Lesson 14: Derivatives of Logarithmic and Exponential Functions

The document summarizes the Toda-Yamamoto augmented Granger causality test. [1] The test allows checking for causality between integrated variables of different orders without needing to determine cointegration. It involves estimating a VAR model with maximal order of integration lags added. [2] The test procedure involves determining the order of integration (d), selecting the optimal lag length (k), setting the null and alternative hypotheses of no causality and causality, and calculating an F-statistic to test for causality. [3] If the F-statistic exceeds the critical value, the null of no causality is rejected, indicating causality between the variables.

The document discusses methods for solving dynamic stochastic general equilibrium (DSGE) models. It outlines perturbation and projection methods for approximating the solution to DSGE models. Perturbation methods use Taylor series approximations around a steady state to derive linear approximations of the model. Projection methods find parametric functions that best satisfy the model equations. The document also provides an example of applying the implicit function theorem to derive a Taylor series approximation of a policy rule for a neoclassical growth model.

The document discusses notes for a Calculus I class section on definite integrals. It provides announcements for upcoming quizzes and exams. The objectives are to compute definite integrals using Riemann sums, estimate integrals using techniques like the midpoint rule, and use properties of integrals. The professor outlines the topics to be covered, which include the definition of the definite integral as a limit of Riemann sums and properties of integrals. An example computes the integral of x from 0 to 3.

This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.

The document introduces perturbation methods as a way to solve functional equations that describe economic problems. It presents a basic real business cycle model as an example problem that can be solved using perturbation methods. Specifically, it: 1) Defines the real business cycle model as a functional equation system that is difficult to solve directly. 2) Proposes using perturbation methods by introducing a small perturbation parameter (the standard deviation of technology shocks) and solving the problem when this parameter equals zero. 3) Expands the decision rules as Taylor series in terms of the state variables and perturbation parameter to build a local approximation around the deterministic steady state. This leads to a system of equations that can be solved order-by-order for

The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trig functions like arcsin, arccos, and arctan and discusses their domains, ranges, and relationships to the original trig functions. It also provides examples of evaluating inverse trig functions at specific values.

The document discusses Euclidean space and linear algebra. It defines Euclidean space as the geometric spaces of the Euclidean plane and three-dimensional space. It describes how Euclidean n-space is the set of all n-tuples of real numbers and can be represented by Rn. It provides examples of R1 as the real line, R2 as the Euclidean plane, and R3 as three-dimensional space. It also discusses how systems of linear equations can have unique solutions, no solutions, or infinite solutions and how elementary row operations can be used to solve such systems, which can be represented using matrix notation.

This document provides an overview of integration by substitution. It begins with announcements about an upcoming review session, evaluations, and final exam. It then discusses the objectives and outline of the section, which are to transform integrals using substitutions, evaluate indefinite integrals using substitutions, and evaluate definite integrals using substitutions. An example is provided to illustrate how to use substitution to evaluate the indefinite integral of x/(x^2 + 1) by letting u = x^2 + 1. The solution uses a new notation of letting u = x^2 + 1 and du = 2x dx to rewrite the integral in terms of u.

This document is a master's thesis written in Chinese that investigates the existence and uniqueness of solutions to stochastic differential equations (SDEs) with Lévy noise and non-Lipschitz coefficients. It introduces Lévy processes and their properties, including the Lévy-Itô decomposition. It defines stochastic integration with respect to compensated Poisson processes and provides Itô's formula for Lévy diffusions. The thesis proves that if weak existence and pathwise uniqueness hold for an SDE with Lévy noise, then it has a unique strong solution. It establishes conditions on the coefficients that ensure infinite lifetime and pathwise uniqueness of the solution.

linear function, quadratic functions, cubic functions, power functions, transformations, and compositions.

This document discusses tensor factorizations and decompositions and their applications in data mining. It introduces tensors as multi-dimensional arrays and covers 2nd order tensors (matrices) and 3rd order tensors. It describes how tensor decompositions like the Tucker model and CANDECOMP/PARAFAC (CP) model can be used to decompose tensors into core elements to interpret data. It also discusses singular value decomposition (SVD) as a way to decompose matrices and reduce dimensions while approximating the original matrix.

