# Multivariable Calculus Ppt

3 Extrema of Multivariable Functions Question 1: What is a relative extrema and saddle point? Question 2: How do you find the relative extrema of a surface? In an earlier chapter, you learned how to find relative maxima and minima on functions of one variable. See the complete profile on LinkedIn and discover Zachary’s. If we combine the elements of each, then we can form“vector– valued functions of many variables”. 9: Change of Variables in Multiple Integralsin Multiple Integrals Monday, November 24 andMonday, November 24 and Tuesday, November 25, 2008Tuesday, November 25, 2008. The following are lectures for Calculus III - Multivariable. 2 Limits and Continuity In this section, we will learn about: Limits and continuity of various types of functions. 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ORGStudent Solutions Manual For Calculus ePubDownload Student Solutions Manual For Calculus ePub Ebook PDF:Student Solutions Manual For Calculus This book list for those who looking for to read and enjoy the Student Solutions. Learning outcomes. It is easy to understand and easy to implement. Multivariable Calculus (Stewart) by James Stewart difference between 8th and 7th editions; full length table of contents. A little suffering is good for youand it helps you learn. Inequalities questions for your custom printable tests and worksheets. Find PowerPoint Presentations and Slides using the power of XPowerPoint. The power-point slides should be put up on the web-site of. The area A of the rectangle is given by A = W L. There are still more general functions than those two or three types above. We'll call it R. 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Calculus is a branch of mathematics containing limits, derivatives, integrals and functions. Solving Trigonometric Equations She Loves Math. A Primeron Tensor Calculus 1 Introduction In physics, there is an overwhelming need to formulate the basic laws in a so-called invariant form; that is, one that does not depend on the chosen coordinate system. Partial derivatives are derivatives in multivariable functions, BUT WITH RESPECT TO ONE VARIABLE. Practical Applications : QSRP - Chapter 17 7 Practical Applications Manufacturing setting Produce 2 or more products Joint-cost function Marginal cost wrt each product Examples 1 & 3 from p. Digital Art and Tables Use this material to help teach your course. Diffeial Equations Math100 Revision Exercises Resources. Depending on your job as an EE, you will use calculus with a frequency ranging from every day, to never at all. Zachary has 4 jobs listed on their profile. Moreover, it is an exciting and beautiful subject in its own right, a true adventure in many dimensions. – Definitions, proofs, problem solving •Both differential and integral calculusare important and useful. 4 Green’s The-orem 15. The change in Calculus I also forced major changes to Calculus II. 10 GRADIENT OF ASCALARSuppose is the temperature at ,and is the temperature atas shown. The following Exploration allows you to approximate the area under various curves under the interval $[0, 5]$. 7) Our goal is to now ﬁnd maximum and/or minimum values of functions of several variables, e. Bressoud, Macalester College. Covers multivariable calculus, Allowed file types: gif jpg jpeg png txt rtf html pdf doc docx odt ppt pptx odp xls xlsx ods xml bz2 dmg gz jar rar sit tar zip. of 5 stars Calculus 6th edition by Edwards and Penney. Section 1-4 : Quadric Surfaces. analysis, topology, diﬀerential equations, Lie groups) and physics (e. Thomas, Jr. If you continue browsing the site, you agree to the use of cookies on this website. Single variable derivatives are the rate of change in one dimension. These websites will give you an indication of the current market value Step 4: Techniques for getting the best deal For me, I needed to find deals on four books: University Physics ($241. You must enable JavaScript in order to use this site. If I have some region-- so this is my region right over here. The applet is used with permission. Success! A copy of this quiz is in your dashboard. You may click on either the VIDEO link or the YouTube link, whichever works better for you. This book is a revised and expanded version of the lecture notes for Basic Calculus and other similar courses o ered by the Department of Mathematics, University of Hong Kong, from the ﬁrst semester of the academic year 1998-1999 through the second semester of 2006-2007. College Algebra: This library of 20 questions in PowerPoint format was developed by Mark Schlatter at Centenary College. 1 Cell References 5 0. Awards for Flash and Math Applets. DOWNLOAD HERE Precalculus RonLarson, Robert Hostetler,Jan 26, 2006, Mathematics, 1056 pages. 