relates an independent variable, dependent variable, and derivatives of the dependent variable with respect to the independent variable.
- The order of a differential equation is the order of the highest derivative, and the degree is the degree of the highest derivative.
- Differential equations can be classified based on their order (first order vs higher order) and linearity (linear vs nonlinear).
- The general solution of a differential equation contains arbitrary constants, while a particular solution gives specific values for those constants.

Concepts of Maxima And Minima

This document discusses concepts related to finding maximum and minimum values of functions. It provides examples of max-min problems from history involving projectiles and planetary motion. The max-min theorem states that continuous functions on closed intervals attain both maximum and minimum values. A strategy is outlined for solving max-min problems which involves drawing diagrams, writing equations, finding critical points and endpoints, and listing function values to determine local and absolute extrema. An example problem applying the strategy finds the maximum area of a fence enclosure as a 9x9 square.

PPt on Functions

1. A function is a relation where each input is paired with exactly one output.
2. To determine if a relation is a function, use the vertical line test - if any vertical line intersects more than one point, it is not a function.
3. To find the value of a function, substitute the given value for x into the function equation and simplify.

Partial differentiation B tech

Partial differentiation B tech

Derivation of Simpson's 1/3 rule

Derivation of Simpson's 1/3 rule

Newton's forward & backward interpolation

Newton's forward & backward interpolation

DIFFERENTIAL EQUATIONS

DIFFERENTIAL EQUATIONS

Limits And Derivative

Limits And Derivative

Rolles theorem

Rolles theorem

Partial Differentiation & Application

Partial Differentiation & Application

Applications of maxima and minima

Applications of maxima and minima

Real life Application of maximum and minimum

Real life Application of maximum and minimum

Double Integral Powerpoint

Double Integral Powerpoint

Applications of partial differentiation

Applications of partial differentiation

1st order differential equations

1st order differential equations

Application of derivative

Application of derivative

Continuity and differentiability

Continuity and differentiability

Complex number

Complex number

Differential calculus maxima minima

Differential calculus maxima minima

Maxima & Minima for IIT JEE | askIITians

Maxima & Minima for IIT JEE | askIITians

Differential equations

Differential equations

Concepts of Maxima And Minima

Concepts of Maxima And Minima

PPt on Functions

PPt on Functions

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Antarctica

The document discusses pollution in Antarctica from human activities. It notes that 98% of Antarctica is covered by thick ice sheets, and if all the ice melted, sea levels would rise 60 meters. Various forms of pollution like heavy metals, waste, and increased CO2 levels are degrading the Antarctic environment. The melting of Antarctic ice sheets is accelerating due to global warming, which could cause sea level rise and threaten wildlife like penguin populations. Several countries are working to implement sustainable practices and environmental protections for Antarctica through international agreements. Unchecked pollution poses risks not just for Antarctica but for global ecosystems and sea level rise.

Tài liệu hướng dẫn trình bày đồ án tốt nghiệp

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đề Thi tốt nghiệp nghề may thời trang 10

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Aprendizaje significativo

El documento habla sobre el aprendizaje significativo y las estrategias de aprendizaje. Explica que el aprendizaje significativo implica integrar nueva información con conocimientos previos de manera activa y personal. También describe características como que es un proceso activo, personal, asimilado y aplicable. Finalmente, menciona algunas estrategias de aprendizaje como la repetición, gestión de información, control metacognitivo y estrategias motivacionales.

Luận văn một số giải pháp nâng cao khả năng thắng thầu của công ty xây dựng h...

Luận văn một số giải pháp nâng cao khả năng thắng thầu của công ty xây dựng hồng hà tổng công ty đầu tư và phát triển nhà hà nội

Hoàn thiện công tác phân tích tài chính tại công ty cổ phần thương mại và xuấ...

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Ple informática básica para primaria

Este documento presenta un plan de estudios básico de informática para primaria. Consta de 4 temas principales: componentes de hardware y software, Microsoft Word, PowerPoint y navegadores de Internet. El objetivo es que los estudiantes adquieran conocimientos básicos sobre tecnología para su educación, trabajo y vida social. Al final, se enumeran las herramientas que se utilizarán como Wikipedia, YouTube y software educativo.

Kinesics

Kinesics is the study of body movements including gestures, head movements, posture, eye contact, and facial expressions. It examines how these nonverbal cues accompany and illustrate verbal communication, convey emotions, establish connections, and regulate social interactions. Key types of gestures are emblems, illustrators, adaptors, and touch behaviors which provide information about arousal. Head movements, eye contact, and posture also signal interest, attentiveness, dominance and formality in interactions. Facial expressions particularly communicate core emotions.

Aprendizaje, metacognición y autorregulación

Este documento presenta definiciones de aprendizaje de autores como Feldman, Hilgard y Gagné, los cuales describen el aprendizaje como un proceso de cambio en el comportamiento o capacidad de una persona generado por la experiencia. También describe características del aprendizaje como que es un proceso mediador, se origina en la experiencia práctica y es relativamente estable. Además, presenta diferentes tipos de aprendizaje como el receptivo, por descubrimiento, repetitivo y significativo. Finalmente, introduce conceptos de metac

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Giải pháp marketing nhằm tăng khả năng cạnh tranh của công ty cổ phần và dịch...