Many problems in nature are expressible in terms of a certain differential equation that has a solution in terms of exponential functions. We look at the equation in general and some fun applications, including radioactivity, cooling, and interest.

This document contains lecture notes on exponential and logarithmic functions from a Calculus I class at New York University. The notes cover definitions of exponential functions, properties of exponential functions including laws of exponents, the natural exponential function e, and logarithmic functions. The objectives are to understand exponential functions, their properties, and laws of logarithms including the change of base formula.

This document contains lecture notes on exponential and logarithmic functions from a Calculus I class at New York University. The notes cover definitions of exponential functions, properties of exponential functions including laws of exponents, the natural exponential function e, and logarithmic functions. The objectives are to understand exponential functions, their properties, and laws of logarithms including the change of base formula.

This document summarizes sections 3.1-3.2 of a Calculus I course at New York University on exponential and logarithmic functions taught on October 20, 2010. It outlines definitions and properties of exponential functions, introduces the special number e and natural exponential function, and defines logarithmic functions. Announcements are made that the midterm exam is nearly graded and a WebAssign assignment is due the following week.

The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.

This document contains lecture notes from a Calculus I class at New York University on October 21, 2010. It discusses the objectives and outline for sections 3.1-3.2 on exponential and logarithmic functions. Key points include definitions of exponential functions, properties like ax+y = axay, and conventions for extending exponents to non-positive integers and irrational numbers.

This document is from a Calculus I class at New York University and covers derivatives of exponential and logarithmic functions. It includes objectives, an outline, explanations of properties and graphs of exponential and logarithmic functions, and derivations of derivatives. Key points covered are the derivatives of exponential functions with any base equal the function times a constant, the derivative of the natural logarithm function, and using logarithmic differentiation to find derivatives of more complex expressions.

This document contains lecture notes on exponential and logarithmic functions from a Calculus I class at New York University. It begins with announcements about a graded midterm exam and an upcoming homework assignment. It then provides objectives and an outline for sections 3.1 and 3.2 on exponential functions. The bulk of the document derives definitions and properties of exponential functions for various exponents through examples and conventions to preserve desired properties.

The document is notes from a Calculus I class covering exponential growth and decay. It discusses solving differential equations of the form y' = ky, with applications to population growth, radioactive decay, cooling, and interest. It provides examples of solving equations for various growth rates k, and uses an example of bacterial population growth over time to find the initial population from given later populations.

This document contains lecture notes from a Calculus I class at New York University. It discusses the definition of continuity for functions, examples of continuous and discontinuous functions, and properties of continuous functions like sums, products, and compositions of continuous functions being continuous. It also addresses trigonometric functions like sin, cos, tan, and sec being continuous on their domains.

This document contains lecture notes from a Calculus I class covering exponential and logarithmic functions. The notes discuss definitions and properties of exponential functions, including the number e and the natural exponential function. Conventions for rational, irrational and negative exponents are also defined. Examples are provided to illustrate approximating exponential expressions with irrational exponents using rational exponents. The objectives are to understand exponential functions, their properties, and apply laws of logarithms including the change of base formula.

No, this is not a function because the same input of 2 is mapped to two different outputs of 4 and 5. For a relation to be a function, each input must map to a unique output. V63.0121.021/041, Calculus I (NYU) Section 1.1 Functions September 8, 2010 17 / 33

This document is from a Calculus I class at New York University. It provides an overview of functions, including the definition of a function, different ways functions can be represented (formulas, tables, graphs, verbal descriptions), properties of functions like monotonicity and symmetry, and examples of determining domains and ranges of functions. It aims to help students understand functions and their representations as a foundation for calculus.

