Calculus 2 topics - CALC 2 Midterm PREP - Topics New. 7 pages 2023/2024 None. 2023/2024 None. Save. Mat1322-practice Test 2 New. 2 pages 2022/2023 None. 2022/2023 None. Save. CALC 2 Practice Midterm Answers New. 8 pages 2020/2021 None. 2020/2021 None. Save. MAT 1322 - Fall 2019 - Kaimanovich - Final Exam Solutions ; …

 
Practice more questions on calculus class 11 and calculus class 12 topics such as limits and derivatives, integration using different methods, continuity etc. To learn more about calculus in Maths, …. Wood kitchens cabinets

Safety is an important topic for any organization, but it can be difficult to teach safety topics in an engaging and memorable way. Fortunately, there are a variety of creative met...To use integration by parts in Calculus, follow these steps: Decompose the entire integral (including dx) into two factors. Let the factor without dx equal u and the factor with dx equal dv. Differentiate u to find du, and integrate dv to find v. Use the formula: Evaluate the right side of this equation to solve the integral.Students will apply their knowledge to solve problems concerning topics that include, but are not limited to, techniques of integration, calculation of ...1.1. Limits Definition 1.1 A function f: R →R is continuous at aif lim x→a f(x) = f(a). fis called continuous if it is continuous at every point in its domain. Theorem 1.2 Any function which is the quotient of functions made up of powers of x, sines, cosines, arcsines, arctangents, exponentials and/or logarithms is continuous everywhere …Outline of calculus. Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is ...We would like to show you a description here but the site won’t allow us. Get good at integration. You’re gonna do a lot of it. Make sure you understand substitution techniques. Calc 2 focuses on new integration techniques and a lot of them involve new types of substitutions. I also recommend learning how to visualize problems if you’re not good at that either. Calculus II (4 units). Course Outline. Sections. Topics. # of weeks. 2.1–2.7. Applications of Integration: Areas between curves; vol- umes of revolution ... Its called Taylor Series. Sequences and series were the part of calc 2 that I found to be more intuitive. The rest of the course was having crazy integrals thrown at you and having to figure out how to solve them. Sequences and Series are a bit difficult to wrap your head around the first time they're thrown at you. In a poll of 140 past and present calculus students, the overwhelming consensus ( 72% of pollers) is that Calculus 3 is indeed the hardest Calculus class. This is contrary to the popular belief that Calculus 2 is the hardest Calculus class. So, Calculus 3 is the hardest Calculus class. That question is answered. Calculus II Sample Syllabus. website creator Please note that is just a sample syllabus, actual syllabi for the various sections of the course will likely be different each semester. Different instructors may choose somewhat different material. The number of class sessions varies between fall and spring semesters, Monday-Wednesday and Tuesday ... DMAT 263 - STEM Calculus II - Syllabus of Topics 1. Getting Started 1.1 Email and Chat 1.2 Learning About the Course 1.3 Required Hardware 1.4 Software Fundamentals 2. ... Calculus 2 (Calculus II) is a notoriously long course, with lots of topics of varying difficulty.Semester 2 - Dual-Delivery. Fees. Look up fees. This subject will extend knowledge of calculus from school. Students are introduced to hyperbolic functions and their inverses, the complex exponential and functions of two variables. Techniques of differentiation and integration will be extended to these cases. Students will be exposed …BC can be viewed as an offshoot of Calculus AB since all of the topics in Calculus AB (single-variable calculus) are also included in Calculus BC, plus some. Unlike courses like Algebra I and Algebra II, Calculus AB (Advanced Placement Calculus) and Calculus BC do not have to be taken in a specific sequence.Math 1220 | Calculus II. These lecture videos are organized in an order that corresponds with the current book we are using for our Math1220, Calculus 2, courses ( Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson ). We have numbered the videos for quick reference …Calculus 2 also emphasizes applications of integration, which allow me to calculate: Areas between curves; Volumes of solids (via methods like discs and shells) …Learn Calculus 2 in this full college