15 LAPLACIAN OF A SCALAR 2. Multivariable Calculus Sections 001-008 Syllabus Page: General Information Grading and Policies Homeworks - Exams Back Main page: Lecture Slides Week 01 Handout Lecture Week 02 Handout Lecture Week 03 Handout Lecture Week 04 Handout Lecture Week 05 Handout Lecture Week 06 Handout Lecture. These are the books for those you who looking for to read the Multivariable Calculus, try to read or download Pdf/ePub books and some of authors may have disable the live reading. The sums of step 5 are the Riemann sums that approximate the integral. Differentiation/Basics of Differentiation/Exercises Navigation : Main Page · Precalculus · Limits · Differentiation · Integration · Parametric and Polar Equations · Sequences and Series · Multivariable Calculus & Differential Equations · Extensions · References. " Includes bibliographical references and index. TWO PARTS IN THIS LECTURE 1. 1a (pt 2) - The Calculus of Parametric Equations Sect 11. Multivariate Statistics 1. For details on all of the above, visit our online catalog for Calculus or Calculus, Early Transcendentals. The focus lies mainly on acquiring an understanding of the principles and ideas underlying the concept of ‘tensor’. Vectors in Three Dimensional Space. Course Description The course emphasizes in understanding of basic concepts of calculus including limits, the derivative, the integral,. Lecture 10 Optimization problems for multivariable functions Local maxima and minima - Critical points (Relevant section from the textbook by Stewart: 14. Test Bank PTB Classroom Project Worksheets Answers PDF PPT Concept Tests. 2 Limits and Continuity In this section, we will learn about: Limits and continuity of various types of functions. Harold’s Calculus Notes Cheat Sheet 17 November 2017 AP Calculus Limits Definition of Limit Let f be a function defined on an open interval containing c and let L. Read 24 reviews from the world's largest community for readers. The most important applications of multivariable integration to economics and finance are in statistics, especially expectations with multivariate probabilities. 18) is often taken as a de nition for the gamma function ( z). Classroom Voting Questions: Multivariable Calculus This library contains questions from Mark Schlatter, ConcepTests to Accompany Calculus, by Hughes-Hallett et al, and others we have written ourselves. The Changing Face of Calculus: First-Semester Calculus as a High School Course *This article will appear in the August/September issue of FOCUS. market-leadingtext continues. Our solutions are written by Chegg experts so you can be assured of the highest quality!Calculus Single and Multivariable Solutions Manual. NetTutor is research‐based and has a rich history of providing online tutoring and academic support to education institutions in a variety of disciplines and academic programs. In particular, calculus gave a clear and precise definition of infinity, both in the case of the. We will assume you are familiar with the basics of partial derivatives, including the. The pioneers were Isaac Newton (1642-1737) and Gottfried Wilelm Leibniz (1646-1716). edu (Many of the original photos are by Vickie Kelly). A two-dimensional vector ﬁeld is a function f that maps each point (x,y) in R2 to a two-dimensional vector hu,vi, and similarly a three-dimensional vector ﬁeld maps (x,y,z) to hu,v,wi. View Multivariable Calculus PPTs online, safely and virus-free! Many are downloadable. My goal for this page is to be the ultimate resource for solving limits. Come to Sofsource. So, first of all we have operators and functions that are of considerable importance in physics and engineering. In those sections, we used the first derivative to find critical numbers. Bressoud, Macalester College. 1 Vector Fields This chapter is concerned with applying calculus in the context of vector ﬁelds. 4 Green's The-orem 15. Head of School Commendation. A Primeron Tensor Calculus 1 Introduction In physics, there is an overwhelming need to formulate the basic laws in a so-called invariant form; that is, one that does not depend on the chosen coordinate system. Vector Calculus 16. teacherpress. MULTIPLE INTEGRATION MATH23 MULTIVARIABLE CALCULUS GENERAL OBJECTIVE At the end of the lesson the students are. 1 Snell's Law Warm-up problem: You are standing at point (x1,y1) on the beach and you want to get to a point (x2,y2) in the water, a few meters oﬀshore. Textbook: Stewart. Digital Art and Tables Use this material to help teach your course. Differential Calculus Partial derivatives Introduction to partial derivatives. Visualization of 3D Mathematics. Laplace transform function, table, propertiesand examples. 