Giải pháp marketing nhằm tăng khả năng cạnh tranh của công ty cổ phần và dịch...

Antarctica

Antarctica

Tài liệu hướng dẫn trình bày đồ án tốt nghiệp

Tài liệu hướng dẫn trình bày đồ án tốt nghiệp

Hoàn thiện công tác phân tích tình hình tài chính tại công ty tnhh đầu tư phá...

Hoàn thiện công tác phân tích tình hình tài chính tại công ty tnhh đầu tư phá...

đề Thi tốt nghiệp nghề may thời trang 10

đề Thi tốt nghiệp nghề may thời trang 10

đồ áN công nghệ may thực tế sản xuất mẫu rập trong may công nghiệp - sản ph...

đồ áN công nghệ may thực tế sản xuất mẫu rập trong may công nghiệp - sản ph...

Aprendizaje significativo

Aprendizaje significativo

Luận văn một số giải pháp nâng cao khả năng thắng thầu của công ty xây dựng h...

Luận văn một số giải pháp nâng cao khả năng thắng thầu của công ty xây dựng h...

Hoàn thiện công tác phân tích tài chính tại công ty cổ phần thương mại và xuấ...

Hoàn thiện công tác phân tích tài chính tại công ty cổ phần thương mại và xuấ...

Ple informática básica para primaria

Ple informática básica para primaria

Kinesics

Kinesics

Aprendizaje, metacognición y autorregulación

Aprendizaje, metacognición y autorregulación

đồ áN ngành may xử lý các vấn đề phát sinh trong phân xưởng cắt

đồ áN ngành may xử lý các vấn đề phát sinh trong phân xưởng cắt

Maxima and minima

To find the extreme values (maximum or minimum) of a function f(x,y) of two variables:
1. Take the partial derivatives fx(x,y) and fy(x,y) and set them equal to 0 to find the stationary points.
2. At each stationary point, calculate the second partial derivatives fxx, fyy, and fxy.
3. Use the signs of fxx and the determinant of the Hessian (fxx*fyy - fxy^2) to determine whether the stationary point is a maximum or minimum. If the determinant is positive and fxx is negative, it is a maximum; if the determinant is positive and fxx is positive, it

APPLICATION OF PARTIAL DIFFERENTIATION

This document provides information on several multivariable calculus topics:
1) Finding maxima and minima of functions of two variables using partial derivatives and the second derivative test.
2) Finding the tangent plane and normal line to a surface.
3) Taylor series expansions for functions of two variables.
4) Standard expansions for common functions like e^x, cosh(x), and tanh(x) using Maclaurin series.
5) Linearizing functions around a point using the tangent plane approximation.
6) Lagrange's method of undetermined multipliers for finding extrema with constraints.

Application of derivatives 2 maxima and minima

This document discusses key concepts related to derivatives and their applications:
- It defines increasing and decreasing functions and explains how to determine if a function is increasing or decreasing based on the sign of the derivative.
- It introduces the use of derivatives to find maximum and minimum values, extreme points, and critical points of functions.
- Theorems 1 and 2 provide rules for determining if a critical point represents a maximum or minimum.
- Examples are provided to demonstrate finding the intervals where a function is increasing/decreasing, identifying extrema, and determining the greatest and least function values over an interval.

19 min max-saddle-points

The document defines relative and absolute maxima and minima for functions z=f(x,y). A relative maximum occurs when f(a,b) is greater than f(x,y) within a neighborhood circle of (a,b). An absolute maximum occurs when f(a,b) is greater than f(x,y) over the entire domain. Similarly for minima with the inequalities reversed. Extrema refer to maxima and minima. For a continuous function over a closed and bounded domain, absolute extrema exist and occur either in the interior or on the boundary. Examples find and classify extrema of functions.