This document is from a Calculus I class at New York University and covers antiderivatives. It begins with announcements about an upcoming quiz. The objectives are to find antiderivatives of simple functions, remember that a function whose derivative is zero must be constant, and solve rectilinear motion problems. It then outlines finding antiderivatives through tabulation, graphically, and with rectilinear motion examples. The document provides examples of finding antiderivatives of power functions by using the power rule in reverse.

This document is from a Calculus I class at New York University and covers antiderivatives. It begins with announcements about an upcoming quiz. The objectives are to find antiderivatives of simple functions, remember that a function whose derivative is zero must be constant, and solve rectilinear motion problems. It then outlines finding antiderivatives through tabulation, graphically, and with rectilinear motion examples. Examples are provided of finding the antiderivative of power functions like x^3 through identifying the power rule relationship between a function and its derivative.

This document is from an NYU Calculus I class and outlines the topics of exponential growth and decay that will be covered in Section 3.4. It includes announcements about an upcoming quiz, objectives to solve differential equations involving exponential functions, and an outline of topics like modeling population growth, radioactive decay, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving simple differential equations and finding general solutions that involve exponential and logarithmic functions.

Many problems in nature are expressible in terms of a certain differential equation that has a solution in terms of exponential functions. We look at the equation in general and some fun applications, including radioactivity, cooling, and interest.

An antiderivative of a function is a function whose derivative is the given function. The problem of antidifferentiation is interesting, complicated, and useful, especially when discussing motion. This is the handout version to take notes on.

The document introduces deterministic and stochastic observers. Deterministic observers estimate states using a model and measurements, like the Luenberger observer. Stochastic observers, like the Kalman filter, also account for noise. The document discusses open-loop and closed-loop observer designs, how to select observer eigenvalues, and approaches for partial state estimation.

The exponential function is pretty much the only function whose derivative is itself. The derivative of the natural logarithm function is also beautiful as it fills in an important gap. Finally, the technique of logarithmic differentiation allows us to find derivatives without the product rule.

The document is a section from a Calculus I course at NYU from June 22, 2010. It discusses using the substitution method to evaluate indefinite integrals. Specifically, it provides an example of using the substitution u=x^2+3 to evaluate the integral of (x^2+3)^3 4x dx. The solution transforms the integral into an integral of u^3 du and evaluates it to be 1/4 u^4 + C.

The document is a lecture on inverse trigonometric functions from a Calculus I class at New York University. It defines inverse trigonometric functions as the inverses of restricted trigonometric functions, gives their domains and ranges, and discusses their derivatives. The document also provides examples of evaluating inverse trigonometric functions.

Implicit differentiation allows us to find slopes of lines tangent to curves that are not graphs of functions. Almost all of the time (yes, that is a mathematical term!) we can assume the curve comprises the graph of a function and differentiate using the chain rule.

This document summarizes a calculus lecture on linear approximations. It provides examples of using the tangent line to approximate the sine function at different points. Specifically, it estimates sin(61°) by taking linear approximations about 0 and about 60°. The linear approximation about 0 is x, giving a value of 1.06465. The linear approximation about 60° uses the fact that the sine is √3/2 and the derivative is √3/2 at π/3, giving a better approximation than using 0.

This document contains lecture notes on related rates from a Calculus I class at New York University. It begins with announcements about assignments and no class on a holiday. It then outlines the objectives of learning to use derivatives to understand rates of change and model word problems. Examples are provided, including an oil slick problem worked out in detail. Strategies for solving related rates problems are discussed. Further examples on people walking and electrical resistors are presented.

This document contains lecture notes on exponential growth and decay from a Calculus I class at New York University. It begins with announcements about an upcoming review session, office hours, and midterm exam. It then outlines the topics to be covered, including the differential equation y=ky, modeling population growth, radioactive decay including carbon-14 dating, Newton's law of cooling, and continuously compounded interest. Examples are provided of solving various differential equations representing exponential growth or decay. The document explains that many real-world situations exhibit exponential behavior due to proportional growth rates.