course.This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check...1.1. Limits Definition 1.1 A function f: R →R is continuous at aif lim x→a f(x) = f(a). fis called continuous if it is continuous at every point in its domain. Theorem 1.2 Any function which is the quotient of functions made up of powers of x, sines, cosines, arcsines, arctangents, exponentials and/or logarithms is continuous everywhere …This is an introductory pure mathematics course in calculus that is divided into the following topics: Integral Calculus; Techniques of integration ...The AP Calculus BC Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes … Calculus 2 is a course notes pdf for students who have completed Calculus 1 at Simon Fraser University. It covers topics such as integration, differential equations, sequences and series, and power series. The pdf is written by Veselin Jungic, a mathematics professor at SFU, and contains examples, exercises, and solutions. Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include just because I wanted to.The AP Calculus BC Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes …Applying differential calculus. Optimization is used to find the greatest/least value (s) a function can take. This can involve creating the expression first. Also find the rate of change by ...Calculus 2 (MAST10006) Undergraduate level 1Points: 12.5 Dual-Delivery (Parkville) and On Campus (Parkville) Undergraduate programs will be delivered on campus. Graduate programs will mainly be delivered on campus, with dual-delivery and online options available to a select number of subjects within some programs. Calculus 2 is a bit of a mixed assortment of mathematical topics. The beginning of Calculus 2 deals with building on those aforementioned fundamentals of derivatives you should have touched on in Calculus 1. You'll spend your early time formalizing antiderivatives, Riemann sums, the fundamental theorem, etc. Calculus was hard for me until I learned how to visualize things. Learning calculus only by writing symbols and solving problems with many $\varepsilon$'s will not make anyone understand it. If you learn to visualize all the basic concepts as limit, derivative, integration, etc. then the symbolic part is a lot easier. Equation of a circle = (x − h) 2 + (y − k) 2 = r 2, with the center at (h, k) Equation of a parabola is: y = a(x - h) 2 + k or x = a(y - k) 2 + h; How Hard is Precalculus? Precalculus is a very vast subject that includes many topics. However, by building crystal clear mathematical concepts and regular revision of topics, precalculus will be ... Calculus II | Lumen LearningCalculus 2 (MAST10006) Undergraduate level 1Points: 12.5 Dual-Delivery (Parkville) and On Campus (Parkville) Undergraduate programs will be delivered on campus. Graduate programs will mainly be delivered on campus, with dual-delivery and online options available to a select number of subjects within some programs.Math 142 Calculus II Sample Syllabus. Spring 2012. Instructor: Office: Phone: Email: Webpage: Office Hours: Course Description: Standard second-semester ...As the world continues to evolve and new challenges arise, so too do the research topics pursued by PhD students. These individuals are at the forefront of innovation and discovery...For problems 12 – 14 write down a set of parametric equations for the given equation that meets the given extra conditions (if any). y = 3x2−ln(4x +2) y = 3 x 2 − ln. ⁡. ( 4 x + 2) Solution. x2 +y2 = 36 x 2 + y 2 = 36 and the parametric curve resulting from the parametric equations should be at (6,0) ( 6, 0) when t = 0 t = 0 …Calculus 2 - Lecture notes 1; Related Studylists second sem Physics Que. Preview text. Calculus II. Integral Calculus. Lecture Notes. ... MATH 126 Exercise 2 - MATH 126 PAST QUESTIONS. Calculus 2 100% (2) More from: Lord Caesar. More from: LC. LC. Lord Caesar 999+ impact 999+ University of Ghana. Discover more. 137.Basically, you'll have single-variable then multi-variable calculus treaments so you'll want a 2 volume set when you're ready. I would suggest Richard Courant's work along with Tom Apostol. Linear Algebra - I don't know why this subject doesn't get more attention, maybe because it's the actual key to a lot of fields, like computer …Learn Calculus 1 in this full college course.This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check...The way my professor taught calc 2 was basically you need to know how to do every computation without a calculator, and barely touched