02 Multivariable Calculus, Fall 2007 MIT OpenCourseWare Lec 2 | MIT 18. Preliminaries 1 0. This document is a sketch of what occurs in lecture. If we combine the elements of each, then we can form“vector– valued functions of many variables”. Where many texts present a general theory of calculus followed by substantial. This document is a sketch of what occurs in lecture. A function for which every element of the range of the function corresponds to exactly one element of the domain. The Citadel has Practice Problems and Solutions for the Placement Test for Calculus I/Precalculus. Multivariable_Calculus - authorSTREAM Presentation. Download with Google Download with Facebook or download with email. The worksheets are presented in two levels of difficulty. From here takes a little math trickery to solve for β… Slope (beta coefficient) = Intercept= Regression line always goes through the point: In correlation, the two variables are treated as equals. ( means "is a subset of. More Calculus Quizzes. Chapter 12 (Vectors and the Geomery of Space). Oct 18, 2019- Student Solutions Manual Chapters 10-17 for Stewart's Multivariable Calculus 8th (eBook Rental). We’ll start with straight lines, then expand the concept. can take them or opt out. The ideas of partial derivatives and multiple integrals are not too di erent from their single-variable coun-terparts, but some of the details about manipulating them are not so obvious. 2 Population Versus Sample 2 1. Calculus is an essential tool in many sciences. So, let's start this discussion off with a function of two variables, \(z = f\left( {x,y} \right)\). Multivariable Calculus 515Multivariable Calculus 515 16. Exercises and Problems in Calculus John M. Exploring Multivariable Calculus: Paul Seeburger's website for exploring calculus visually. Notes on Multivariable Calculus Summary and Exercise are very important for perfect preparation. We rst list several results you should know and then many review problems, which are followed by detailed solutions. Calculus, 11th edition, by Larson and Edwards carefully integrates engaging and challenging content with technology products for successful teaching and learning, ensuring that the exercise sets are rigorous and relevant. Jeff Morgan Department of Mathematics University of Houston. MIT OpenCourseWare 511,398 views. The integral is the limit of the Riemann sums as the size of the rectangles goes to zero. But why do you justify everything in such a detail, and why do you give us proofs of theorems. Jamshidi 4. MULTIVARIATE PROBABILITY DISTRIBUTIONS 3 Once the joint probability function has been determined for discrete random variables X 1 and X 2, calculating joint probabilities involving X 1 and X 2 is straightforward. Assume f = f(x) is a function of one variable. Within minutes, you can have the software installed and create the precise worksheets you need -- even for today's lesson. Thread: Multivariable calculus. 4 Green's The-orem 15. From Multivariable Equation Solver to scientific notation, we have got all kinds of things covered. I enjoy making animations of. Calculus: Single and Multivariable, 6th Edition. Complementary materials: You can find the suggestive answer key here (the 7th edition) and here (the 8th edition). By DORON ZEILBERGER These are the handouts I gave out when I taught Multivariable Calculus (Math 251), during the Fall Semester of 2006-2007. Jeff Morgan Department of Mathematics University of Houston | PowerPoint PPT presentation | free to view. With MULTIVARIABLE CALCULUS, Seventh Edition, Stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. As in the case of single-variable functions, we must ﬁrst. The ideas of partial derivatives and multiple integrals are not too di erent from their single-variable coun-terparts, but some of the details about manipulating them are not so obvious. Students say: "All right, if you insist that badly we will study calculus. You can also find Notes on Multivariable Calculus ppt and other slides as well. View Zachary Fregin’s profile on LinkedIn, the world's largest professional community. Some are downright tricky. Instantaneity of the changes and variability of the inputs are handled by infinitesimal quantities. 3 Extrema of Multivariable Functions Question 1: What is a relative extrema and saddle point? Question 2: How do you find the relative extrema of a surface? In an earlier chapter, you learned how to find relative maxima and minima on functions of one variable. 5 Concepts from Matrix Algebra 7 1. The ideas of partial derivatives and multiple integrals are not too di erent from their single-variable coun-terparts, but some of the details about manipulating them are not so obvious. But you can’t bypass calculus, by deciding that you will get one of those “never at all” jobs. Brian Vick Mechanical Engineering Department Virginia Tech General Purpose Commands Operators and Special Characters / 3 Commands for Managing a Session / 3 Special Variables and Constants / 4 System and File Commands / 4 Input/Output and Formatting Commands Input/Output Commands / 5 Format Codes for fprintf. 