This document is from a Calculus I class lecture on L'Hopital's rule given at New York University. It begins with announcements and objectives for the lecture. It then provides examples of limits that are indeterminate forms to motivate L'Hopital's rule. The document explains the rule and when it can be used to evaluate limits. It also introduces the mathematician L'Hopital and applies the rule to examples introduced earlier.

The document provides an overview of curve sketching in calculus including objectives, rationale, theorems for determining monotonicity and concavity, and a checklist for graphing functions. It then gives examples of graphing cubic and quartic functions step-by-step, demonstrating how to analyze critical points, inflection points, and asymptotic behavior to create the curve. The examples illustrate applying differentiation rules to determine monotonicity from the derivative sign chart and concavity from the second derivative test.

This document is a section from a Calculus I course at New York University covering maximum and minimum values. It begins with announcements about exams and assignments. The objectives are to understand the Extreme Value Theorem and Fermat's Theorem, and use the Closed Interval Method to find extreme values. The document then covers the definitions of extreme points/values and the statements of the Extreme Value Theorem and Fermat's Theorem. It provides examples to illustrate the necessity of the hypotheses in the theorems. The focus is on using calculus concepts like continuity and differentiability to determine maximum and minimum values of functions on closed intervals.

This document is the notes from a Calculus I class at New York University covering Section 4.2 on the Mean Value Theorem. The notes include objectives, an outline, explanations of Rolle's Theorem and the Mean Value Theorem, examples of using the theorems, and a food for thought question. The key points are that Rolle's Theorem states that if a function is continuous on an interval and differentiable inside the interval, and the function values at the endpoints are equal, then there exists a point in the interior where the derivative is 0. The Mean Value Theorem similarly states that if a function is continuous on an interval and differentiable inside, there exists a point where the average rate of change equals the instantaneous rate of

This document discusses the definite integral and its properties. It begins by stating the objectives of computing definite integrals using Riemann sums and limits, estimating integrals using approximations like the midpoint rule, and reasoning about integrals using their properties. The outline then reviews the integral as a limit of Riemann sums and how to estimate integrals. It also discusses properties of the integral and comparison properties. Finally, it restates the theorem that if a function is continuous, the limit of Riemann sums is the same regardless of the choice of sample points.

The document summarizes the steps to solve optimization problems using calculus. It begins with an example of finding the rectangle with maximum area given a fixed perimeter. It works through the solution, identifying the objective function, variables, constraints, and using calculus techniques like taking the derivative to find critical points. The document then outlines Polya's 4-step method for problem solving and provides guidance on setting up optimization problems by understanding the problem, introducing notation, drawing diagrams, and eliminating variables using given constraints. It emphasizes using the Closed Interval Method, evaluating the function at endpoints and critical points to determine maximums and minimums.

The document is about calculating areas and distances using calculus. It discusses approximating areas of curved regions by dividing them into rectangles and letting the number of rectangles approach infinity. It provides examples of calculating areas of basic shapes like rectangles, parallelograms, and triangles. It then discusses Archimedes' work approximating the area under a parabola by inscribing sequences of triangles. The objectives are to compute areas using limits of approximating rectangles and to compute distances as limits of approximating time intervals.

- The document is about evaluating definite integrals and contains sections on: evaluating definite integrals using the evaluation theorem, writing antiderivatives as indefinite integrals, interpreting definite integrals as net change over an interval, and examples of computing definite integrals. - It discusses properties of definite integrals such as additivity and comparison properties, and provides examples of definite integrals that can be evaluated using known area formulas or by direct computation of antiderivatives.

Here are the key points about g given f: - g represents the area under the curve of f over successive intervals of the x-axis - As x increases over an interval, g will increase if f is positive over that interval and decrease if f is negative - The concavity (convexity or concavity) of g will match the concavity of f over each interval In summary, the area function g, as defined by the integral of f, will have properties that correspond directly to the sign and concavity of f over successive intervals of integration.

This document provides information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences at NYU. The course will include weekly lectures, recitations, homework assignments, quizzes, a midterm exam, and a final exam. Grades will be determined based on exam, homework, and quiz scores. The required textbook is available in hardcover, looseleaf, or online formats through the campus bookstore or WebAssign. Students are encouraged to contact the professor or TAs with any questions.