on the conceptual side. So knowing u sub, by parts, trig sub, and partial fractions like the back of your hand was needed to pass the class, and also other topics like volumes and series.Calculus 1 8 units · 171 skills. Unit 1 Limits and continuity. Unit 2 Derivatives: definition and basic rules. Unit 3 Derivatives: chain rule and other advanced topics. Unit 4 Applications of derivatives. Unit 5 Analyzing functions. Unit 6 Integrals. Unit 7 Differential equations. Unit 8 Applications of integrals.Here are a set of practice problems for the Series and Sequences chapter of the Calculus II notes. If you’d like a pdf document containing the solutions the download tab above contains links to pdf’s containing the solutions for the full book, chapter and section. At this time, I do not offer pdf’s for solutions to individual problems.Techniques of integration. Further applications. Plane analytic geometry. Polar coordinates and parametric equations. Infinite series, including power series.Strategies to Test an Infinite Series for Convergence. Harmonic Series. Indeterminate Forms and de L'hospital's Rule. Partial Sums of Infinite Series. Watch the best videos and ask and answer questions in 148 topics and 19 chapters in Calculus. Get smarter in Calculus on Socratic.Calculus 2 (MAST10006) Undergraduate level 1Points: 12.5 Dual-Delivery (Parkville) and On Campus (Parkville) Undergraduate programs will be delivered on campus. Graduate programs will mainly be delivered on campus, with dual-delivery and online options available to a select number of subjects within some programs.Students will apply their knowledge to solve problems concerning topics that include, but are not limited to, techniques of integration, calculation of ...Figure 5.3.1: By the Mean Value Theorem, the continuous function f(x) takes on its average value at c at least once over a closed interval. Exercise 5.3.1. Find the average value of the function f(x) = x 2 over the interval [0, 6] and find c such that f(c) equals the average value of the function over [0, 6]. Hint.Desquam-X Wash (Topical) received an overall rating of 10 out of 10 stars from 1 reviews. See what others have said about Desquam-X Wash (Topical), including the effectiveness, eas...Many STEP 2 questions will expect you to be fluent with A-Level Calculus techniques, even if they do not look like "Calculus questions" at first glance. Using Calculus to find maxima and minima is a particularly widespread technique. There are 5 questions in this assignment: Question 5 is a STEP 1 question which tests the same ideas as Question ...Unit 1 Limits and continuity. Unit 2 Derivatives: definition and basic rules. Unit 3 Derivatives: chain rule and other advanced topics. Unit 4 Applications of derivatives. Unit 5 Analyzing functions. Unit 6 Integrals. Unit 7 Differential equations. Unit 8 Applications of integrals. Course challenge. Calculus also provides important tools in understanding functions and has led to the development of new areas of mathematics including real and complex analysis, topology, and non-euclidean geometry. The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of several variables. Calculus II ; Session 1, Review of Calculus I ; Session 2, Limit and continuity of two-variable functions ; Session 3, Partial derivative ; Session 4 ...This course covers a range of topics related to calculus 2, including the natural log function, derivatives and integrals of exponential functions, inverse trigonometric …Calculus 2. Calculus 2 (integral calculus) might have you start with FTC (the Fundamental Theorem of Calculus) and then work through integration techniques. Here you will learn how to calculate the area under a curve and between two curves. This is solved by using integrals. Typical Topic in Calc 2: The IntegralSafety is an important topic for any organization, but it can be difficult to teach safety topics in an engaging and memorable way. Fortunately, there are a variety of creative met...This text comprises a three–text series on Calculus. The first part covers material taught in many “Calc 1” courses: limits, derivatives, and the basics of integration, found in Chapters 1 through 6.1. The second text covers material often taught in “Calc 2:” integration and its applications, along with an introduction to …Calculus II (MATH 102) ... Calculus II (MATH102) · Differential Equations · Applied Mathematics for Engineers ... Topics in vector calculus. Prerequisites: MATH101.There are 5 modules in this