maxima & Minima thoeyr&solved.Module-4pdf

In this chapter we shall study those points of the domain of a function where its graph changes its direction from upwards to downwards or from downwards to upwards. At such points the derivative of the function, if it exists, is necessarily zero.
The value of a function f (x) is said to be maximum at x = a, if there exists a very small positive number h, such that
f(x) < f(a) x (a – h,a + h) , x a
In this case the point x = a is called a point of maxima for the function f(x).
Simlarly, the value of f(x) is said to the minimum at x = b, If there exists a very small positive number, h, such that
f(x) > f(b), x (b – h,b + h), x b
In this case x = b is called the point of minima for the function f(x).
Hene we find that,
(i) x = a is a maximum point of f(x)
f(a) f(a h) 0
f(a) f(a h) 0
(ii) x = b is a minimum point of f(x)
Rf(b) f(b h) 0
f(b) f(b h) 0
(iii) x = c is neither a maximum point nor a minimum point
Note :
(i) The maximum and minimum points are also known as extreme points.
(ii) A function may have more than one maximum and minimum points.
(iii) A maximum value of a function f(x) in an interval [a,b] is not necessarily its greatest value in that interval. Similarly, a minimum value may not be the least value of the function. A minimum value may be greater than some maximum value for a function.
(iv) If a continuous function has only one maximum (minimum) point, then at this point function has its greatest (least) value.
(v) Monotonic functions do not have extreme points.
Ex. Function y = sin x, x (0, ) has a maximum point at x = /2 because the value of sin /2 is greatest in the given interval for sin x.
Clearly function y = sin x is increasing in the interval (0, /2) and decreasing in the interval ( /2, ) for that reason also it has maxima at x = /2. Similarly we can see from the graph of cos x which has a minimum point at x = .
Ex. f(x) = x2 , x (–1,1) has a minimum point at x = 0 because at x = 0, the value of x2 is 0, which is
less than the all the values of function at different points of the interval.
Clearly function y = x2 is decreasing in the interval
Rf(c) f(c h)
Sand
Tf(c) f(c h) 0
|V| have opposite signs.
(–1, 0) and increasing in the interval (0,1) So it has minima at x = 0.
Ex. f(x) = |x| has a minimum point at x = 0. It can be easily observed from its graph.
A. Necessary Condition : A point x = a is an extreme point of a function f(x) if f’(a) = 0, provided f’(a) exists. Thus if f’ (a) exists, then
x = a is an extreme point f’(a) = 0
or
f’ (a) 0 x = a is not an extreme point.
But its converse is not true i.e.
f’ (a) = 0 x = a is an extreme point.
For example if f(x) = x3 , then f’ (0) = 0 but x = 0 is not an extreme point.
B. Sufficient Condition :
(i) The value of the function f(x) at x = a is maximum, if f’ (a) = 0 and f” (a) < 0.
(ii) The value of

Derivatives

This document provides information about derivatives and their applications:
1. It defines the derivative as the limit of the difference quotient, and explains how to calculate derivatives using first principles. It also covers rules for finding derivatives of sums, products, quotients, exponentials, and logarithmic functions.
2. Higher order derivatives are introduced, with examples of how to take second and third derivatives.
3. Applications of derivatives like finding velocity and acceleration from a position-time function are demonstrated. Maximum/minimum values and how to find local and absolute extrema are also discussed with an example.

functions limits and continuity

This document provides an overview of functions, limits, and continuity. It defines key concepts such as domain and range of functions, and examples of standard real functions. It also covers even and odd functions, and how to calculate limits, including left and right hand limits. Methods for evaluating algebraic limits using substitution, factorization, and rationalization are presented. The objectives are to understand functions, domains, ranges, and how to evaluate limits of functions.

Functions limits and continuity

This document discusses functions, limits, and continuity. It begins by defining functions, domains, ranges, and some standard real functions like constant, identity, modulus, and greatest integer functions. It then covers limits of functions including one-sided limits and properties of limits. Examples are provided to illustrate evaluating limits using substitution and factorization methods. The overall objectives are to understand functions, domains, ranges, limits of functions and methods to evaluate limits.

Chain rule

1. The chain rule describes how to take the derivative of a function composed of other functions. It states that if z = f(x, y) and x and y are functions of t, then the derivative of z with respect to t is the sum of the partial derivatives multiplied by the derivatives of x and y with respect to t.
2. The chain rule is applied to find the derivative of two example functions, w = xy and w = xy + z, with respect to t along given paths for x, y, and z in terms of t.
3. The chain rule is generalized to the case of a function u of n variables, where each variable is a function of m other variables

AEM.pptx

1) Maxima and minima refer to the highest and lowest points of a function's curve and can be found using calculus without graphing.
2) For functions of two variables, a stationary point occurs where the partial derivatives are zero. If the second derivative test is positive and the first derivative is negative, it is a relative maximum; if the second derivative test is positive and the first derivative is positive, it is a relative minimum.
3) Applications of finding maxima and minima exist in fields like economics and engineering to optimize objectives like profit or cost subject to constraints.

CalculusStudyGuide

The document provides examples and explanations of concepts related to calculus including continuity, differentiability, limits, derivatives, and the mean value theorem. Some key points:
- It gives examples of determining if functions are continuous and differentiable at various points, including functions with absolute value.
- The mean value theorem is explained and examples are worked through showing a function satisfies the mean value theorem and finding the value of c.
- Numerous examples demonstrate calculating derivatives using rules like product, quotient, chain and implicit differentiation. Examples include derivatives of trigonometric, exponential and logarithmic functions.
- Implicit differentiation is used to find the equation of a tangent line to a curve at a given point.

Maths 301 key_sem_1_2009_2010

This document contains the solutions to 5 questions related to calculus concepts like integration, derivatives, series approximation, and geometry of curves and surfaces. Some of the key steps include:
- Using integration to find volumes, masses, and centroids
- Finding critical points and classifying extrema
- Approximating a series to evaluate an integral
- Solving a geometric series problem to find an initial height
- Analyzing motion problems using kinematic equations
- Finding equations of planes and tangent lines to surfaces

03 convexfunctions

The document discusses convex functions and related concepts. It defines convex functions and provides examples of convex and concave functions on R and Rn, including norms, logarithms, and powers. It describes properties that preserve convexity, such as positive weighted sums and composition with affine functions. The conjugate function and quasiconvex functions are also introduced. Key concepts are illustrated with examples throughout.