11 DIVERGENCE OF A VECTOR1. You can also find Notes on Multivariable Calculus ppt and other slides as well. Slide 7/35 Daniel Kaplan Using R for Introductory Calculus and Statistics. From this point there are still many different possibilities that we can look at. Changing tslightly has two e ects: it changes xslightly, and it changes yslightly. So now, not only can we use integral calculus to find the area under a curve, but we can find the volume beneath a surface, such as the surface of a hill. The mathematics of Lagrange multipliers. We have numbered the videos for quick reference so it's. So, first of all we have operators and functions that are of considerable importance in physics and engineering. Objectives. Learning outcomes. The area A of the rectangle is given by A = W L. Syllabus for MAT 203 - Multivariable Calculus Stony Brook University Summer Session I, 2016 May 31, 2016 1 Welcome! Congratulations on your successes in mathematics so far and welcome now to your next big challenge,. edu Funded by the National Science Foundation The Status Quo Biology majors Calculus I (5 credits) Baby Stats (3 credits) Biochemistry majors Calculus I (5 credits) Calculus II (5 credits) No statistics No partial derivatives Design Requirements Calculus I + a second course Five credits each Biologists want. Following are some areas of computer science where calculus/analysis is applicable. 2 Line Integral 15. *New* Computer Science clicker questions — Peer Instruction 4 CS. As in the case of single-variable functions, we must ﬁrst. , Massachusetts Institute of Technology Maurice D. 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The joint CDF of X1, X2, …, Xk will have the form: P(x1, x2, …, xk) when the RVs are discrete F(x1, x2, …, xk) when the RVs are continuous. Multi variable partial derivatives are the rates of change with. Drew Fleming from Cape Coral was looking for essay on eid ul adha 2010 Howard Palmer found the answer to a search query essay on eid ul adha 2010 essay on eid ul adha. Prerequisites are kept to an absolute minimum – nothing beyond first courses in linear algebra and multivariable calculus – and the most direct a. This course is devoted to the study of vectors, solid analytic geometry, and calculus of several variables. Download Free: Calculus Multivariable 7th Edition Online Reading at 085. Slide 7/35 Daniel Kaplan Using R for Introductory Calculus and Statistics. Get ideas for your own presentations. Some are downright tricky. -Statisticians can make accurate predictions when evaluating survey data due to the large range. They are abbreviated x n to refer to individuals or x to refer to them as a group. 7) Our goal is to now ﬁnd maximum and/or minimum values of functions of several variables, e. Why Study the Anatomy of Other Organisms? Homologous and analogous structures are often confusing topics to grasp in biology class. However, some notes are copyrighted and may be used for private use only. 3 Extrema of Multivariable Functions Question 1: What is a relative extrema and saddle point? Question 2: How do you find the relative extrema of a surface? In an earlier chapter, you learned how to find relative maxima and minima on functions of one variable. • Bottom line, we offer over 4 million professionally designed PowerPoint templates - far more than anyone else in the world - that are available for your immediate download and use 24/7! • They can be purchased individually for a very low price. For example, it allows us to find the rate of change of velocity with respect to time (which is acceleration). We rst list several results you should know and then many review problems, which are followed by detailed solutions. Absolute References 7. In multivariable calculus, the gradient of a function h (written ∇h) is a normal vector to a curve (in two dimensions) or a surface (in higher dimensions) on which h is constant: n = ∇h(P). Z's Multivariable Calculus Handouts. Chapter 17. If we combine the elements of each, then we can form“vector– valued functions of many variables”. Larson Texts is committed to providing free instructional internet content in mathematics. Multivariable Calculus, also known as Vector Calculus, deals with functions of two variables in 3 dimensional space, as well as computing with vectors instead of lines. Karcher had learned calculus this way from his teacher, Heinz Schwarze. net contains essential resources on algebra 1 help. Nice explanations of some topics. (PowerPoint) 7/1/13 VIDEO. 