course. The focus and themes of the Introduction to Calculus course address the most important foundations for applications of mathematics in science, engineering and commerce. The course emphasises the key ideas and historical motivation for calculus, while at the same time striking a …MAT 176: Calculus II Syllabus. MAT176 Calculus II: 4 hours, 4 credits. Riemann sums, logarithmic and exponential functions, integration of functions ...Limits intro. Google Classroom. Limits describe how a function behaves near a point, instead of at that point. This simple yet powerful idea is the basis of all of calculus. To understand what limits are, let's look at an example. We start with the function f ( x) = x + 2 .Only Wolfram Problem Generator directly integrates the popular and powerful Step-by-step Solutions from Wolfram|Alpha. You can use a single hint to get unstuck, or explore the entire math problem from beginning to end. Online practice problems for math, including arithmetic, algebra, calculus, linear algebra, number theory, and statistics.DMAT 263 - STEM Calculus II - Syllabus of Topics 1. Getting Started 1.1 Email and Chat 1.2 Learning About the Course 1.3 Required Hardware 1.4 Software Fundamentals 2. ... Calculus 2 (Calculus II) is a notoriously long course, with lots of topics of varying difficulty.OpenStax offers free college textbooks for all types of students, making education accessible & affordable for everyone. Browse our list of available subjects!The AP Calculus BC Exam has consistent question types, weighting, and scoring guidelines every year, so you and your students know what to expect on exam day. Section I: Multiple Choice. 45 Questions | 1 Hour 45 minutes | 50% of Exam Score. Part A: 30 questions; 60 minutes (calculator not permitted). Part B: 15 questions; 45 minutes …BASIC TOPICS - CALCULUS . These booklets are suitable for . students covering the first year (AS) Calculus material, of a two year course in A Level mathematics. revising/introducing Calculus to undergraduate students in degrees not requiring A …See MATH 1552, 1553, 1554, 1564. Concludes the treatment of single variable calculus, and begins linear algebra; the linear basis of the multivariable theory. The first 1/3 of this course covers more advanced single variable calculus. The remaining 2/3 is an introduction to linear algebra, the theory of linear equations in several variables.The definition of a limit in calculus is the value that a function gets close to but never surpasses as the input changes. Limits are one of the most important aspects of calculus,...Calculus II Sample Syllabus. website creator Please note that is just a sample syllabus, actual syllabi for the various sections of the course will likely be different each semester. Different instructors may choose somewhat different material. The number of class sessions varies between fall and spring semesters, Monday-Wednesday and Tuesday ...The units feature the study material you will learn in your AP Calculus BC course. Although the curriculum for AP Calculus BC is similar to that of the AP Calculus AB course curriculum, BC contains two additional units (Units 9 and 10), plus some extra topics in Units 6 to 8. We’ll discuss these extra units in detail, but below is a table to ...Calculus A-Level Maths Revision section covering: Differentiation From First Principles, Differentiation, Tangents and Normals, Uses of Differentiation, The Second Derivative, Integration, Area Under a Curve Exponentials and Logarithms, The Trapezium Rule, Volumes of Revolution, The Product and Quotient Rules, …Learning Objectives. 4.1.1 Identify the order of a differential equation.; 4.1.2 Explain what is meant by a solution to a differential equation.; 4.1.3 Distinguish between the general solution and a particular solution of a differential equation.; 4.1.4 Identify an initial-value problem.; 4.1.5 Identify whether a given function is a solution to a …Our Calculus 2 tutorials are comprehensive, which means that we can answer any Calculus 2 questions that you may have. Whether it be Riemann Sum, Trig substitution, Alternating series test, Integral of trig functions, or P series test, StudyPug will provide answers you seek. Our Calculus 2 practice is available immediately after each Calculus …MATH 1226 is a four-credit second-semester calculus course that is included in the Pathways curriculum for Quantitative and Computational Thinking. Topics of study include techniques and applications of integration, Trapezoidal