Crib Sheet AP Calculus AB and BC exams

This document provides a summary of key concepts that must be known for AP Calculus, including:
- Curve sketching and analysis of critical points, local extrema, and points of inflection
- Common differentiation and integration rules like product rule, quotient rule, trapezoidal rule
- Derivatives of trigonometric, exponential, logarithmic, and inverse functions
- Concepts of limits, continuity, intermediate value theorem, mean value theorem, fundamental theorem of calculus
- Techniques for solving problems involving solids of revolution, arc length, parametric equations, polar curves
- Series tests like ratio test and alternating series error bound
- Taylor series approximations and common Maclaurin series

LAGRANGE_MULTIPLIER.ppt

The Lagrange multiplier method provides a strategy for finding the maxima and minima of a function subject to constraints. It involves setting up a system of equations involving the function, its derivatives, and the constraints and their derivatives. Solving this system of equations yields candidate maxima/minima points, which are then checked in the original function to determine if they are actually maxima or minima. The document provides examples of applying the Lagrange multiplier method to problems with single and multiple constraints.

maths Individual assignment on differentiation

The document contains an individual assignment with 14 math problems. The assignment includes problems on calculus topics such as derivatives, limits, implicit differentiation, and optimization. The solutions show the steps and work to arrive at the answers for each problem.

Directional derivative and gradient

1) The document discusses directional derivatives and the gradient of functions of several variables. It defines the directional derivative Duf(c) as the slope of the function f in the direction of the unit vector u at the point c.
2) It shows that the partial derivatives of f can be computed by treating all but one variable as a constant. The gradient of f is defined as the vector of its partial derivatives.
3) It derives an expression for the directional derivative Duf(c) in terms of the partial derivatives of f and the components of the unit vector u, showing the relationship between directional derivatives and the gradient.

Twinkle

Vector calculus is used extensively in physics and engineering applications like electromagnetic fields and fluid mechanics. Some key applications of vector calculus include analyzing the center of mass, studying field theory, modeling kinematics, and weather analysis. Vector calculus operations like vector addition, scalar multiplication, and dot and cross products are used to model real-world phenomena like wind speed and direction. Vector fields and differential operators allow modeling physical quantities with direction and magnitude, like velocity, in multiple applications.

Continuity of functions by graph (exercises with detailed solutions)

The document contains 11 exercises analyzing the continuity of various functions. It begins by verifying the continuity of square root and rational functions at specific points. Later exercises involve determining the domains of piecewise functions and studying their continuity by analyzing limits. Graphs are drawn to illustrate discontinuity points for functions involving floor, trigonometric, and fractional expressions. The solutions find appropriate definitions or parameters to extend functions to continuous forms at boundaries between pieces.

Grph quad fncts

The document discusses graphing quadratic functions. It defines a quadratic function as f(x) = ax^2 + bx + c where a, b, and c are real numbers and a is not equal to 0. The graph of a quadratic function is a parabola that is symmetrical about an axis. When the leading coefficient a is positive, the parabola opens upward and the vertex is a minimum. When a is negative, the parabola opens downward and the vertex is a maximum. Standard forms for quadratic functions and methods for finding characteristics like the vertex, axis of symmetry, and x-intercepts from the equation are also presented.

Maxima and minima

Maxima and minima

APPLICATION OF PARTIAL DIFFERENTIATION

APPLICATION OF PARTIAL DIFFERENTIATION

Application of derivatives 2 maxima and minima

Application of derivatives 2 maxima and minima

19 min max-saddle-points

19 min max-saddle-points

maxima & Minima thoeyr&solved.Module-4pdf

maxima & Minima thoeyr&solved.Module-4pdf

Derivatives

Derivatives

functions limits and continuity

functions limits and continuity

Functions limits and continuity

Functions limits and continuity

Chain rule

Chain rule

AEM.pptx

AEM.pptx

CalculusStudyGuide

CalculusStudyGuide

Maths 301 key_sem_1_2009_2010

Maths 301 key_sem_1_2009_2010

03 convexfunctions

03 convexfunctions

Crib Sheet AP Calculus AB and BC exams

Crib Sheet AP Calculus AB and BC exams

LAGRANGE_MULTIPLIER.ppt

LAGRANGE_MULTIPLIER.ppt

maths Individual assignment on differentiation

maths Individual assignment on differentiation

Directional derivative and gradient

Directional derivative and gradient

Twinkle

Twinkle

Continuity of functions by graph (exercises with detailed solutions)

Continuity of functions by graph (exercises with detailed solutions)

Grph quad fncts

Grph quad fncts

Cryogenic grinding

Normal grinding processes which do not use a cooling system can reach up to 200°F.
These high temperatures can reduce volatile components and heat-sensitive constituents in herbs.
But cryogenic grinding process does not damage or alter the chemical composition of the plant in any way.
Materials which are elastic in nature, having low melting points, low combustion temperatures , sensitive to oxygen can be ideally machined by cryogenic grinding process.