This document outlines information about a Calculus I course taught by Professor Matthew Leingang at the Courant Institute of Mathematical Sciences. It provides details on the course staff, contact information for the professor, an overview of assessments including homework, quizzes, a midterm and final exam. Grading breakdown is also included, as well as information on purchasing the required textbook and accessing the course on Blackboard. The document aims to provide students with essential logistical information to succeed in the Calculus I course.

This document contains lecture notes from a Calculus I class at New York University on September 14, 2010. The notes cover announcements, guidelines for written homework, a rubric for grading homework, examples of good and bad homework, and objectives for the concept of limits. The bulk of the document discusses the heuristic definition of a limit using an error-tolerance game approach, provides examples to illustrate the game, and outlines the path to a precise definition of a limit.

This document contains lecture notes on the concept of limit from a Calculus I course at New York University. It includes announcements about homework and deadlines. It then discusses guidelines for written homework assignments and a rubric for grading. The bulk of the document explains the concept of limit intuitively through an "error-tolerance game" and provides examples to illustrate the idea. It aims to build an informal understanding of limits before providing a precise definition.

This document is a section from a Calculus I course at New York University dated September 20, 2010. It discusses continuity of functions, beginning with definitions and examples of determining continuity. Key points covered include the definition of continuity as a function having a limit equal to its value, and theorems stating polynomials, rational functions, and combinations of continuous functions are also continuous. Trigonometric functions like sin, cos, tan, and cot are shown to be continuous on their domains. The document provides examples, explanations, and questions to illustrate the concept of continuity.

This document is from a Calculus I class at New York University and covers continuity. It provides announcements about office hours and homework deadlines. It then discusses the objectives of understanding the definition of continuity and applying it to piecewise functions. Examples are provided to demonstrate how to show a function is continuous at a point by evaluating the limit as x approaches the point and showing it equals the function value. The students are asked to determine at which other points the example function is continuous.

Sustainability requires ingenuity and stewardship. Did you know Pigging Solutions pigging systems help you achieve your sustainable manufacturing goals AND provide rapid return on investment. How? Our systems recover over 99% of product in transfer piping. Recovering trapped product from transfer lines that would otherwise become flush-waste, means you can increase batch yields and eliminate flush waste. From raw materials to finished product, if you can pump it, we can pig it.

accommodate the strengths, weaknesses, threats and opportunities of autonomous vehicles

This brochure gives introduction of MYIR Electronics company and MYIR's products and services. MYIR Electronics Limited (MYIR for short), established in 2011, is a global provider of embedded System-On-Modules (SOMs) and comprehensive solutions based on various architectures such as ARM, FPGA, RISC-V, and AI. We cater to customers' needs for large-scale production, offering customized design, industry-specific application solutions, and one-stop OEM services. MYIR, recognized as a national high-tech enterprise, is also listed among the "Specialized and Special new" Enterprises in Shenzhen, China. Our core belief is that "Our success stems from our customers' success" and embraces the philosophy of "Make Your Idea Real, then My Idea Realizing!"

The DealBook is our annual overview of the Ukrainian tech investment industry. This edition comprehensively covers the full year 2023 and the first deals of 2024.

This is the combined Sessions of ACE Atlassian Coimbatore event happened on 22nd June 2024 The session order is as follows: 1.AI and future of help desk by Rajesh Shanmugam 2. Harnessing the power of GenAI for your business by Siddharth 3. Fallacies of GenAI by Raju Kandaswamy

MuleSoft Meetup on APM and IDP

This is a powerpoint that features Microsoft Teams Devices and everything that is new including updates to its software and devices for May 2024

Recent advancements in the NIST-JARVIS infrastructure: JARVIS-Overview, JARVIS-DFT, AtomGPT, ALIGNN, JARVIS-Leaderboard

An invited talk given by Mark Billinghurst on Research Directions for Cross Reality Interfaces. This was given on July 2nd 2024 as part of the 2024 Summer School on Cross Reality in Hagenberg, Austria (July 1st - 7th)

Blockchain technology is transforming industries and reshaping the way we conduct business, manage data, and secure transactions. Whether you're new to blockchain or looking to deepen your knowledge, our guidebook, "Blockchain for Dummies", is your ultimate resource.