and Simpson’s rules, improper integrals, sequences and series, power series, parametric curves and polar coordinates.Calculus II | Lumen LearningMultivariable Calculus. In Mathematics, multivariable calculus or multivariate calculus is an extension of calculus in one variable with functions of several variables. The differentiation and integration process involves multiple variables, rather than once. Let us discuss the definition of multivariable calculus, basic concepts covered in ...Calculus III is a course that covers topics such as vectors, surfaces, multivariable functions, integration, and differential equations. Lumen Learning offers an online, interactive, and affordable way to learn calculus with engaging examples, exercises, and videos. Whether you need to review or advance your skills, this course will help you …Active Calculus is different from most existing calculus texts in at least the following ways: the text is freely readable online in HTML format and is also available for in PDF; in the electronic format, graphics are in full color and there are live links to java applets; version 2.0 now contains WeBWorK exercises in each chapter, which are …Graphing Trigonometric Functions with Critical Points. Graphing Trigonometric Functions with Translations and Asymptotes. Graphing Sine and Cosine. Translations of Sinusodial Graphs. Watch the best videos and ask and answer questions in 164 topics and 35 chapters in Precalculus. Get smarter in Precalculus on Socratic.The word Calculus comes from Latin meaning "small stone", Because it is like understanding something by looking at small pieces. Differential Calculus cuts something into small pieces to find how it changes. Integral Calculus joins (integrates) the small pieces together to find how much there is. Read Introduction to Calculus or "how fast right ...Its called Taylor Series. Sequences and series were the part of calc 2 that I found to be more intuitive. The rest of the course was having crazy integrals thrown at you and having to figure out how to solve them. Sequences and Series are a bit difficult to wrap your head around the first time they're thrown at you.respectively. While ideas related to calculus had been known for some time (Archimedes' method of exhaustion was a form of calculus), it was not until the independent work of Newton and Leibniz that the modern elegant tools and ideas of calculus were developed. Even so, many years elapsed until the subject was put on a …Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral …Calculus is the mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizations of arithmetic operations.. Originally called infinitesimal calculus or "the calculus of infinitesimals", it has two major branches, differential calculus and integral …Calculus 1. 17,100 possible mastery points. Mastered. Proficient. Familiar. Attempted. Not started. Quiz. Unit test. Course challenge. Test your knowledge of the skills in this …The 6 Best Online Calculus Tutoring Services of 2024. Best Overall: Wyzant. Best Value: Skooli. Best for on-the-Go: Varsity Tutors. Best for Quick Homework Help: Chegg. Best for Students With Special Needs: SpecialEdTutoring.com. Best for Advanced Topics: Princeton Review.Unit 1 Limits and continuity. Unit 2 Derivatives: definition and basic rules. Unit 3 Derivatives: chain rule and other advanced topics. Unit 4 Applications of derivatives. Unit 5 Analyzing functions. Unit 6 Integrals. Unit 7 Differential equations. Unit 8 Applications of integrals. Course challenge.Figure 5.3.1: By the Mean Value Theorem, the continuous function f(x) takes on its average value at c at least once over a closed interval. Exercise 5.3.1. Find the average value of the function f(x) = x 2 over the interval [0, 6] and find c such that f(c) equals the average value of the function over [0, 6]. Hint.Many STEP 2 questions will expect you to be fluent with A-Level Calculus techniques, even if they do not look like "Calculus questions" at first glance. Using Calculus to find maxima and minima is a particularly widespread technique. There are 5 questions in this assignment: Question 5 is a STEP 1 question which tests the same ideas as Question ... With philanthropic support, this book is used in 1,078 classrooms, saving students 45,923,889 dollars this school year. Learn more about our impact and how you can help. Study calculus online free by downloading Volume 2 of OpenStax's college Calculus textbook and using our accompanying online resources.