Values

Values are stable, evaluative beliefs that guide our preferences for outcomes. A value is a principle, a standard, or a quality considered worthwhile or desirable.
Provide understanding of the attitudes, motivation, and behaviors
Influence our perception of the world around us
Represent interpretations of “right” and “wrong”
Imply that some behaviors or outcomes are preferred over others

Personality

After studying this chapter, you should be able to:
Define personality, describe how it is measured, and explain the factors that determine an individual’s personality.
Identify the key traits in the Big Five personality model.
Demonstrate how the Big Five traits predict behavior at work.
Identify other personality traits relevant to OB.
credit: Priyanka Sharma

Motivation

Motive : A inner state that energizes , activates or moves and directs or channels behaviour towards goals. One person induces another person to engage in action or desired behaviour by ensuring that a channel to direct the motive of the person becomes available and accessible to the person
The result of the interaction between the individual and the situation.
Credit: Priyanka Sharma

Organizational change

“A process through which something becomes different.” This is the dictionary definition. Organisational change refers to the alteration in technology, structure, method, people, or their behaviour. Organizational change can be defined as the alteration in structure, technology or people in an organization or behavior by an organization. Here we need to note that change in organizational culture is different from change in an organization. A new method or style or new rule is implemented here.

Intellectual property rights

This will enhance the knowledge about Intellectual Property rights. How its been secured with its remedies.

Green synthesis of gold nano particles

This will enhance the knowledge about the methods of nano particle synthesis. The application of Green method is also described. Gold nano particles are also explained with its toxicity and application.

Acetone

Acetone is a colorless, volatile, flammable liquid that is the simplest ketone. It is widely used as an industrial chemical and solvent. Major methods for producing acetone include the cumene process, oxidation of isopropyl alcohol, and fermentation. Acetone has many applications including use in adhesives, coatings, personal care products, and as an intermediate in chemical synthesis. Worldwide consumption of acetone is several million tons per year.

Pulp industries

The document provides information about the pulp industry. It discusses the history and development of pulping processes like the kraft process. It details the current production of pulp globally and in countries like China, US, Japan, Canada, etc. It describes the key pulping processes of kraft, sulfite, and mechanical pulping. It also discusses utilities, engineering problems, use of different raw materials, energy usage, and recent advances as well as environmental issues in the pulp industry.

Spectroscopy

This document is a 38-page seminar report on spectroscopy submitted by two students, Arpit Modh and Parth Kasodariya. It includes an introduction to spectroscopy, descriptions of various spectroscopy techniques like atomic absorption spectroscopy, infrared absorption spectroscopy, and ultraviolet-visible spectroscopy. The report covers principles, instrumentation, applications, and more for different spectroscopy methods. It aims to provide a basic review of spectroscopy and its uses in various important fields like structure analysis.

Wireless power transmission

This document discusses wireless power transmission (WPT) and its various techniques. It provides an overview of WPT, its history dating back to Nikola Tesla's experiments, and the main types including near-field techniques like inductive coupling and far-field techniques like microwave and laser transmission. The key advantages of WPT are that it is more efficient than wired transmission and has lower maintenance costs. However, it also has disadvantages like distance constraints for near-field and safety concerns. WPT has applications in electric vehicle charging and delivering power to remote areas.

The kansas city hyatt regency walkway collapse

The Kansas City Hyatt Regency walkway collapse was one of the worst structural disasters in US history. On July 17, 1981, two walkways collapsed during a tea dance, killing 114 people and injuring over 200. The failure was due to a modified hanger rod connection design that doubled stresses without being properly analyzed. A lack of oversight and review allowed the unsafe design and construction errors to go unnoticed until it was too late. The disaster exposed deficiencies in the design and construction process.

Nuclear waste

Nuclear waste is classified as low-level, intermediate-level, or high-level waste depending on radioactivity levels. High-level waste poses the greatest danger, as it contains over 95% of total radioactivity and is thermally hot. Current levels of high-level waste are increasing by around 12,000 metric tons per year. Most proposals for managing high-level waste involve deep geological storage, such as at proposed sites like Yucca Mountain. Transmutation and reuse of nuclear waste are also being researched to reduce radioactive waste volumes.

Functions

The document discusses functions in C programming. It covers modular programming and the advantages of using blocks and functions. It defines function declaration, definition, and calls. It discusses actual and formal parameters and different ways to use functions in C including examples of functions without arguments/return values, with return values but no arguments, with arguments but no return values, and with both arguments and return values. The document contains an example of a function to check if a number is prime without and with user-defined functions.

Communication skills

This document discusses various aspects of communication skills, including nonverbal communication cues like kinesics, proxemics, and chronemics. It also examines barriers to effective communication such as intrapersonal barriers stemming from wrong assumptions or varied perceptions. Interpersonal barriers include limited vocabulary, incompatible verbal and nonverbal messages, cultural variations, and noise in the communication channel. Organizational barriers involve fear of superiors, negative tendencies within groups, using inappropriate communication media, and information overload.

Boiler Introduction & Classification

This presentation discusses boilers, which produce steam using heat from fuel combustion. Boilers are classified based on their orientation, whether they have fire or water tubes, furnace location, circulation method, pressure rating, mobility, and number of tubes. Key types include fire tube boilers like Cochran and Lancashire models, and water tube boilers such as Babcock and Wilcox. Selection depends on required steam properties, capacity, cost, and other factors. Proper boiler design considers safety, accessibility, efficiency, and other criteria.