Have you noticed the OpenSSF Scorecard badges on the official Dart and Flutter repos? It's Google's way of showing that they care about security. Practices such as pinning dependencies, branch protection, required reviews, continuous integration tests etc. are measured to provide a score and accompanying badge. You can do the same for your projects, and this presentation will show you how, with an emphasis on the unique challenges that come up when working with Dart and Flutter. The session will provide a walkthrough of the steps involved in securing a first repository, and then what it takes to repeat that process across an organization with multiple repos. It will also look at the ongoing maintenance involved once scorecards have been implemented, and how aspects of that maintenance can be better automated to minimize toil.

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If you’ve ever had to analyze a map or GPS data, chances are you’ve encountered and even worked with coordinate systems. As historical data continually updates through GPS, understanding coordinate systems is increasingly crucial. However, not everyone knows why they exist or how to effectively use them for data-driven insights. During this webinar, you’ll learn exactly what coordinate systems are and how you can use FME to maintain and transform your data’s coordinate systems in an easy-to-digest way, accurately representing the geographical space that it exists within. During this webinar, you will have the chance to: - Enhance Your Understanding: Gain a clear overview of what coordinate systems are and their value - Learn Practical Applications: Why we need datams and projections, plus units between coordinate systems - Maximize with FME: Understand how FME handles coordinate systems, including a brief summary of the 3 main reprojectors - Custom Coordinate Systems: Learn how to work with FME and coordinate systems beyond what is natively supported - Look Ahead: Gain insights into where FME is headed with coordinate systems in the future Don’t miss the opportunity to improve the value you receive from your coordinate system data, ultimately allowing you to streamline your data analysis and maximize your time. See you there!

We all want to build applications that are blazingly fast. We also want to scale them to users all over the world. Can the two happen together? Can users in the slowest of environments also get a fast experience? Learn how we do this at Netflix: how we understand every user's needs and preferences and build high performance applications that work for every user, every time.

The lecture titled "Automating AppSec" delves into the critical challenges associated with manual application security (AppSec) processes and outlines strategic approaches for incorporating automation to enhance efficiency, accuracy, and scalability. The lecture is structured to highlight the inherent difficulties in traditional AppSec practices, emphasizing the labor-intensive triage of issues, the complexity of identifying responsible owners for security flaws, and the challenges of implementing security checks within CI/CD pipelines. Furthermore, it provides actionable insights on automating these processes to not only mitigate these pains but also to enable a more proactive and scalable security posture within development cycles. The Pains of Manual AppSec: This section will explore the time-consuming and error-prone nature of manually triaging security issues, including the difficulty of prioritizing vulnerabilities based on their actual risk to the organization. It will also discuss the challenges in determining ownership for remediation tasks, a process often complicated by cross-functional teams and microservices architectures. Additionally, the inefficiencies of manual checks within CI/CD gates will be examined, highlighting how they can delay deployments and introduce security risks. Automating CI/CD Gates: Here, the focus shifts to the automation of security within the CI/CD pipelines. The lecture will cover methods to seamlessly integrate security tools that automatically scan for vulnerabilities as part of the build process, thereby ensuring that security is a core component of the development lifecycle. Strategies for configuring automated gates that can block or flag builds based on the severity of detected issues will be discussed, ensuring that only secure code progresses through the pipeline. Triaging Issues with Automation: This segment addresses how automation can be leveraged to intelligently triage and prioritize security issues. It will cover technologies and methodologies for automatically assessing the context and potential impact of vulnerabilities, facilitating quicker and more accurate decision-making. The use of automated alerting and reporting mechanisms to ensure the right stakeholders are informed in a timely manner will also be discussed. Identifying Ownership Automatically: Automating the process of identifying who owns the responsibility for fixing specific security issues is critical for efficient remediation. This part of the lecture will explore tools and practices for mapping vulnerabilities to code owners, leveraging version control and project management tools. Three Tips to Scale the Shift Left Program: Finally, the lecture will offer three practical tips for organizations looking to scale their Shift Left security programs. These will include recommendations on fostering a security culture within development teams, employing DevSecOps principles to integrate security throughout the development