This calculus 2 final exam review covers topics such as finding the indefinite integral using integration techniques such as integration by parts and trig su.... New jersey drive movie

calculus 2 topics

2. Calculus 1. Calculus consists of topics mainly focusing on differential calculus and similar concepts like limits and continuity. Some topics under Calculus 1 are, Limits; Derivatives; Applications of Derivatives; 3. Calculus 2. Calculus 2 is all about the mathematical study of change that occurred during the …Oct 9, 2023 · The Calculus III notes/tutorial assume that you've got a working knowledge Calculus I, including limits, derivatives and integration. It also assumes that the reader has a good knowledge of several Calculus II topics including some integration techniques, parametric equations, vectors, and knowledge of three dimensional space. CALCULUS – PAST PAPERS (QUESTIONS & SOLUTIONS) November 2008. Compiled by Navan Mudali NicZenDezigns Page 2 of 121. Compiled by Navan Mudali ... (2) 11.2 Prove that the daughter's land will have a maximum area if she chooses P at the midpoint of MN. (6) [8] x y O T P(x; y) R M (a; 0)Topics include definite and indefinite integrals; the fundamental theorem of calculus, methods of integration; numerical approximation of definite integrals; ...Calculus Questions with Answers (1). The uses of the first and second derivative to determine the intervals of increase and decrease of a function, the maximum and minimum points, the interval (s) of concavity and points of inflections are discussed. Calculus Questions with Answers (2). The behaviors and properties of functions, first ...For problems 12 – 14 write down a set of parametric equations for the given equation that meets the given extra conditions (if any). y = 3x2−ln(4x +2) y = 3 x 2 − ln. ⁡. ( 4 x + 2) Solution. x2 +y2 = 36 x 2 + y 2 = 36 and the parametric curve resulting from the parametric equations should be at (6,0) ( 6, 0) when t = 0 t = 0 …Welcome to my math notes site. Contained in this site are the notes (free and downloadable) that I use to teach Algebra, Calculus (I, II and III) as well as Differential Equations at Lamar University. The notes contain the usual topics that are taught in those courses as well as a few extra topics that I decided to include …Calculus II (4 units). Course Outline. Sections. Topics. # of weeks. 2.1–2.7. Applications of Integration: Areas between curves; vol- umes of revolution ... Equation of a circle = (x − h) 2 + (y − k) 2 = r 2, with the center at (h, k) Equation of a parabola is: y = a(x - h) 2 + k or x = a(y - k) 2 + h; How Hard is Precalculus? Precalculus is a very vast subject that includes many topics. However, by building crystal clear mathematical concepts and regular revision of topics, precalculus will be ... This course is a study of integral calculus, parametric equations and series. Compared with Math 1910, this course offers a more in-depth concentration into ... Calculus II Sample Syllabus. website creator Please note that is just a sample syllabus, actual syllabi for the various sections of the course will likely be different each semester. Different instructors may choose somewhat different material. The number of class sessions varies between fall and spring semesters, Monday-Wednesday and Tuesday ... Calculus 2 is a course notes pdf for students who have completed Calculus 1 at Simon Fraser University. It covers topics such as integration, differential equations, sequences …2.1 Areas between Curves; 2.2 Determining Volumes by Slicing; 2.3 Volumes of Revolution: Cylindrical Shells; 2.4 Arc Length of a Curve and Surface Area; 2.5 Physical Applications; 2.6 Moments and Centers of Mass; 2.7 Integrals, Exponential Functions, and Logarithms; 2.8 Exponential Growth and Decay; 2.9 Calculus of the Hyperbolic FunctionsLearn Calculus 2 in this full college course.This course was created by Dr. Linda Green, a lecturer at the University of North Carolina at Chapel Hill. Check...Students will apply their knowledge to solve problems concerning topics that include, but are not limited to, techniques of integration, calculation of ...3 days ago · In general, "a" calculus is an abstract theory developed in a purely formal way. "The" calculus, more properly called analysis (or real analysis or, in older literature, infinitesimal analysis), is the branch of mathematics studying the rate of change of quantities (which can be interpreted as slopes of curves) and the length, area, and volume of objects. The calculus is sometimes divided into ... We would like to show you a description here but the site won’t allow us.Calculus 2 Online Lessons. There are online and hybrid sections of Math 1152 where the students have online, interactive lessons for each topic instead of the traditional in-person lectures. To benefit all Math 1152 students, the MSLC is making these online, interactive lessons available on their website to all students..

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