Cryogenic grinding

Cryogenic grinding

Values

Values

Personality

Personality

Motivation

Motivation

Organizational change

Organizational change

Intellectual property rights

Intellectual property rights

Green synthesis of gold nano particles

Green synthesis of gold nano particles

Acetone

Acetone

Pulp industries

Pulp industries

Spectroscopy

Spectroscopy

Wireless power transmission

Wireless power transmission

The kansas city hyatt regency walkway collapse

The kansas city hyatt regency walkway collapse

Nuclear waste

Nuclear waste

Functions

Functions

Communication skills

Communication skills

Boiler Introduction & Classification

Boiler Introduction & Classification

Benefits of Studying Artificial Intelligence - KRCE.pptx

Discover the benefits of studying artificial intelligence (AI)! Learn how AI can boost your career, and open limitless opportunities across various fields.
#Benefits of Studying Artificial Intelligence (AI)
#AI at Krce
#Career Opportunities in Artificial Intelligence (AI) at KRCE
#KRCE at Artificial Intelligence
#Advancing Ethical and Responsible AI
#Career Growth in Artificial Intelligence at KRCE
#Exciting Career in Artificial Intelligence
#Best Career in Artificial Intelligence
#Amazing Benefits of Studying Artificial Intelligence

21CV61- Module 3 (CONSTRUCTION MANAGEMENT AND ENTREPRENEURSHIP.pptx

Notes of Construction management and entrepreneurship

Introduction to IP address concept - Computer Networking

Introduction to IP address concept - Computer NetworkingMd.Shohel Rana ( M.Sc in CSE Khulna University of Engineering & Technology (KUET))

An Internet Protocol address (IP address) is a logical numeric address that is assigned to every single computer, printer, switch, router, tablets, smartphones or any other device that is part of a TCP/IP-based network.
Types of IP address-
Dynamic means "constantly changing “ .dynamic IP addresses aren't more powerful, but they can change.
Static means staying the same. Static. Stand. Stable. Yes, static IP addresses don't change.
Most IP addresses assigned today by Internet Service Providers are dynamic IP addresses. It's more cost effective for the ISP and you.
Monitoring and reporting of transparent forest data and information under the...

Monitoring and reporting of transparent forest data and information under the...Pilar Valbuena Perez

T5.13 Forest without borders: National Forest Inventory Networks and their potential for large scale monitoring and reporting
Jenny Wong Lai Ping1
1 United Nations Climate Change Secretariat, Bonn, Germany
The Framework Convention on Climate Change (UNFCCC) recognizes the critical role of forests as terrestrial carbon sinks for combatting climate change and calls for transparency of climate actions, including those in the forest sector. The Paris Agreement continues to uphold the principle of transparency. It established the Enhanced
Transparency Framework (ETF) with the aim to build mutual trust and confidence among countries in their monitoring and reporting of climate actions and to track progress of such mitigation actions. Forests play a key role in all aspects of the implementation of the Paris Agreement. Numerous countries, both developed and developing, have identified forest and land use-related mitigation and adaptation measures and actions as part of their climate targets in their nationally determined contributions to fulfill the goal of the Paris Agreement.
The world is now in an era where transparency of data and information and actions are indispensable for ensuring coordination among relevant ministries and agencies and effective decision-making at all levels. Transparent, robust and comprehensive data and information on greenhouse gas emissions and climate actions are essential for informing national policies, plans and strategies and helping countries meet their international commitments on climate change. The same applies to forest data and information and its reporting to multilateral environmental agreements. Additionally, robust institutional arrangements, including for national forest inventories (NFI) as part of national forest monitoring systems and GHG management systems, form the basis for ensuring transparent data and information from these processes and systems and for meeting the requirements for reporting under the ETF.
The aim of this review analysis is to highlight the importance of transparency in monitoring and reporting and for building trust in climate actions. The analysis will provide an overview of the requirements and necessary elements for monitoring and reporting on the forest and land use sector in the ETF and the challenges faced. This background will serve as a basis for stimulating discussions and exploring potential collaborative solutions offered by strong institutional arrangements and collaborative networks (such as NFI networks) and to facilitate identification of effective capacity-building needs of developing countries.
IWISS Catalog 2024

A brand new catalog for the 2024 edition of IWISS. We have enriched our product range and have more innovations in electrician tools, plumbing tools, wire rope tools and banding tools. Let's explore together!

UNIT I INCEPTION OF INFORMATION DESIGN 20CDE09-ID

20CDE09- INFORMATION DESIGN
UNIT I INCEPTION OF INFORMATION DESIGN
Introduction and Definition
History of Information Design
Need of Information Design
Types of Information Design
Identifying audience
Defining the audience and their needs
Inclusivity and Visual impairment
Case study.

Rotary Intersection in traffic engineering.pptx

Very Important design

Jet Propulsion and its working principle.pdf

What is jet propulsion, air breathing and non-airbreathing engines, components of turboprop, turbojet and turbofan engines

Design and Application of Side Channel Spillways

Description: A comprehensive overview of the types, design principles, hydraulic and structural design considerations for side channel spillways in dam infrastructure.

Quadcopter Dynamics, Stability and Control

A brief introduction to quadcopter (drone) working. It provides an overview of flight stability, dynamics, general control system block diagram, and the electronic hardware.