These fighter aircraft have uses outside of traditional combat situations. They are essential in defending India's territorial integrity, averting dangers, and delivering aid to those in need during natural calamities. Additionally, the IAF improves its interoperability and fortifies international military alliances by working together and conducting joint exercises with other air forces.

Performance budgets have been around for more than ten years. Over those years, we’ve learned a lot about what works, what doesn’t, and what we need to improve. In this session, Tammy revisits old assumptions about performance budgets and offers some new best practices. Topics include: • Understanding performance budgets vs. performance goals • Aligning budgets with user experience • Pros and cons of Core Web Vitals • How to stay on top of your budgets to fight regressions

Are you interested in dipping your toes in the cloud native observability waters, but as an engineer you are not sure where to get started with tracing problems through your microservices and application landscapes on Kubernetes? Then this is the session for you, where we take you on your first steps in an active open-source project that offers a buffet of languages, challenges, and opportunities for getting started with telemetry data. The project is called openTelemetry, but before diving into the specifics, we’ll start with de-mystifying key concepts and terms such as observability, telemetry, instrumentation, cardinality, percentile to lay a foundation. After understanding the nuts and bolts of observability and distributed traces, we’ll explore the openTelemetry community; its Special Interest Groups (SIGs), repositories, and how to become not only an end-user, but possibly a contributor.We will wrap up with an overview of the components in this project, such as the Collector, the OpenTelemetry protocol (OTLP), its APIs, and its SDKs. Attendees will leave with an understanding of key observability concepts, become grounded in distributed tracing terminology, be aware of the components of openTelemetry, and know how to take their first steps to an open-source contribution! Key Takeaways: Open source, vendor neutral instrumentation is an exciting new reality as the industry standardizes on openTelemetry for observability. OpenTelemetry is on a mission to enable effective observability by making high-quality, portable telemetry ubiquitous. The world of observability and monitoring today has a steep learning curve and in order to achieve ubiquity, the project would benefit from growing our contributor community.

Kief Morris rethinks the infrastructure code delivery lifecycle, advocating for a shift towards composable infrastructure systems. We should shift to designing around deployable components rather than code modules, use more useful levels of abstraction, and drive design and deployment from applications rather than bottom-up, monolithic architecture and delivery.

Is your patent a vanity piece of paper for your office wall? Or is it a reliable, defendable, assertable, property right? The difference is often quality. Is your patent simply a transactional cost and a large pile of legal bills for your startup? Or is it a leverageable asset worthy of attracting precious investment dollars, worth its cost in multiples of valuation? The difference is often quality. Is your patent application only good enough to get through the examination process? Or has it been crafted to stand the tests of time and varied audiences if you later need to assert that document against an infringer, find yourself litigating with it in an Article 3 Court at the hands of a judge and jury, God forbid, end up having to defend its validity at the PTAB, or even needing to use it to block pirated imports at the International Trade Commission? The difference is often quality. Quality will be our focus for a good chunk of the remainder of this season. What goes into a quality patent, and where possible, how do you get it without breaking the bank? ** Episode Overview ** In this first episode of our quality series, Kristen Hansen and the panel discuss: ⦿ What do we mean when we say patent quality? ⦿ Why is patent quality important? ⦿ How to balance quality and budget ⦿ The importance of searching, continuations, and draftsperson domain expertise ⦿ Very practical tips, tricks, examples, and Kristen’s Musts for drafting quality applications https://www.aurorapatents.com/patently-strategic-podcast.html