Thermodynamics Digital Material basics subject

basic of thermodynamics

Lecture 3 Biomass energy...............ppt

Biomass energy

Time-State Analytics: MinneAnalytics 2024 Talk

Slides from my talk at MinneAnalytics 2024 - June 7, 2024
https://datatech2024.sched.com/event/1eO0m/time-state-analytics-a-new-paradigm
Across many domains, we see a growing need for complex analytics to track precise metrics at Internet scale to detect issues, identify mitigations, and analyze patterns. Think about delays in airlines (Logistics), food delivery tracking (Apps), detect fraudulent transactions (Fintech), flagging computers for intrusion (Cybersecurity), device health (IoT), and many more.
For instance, at Conviva, our customers want to analyze the buffering that users on some types of devices suffer, when using a specific CDN.
We refer to such problems as Multidimensional Time-State Analytics. Time-State here refers to the stateful context-sensitive analysis over event streams needed to capture metrics of interest, in contrast to simple aggregations. Multidimensional refers to the need to run ad hoc queries to drill down into subpopulations of interest. Furthermore, we need both real-time streaming and offline retrospective analysis capabilities.
In this talk, we will share our experiences to explain why state-of-art systems offer poor abstractions to tackle such workloads and why they suffer from poor cost-performance tradeoffs and significant complexity.
We will also describe Conviva’s architectural and algorithmic efforts to tackle these challenges. We present early evidence on how raising the level of abstraction can reduce developer effort, bugs, and cloud costs by (up to) an order of magnitude, and offer a unified framework to support both streaming and retrospective analysis. We will also discuss how our ideas can be plugged into existing pipelines and how our new ``visual'' abstraction can democratize analytics across many domains and to non-programmers.

Presentation slide on DESIGN AND FABRICATION OF MOBILE CONTROLLED DRAINAGE.pptx

To address increased waste dumping in drains, a low-cost drainage cleaning robot controlled via a mobile app is designed to reduce human intervention and improve automation. Connected via Bluetooth, the robot’s chain circulates, moving a mesh with a lifter to carry solid waste to a bin. This project aims to clear clogs, ensure free water flow, and transform society into a cleaner, healthier environment, reducing disease spread from direct sewage contact. It’s especially effective during heavy rains with high water and garbage flow.

Conservation of Taksar through Economic Regeneration

This was our 9th Sem Design Studio Project, introduced as Conservation of Taksar Bazar, Bhojpur, an ancient city famous for Taksar- Making Coins. Taksar Bazaar has a civilization of Newars shifted from Patan, with huge socio-economic and cultural significance having a settlement of about 300 years. But in the present scenario, Taksar Bazar has lost its charm and importance, due to various reasons like, migration, unemployment, shift of economic activities to Bhojpur and many more. The scenario was so pityful that when we went to make inventories, take survey and study the site, the people and the context, we barely found any youth of our age! Many houses were vacant, the earthquake devasted and ruined heritages.
Conservation of those heritages, ancient marvels,a nd history was in dire need, so we proposed the Conservation of Taksar through economic regeneration because the lack of economy was the main reason for the people to leave the settlement and the reason for the overall declination.

PMSM-Motor-Control : A research about FOC

This is research about a process called field-oriented control (FOC) that is used to control the pmsm motor.

Benefits of Studying Artificial Intelligence - KRCE.pptx

Benefits of Studying Artificial Intelligence - KRCE.pptx

21CV61- Module 3 (CONSTRUCTION MANAGEMENT AND ENTREPRENEURSHIP.pptx

21CV61- Module 3 (CONSTRUCTION MANAGEMENT AND ENTREPRENEURSHIP.pptx

Introduction to IP address concept - Computer Networking

Introduction to IP address concept - Computer Networking

Monitoring and reporting of transparent forest data and information under the...

Monitoring and reporting of transparent forest data and information under the...

IWISS Catalog 2024

IWISS Catalog 2024

UNIT I INCEPTION OF INFORMATION DESIGN 20CDE09-ID

UNIT I INCEPTION OF INFORMATION DESIGN 20CDE09-ID

Rotary Intersection in traffic engineering.pptx

Rotary Intersection in traffic engineering.pptx

Jet Propulsion and its working principle.pdf

Jet Propulsion and its working principle.pdf

STC-TRS-Conventional traction report-01.pdf

STC-TRS-Conventional traction report-01.pdf

Design and Application of Side Channel Spillways

Design and Application of Side Channel Spillways

Quadcopter Dynamics, Stability and Control

Quadcopter Dynamics, Stability and Control

RECENT DEVELOPMENTS IN RING SPINNING.pptx

RECENT DEVELOPMENTS IN RING SPINNING.pptx

Rockets and missiles notes engineering ppt

Rockets and missiles notes engineering ppt

Thermodynamics Digital Material basics subject

Thermodynamics Digital Material basics subject

Lecture 3 Biomass energy...............ppt

Lecture 3 Biomass energy...............ppt

Time-State Analytics: MinneAnalytics 2024 Talk

Time-State Analytics: MinneAnalytics 2024 Talk

Presentation slide on DESIGN AND FABRICATION OF MOBILE CONTROLLED DRAINAGE.pptx

Presentation slide on DESIGN AND FABRICATION OF MOBILE CONTROLLED DRAINAGE.pptx

Conservation of Taksar through Economic Regeneration

Conservation of Taksar through Economic Regeneration

PMSM-Motor-Control : A research about FOC

PMSM-Motor-Control : A research about FOC

lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt

lecture10-efficient-scoring.ppmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmmt

- 1. Maxima & Minima with Constrained Variables BY: Arpit Modh (16BCH035) B.Tech Chemical Nirma University, Ahmedabad.
- 2. Definitions:- Let, u = f (x , y) be a continuous function of x and y. Then u will be maximum at x = a, y = b, if f (a ,b ) > f(a + h , b + k) and will be minimum at x=a, x=b, if f(a, b) < f(a + h, b + k) for small positive or negative values of h and k. The point at which function f(x, y) is either maximum or minimum is known as stationary point. The value of the function at stationary point is known as extreme (maximum and minimum) value of function f(x, y).
- 3. Working Rule:- To determine the maxima and minima (extreme values) of a function f(x, y). Step 1: Solve ∂f/ ∂x = 0 and ∂f/ ∂y = 0 simultaneously for x and y. Step 2: Obtain the values of r= ∂²f/ ∂x², s= ∂²f / ∂x², t= ∂²f/ ∂x².
- 4. Step 3: (i) If rt - s² > 0 and r < 0 (or t < 0) at (a, b) then f(x, y) is maximum at (a, b) and the maximum value of the function is f(a, b). (ii) If rt - s² > 0 and r > 0 (or t > 0) at (a, b) then f(x, y) is minimum value of the function is f(a, b). (iii) If rt - s² < 0 at (a, b) then f(x, y) is either maximum nor minimum at (a, b). Such a point is known as saddle point. (iv) If rt - s² = 0 at (a, b) then no conclusion can be made about the extreme values of f(x, y) and further investigation is required.
- 5. Example 1 Find the minimum value of x² + y² + z² with the constraint x + y + z = 3a. Solution: f = x² + y² + z² x + y + z = 3a z = 3a - x - y …..(1) substituting the value of z in Eq. (1), f = x² + y² + (3a –x- y) ² Step 1 For extreme values, ∂f/ ∂x = 0 and ∂f/ ∂y = 0 2x – 2(3a - x - y ) = 0 2y - 2(3a - x - y) = 0 4x - 6a + 2y = 0 2y - 6a + 2x + 2y = 0 2x + y = 3a x + 2y = 3a ……(2) ….(3)
- 6. Solving Eqs (2) and (3), x = y = a The stationary point is (a, a). Step 2 r = ∂²f/ ∂x² = 4 s = ∂²f/ ∂x ∂y = 2 t = ∂²f/ ∂y² = 4 Step 3 At (a, a), r = 4, s = 2, t = 4 rt - s² = (4)(4) – (2) ² = 12 > 0 Also, r = 4 > 0 Hence, f(x, y) is minimum at (a, a) fmin = a² + a² + (3a - a - a) ² = 3a²
- 7. Example 2 Divide 120 into three parts so that the sum of their products taken two at a time shall be maximum. Solution: Let x, y, z be three numbers. x + y + z = 120 f = xy + yz + xz = xy + y(120 - x - y) + x( 120 - x - y) = xy + 120y – xy - y² + 120x - x² -xy = 120x + 120y - xy - x² - y² For extreme values, ∂f/∂x = 0 120 - y - 2x = 0 …(1) And ∂f/ ∂y = 0 120 - x - 2y = 0 ….(2) Solving Eqs (1) and (2), x = 40 y = 40 Stationary point is (40, 40).
- 8. Step 2 r = ∂f/ ∂x = -2 s = ∂f/ ∂x ∂y = -1 t = ∂f/ ∂y = -2 Step 3 At (40, 40) rt - s² = (-2)(-2) – (-1) ² = 3 > 0 r = -2 < 0 Hence, f(x, y) is maximum at (40, 40).
- 9. Example 3 Find the points on the surface z²=xy+1 nearest to the origin. Also find that distance. Solution: Let p(x, y, z) be any point on the surface z² = xy + 1. Its distance from the origin is given by d² = x² + y² + z² Since p lines on the surface z² = xy + 1 d² = x² + y² + xy + 1 Let f(x, y) = x² + y² + xy + 1 Step 1 For extreme values , ∂f/ ∂x=0 2x+y=o ∂f/ ∂y=0 2y+x=0 Solving Eqs (1) and (2), x=0 , y=0
- 10. Step 2 r = ∂²f/ ∂x² = 2 s = ∂²f/ ∂x ∂y = 1 t = ∂² f/ ∂y² = 2 Step 3 At (0,0), r = 2, t = 2, s = 1 rt - s² = (2)(2) - 1² = 3 > 0 Also, r = 2 > 0 f(x, y) , i.e. d ² is minimum at (0,0) and hence d is minimum at (0,0). At (0,0), z²=xy+1=1 z=+1,z=-1 Hence, d is minimum at (0,0,1) and (0,0,-1). The points (0,0,1) and (0,0,-1) on the surface z² = xy + 1 are the nearest to the origin Minimum distance = 1.