19 The Shape of Di erential Geometry in Geometric Calculus 5 Thus GC uni es the familiar concepts of \divergence" and \curl" into a single vector derivative, which could well be dubbed the \gradient", as it reduces to the usual gradient when the eld is scalar-valued. You must enable JavaScript in order to use this site. Textbook: McCallum, Hughes-Hallett, Gleason. can take them or opt out. If you want Notes on Multivariable Calculus Tests & Videos, you can search for the same too. It is a means of differentiating algebraically complicated functions or functions for which the ordinary rules of differentiation do not apply. Colgate some old exams with solutions. Eventually, Macalester redesigned the entire Calculus I through III sequence to fit this image of calculus as a modeling course with single variable and multivariable functions handled simultaneously. 5x 2 y + y + 2; The following all have multiple variables but are not multivariable polynomials, because they don't qualify as polynomials in the first place. The applet seems to work best with Internet Explorer. The section numbers refer to the textbook, which was `Calculus, fifth edition', by James Stewart, Thompson, Brooks/Cole. Try them ON YOUR OWN first, then watch if you need help. As an introduction, review the essential concept of the function, try your hand at simple problems, and hear Professor Edwards’s recommendations for approaching the course. 2 Derivatives and Integrals of Vector Functions ⇤ I can take the derivative of a vector function. Calculus book answer key keyword after analyzing the system lists the list of keywords related and the list of websites with related content, in addition you can see which keywords most interested customers on the this website. Phi Beta Kappa Honor Society. New to this Edition. Interestingly, in 2 of the 30 articles (7%), the terms multivariate and multivariable were used interchangeably. The notes are available as Adobe Acrobat documents. Using limits, we'll learn a better and far more precise way of defining continuity as well. One of the best books covering rigorous multivariable calculus is “calculus on manifolds” by Spivak, but this is a very brief book and counts more as analysis. Typical max/min problem from calculus…. If you want Notes on Multivariable Calculus Tests & Videos, you can search for the same too. Your heating bill depends on the average temperature outside. Chapter 17 - Multivariable Calculus 1. View and Download PowerPoint Presentations on Applications Of Differential Equations PPT. Download Multivariable Calculus ebook for free in pdf and ePub Format. Phi Beta Kappa Honor Society. Lately I have been particularly interested in the GeoWall, a system which uses polarized filters to display stereo images in three dimensions. In this course we will cover the calculus of real univariate functions, which was developed during more than two centuries. The book looks at half-a-dozen different types of problems (dealing with different numbers of independent and dependent variables). Diffeial Equations Math100 Revision Exercises Resources. Importance of Calculus: An Aside • Calculus is a good means for introducing and reinforcing mathematical rigor. Try them ON YOUR OWN first, then watch if you need help. in single-variable calculus and matrices in multivariable calculus;. From that standpoint, they have many of the same applications as total derivatives in single-variable calculus: directional derivatives, linear approximations, Taylor polynomia. Multivariable Calculus (MATH 211) Natural Language Processing (CS 322) Relativity and Particles (PHYS 151) Honors & Awards. Significant additions to MyMathLab, driven by the Calculus MyMathLab Advisory Panel. This note provides a crash course on this topic. Some are downright tricky. Constrained Optimization: Step by Step Most (if not all) economic decisions are the result of an optimization problem subject to one or a series of constraints: • Consumers make decisions on what to buy constrained by the fact that their choice must be affordable. 1 Calculus Online Quiz. Note: y = f(x) is a function if it passes the vertical line test. We now turn to the problem of integrating complex functions. Project MathQUEST is developing and testing questions for Differential Equations, Linear Algebra, Series, Sequences, and Difference Equations, Multivariable Calculus, Integral Calculus, Differential Calculus, and Precalculus. Multivariable Calculus In thermodynamics, we will frequently deal with functions of more than one variable e. Chapter 17. Throughout these notes, as well as in the lectures and homework assignments, we will present several examples from Epidemiology, Population Biology, Ecology and Genetics that require the methods of Calculus in several variables. Continuing our discussion of calculus, the last topic I want to discuss here is the concepts of gradient, divergence, and curl. Zachary has 4 jobs listed on their profile. We turn to that subject. View and Download PowerPoint Presentations on Applications Of Differential Equations PPT. Calculus is a branch of mathematics containing limits, derivatives, integrals and functions. the equations. But why do you justify everything in such a detail, and why do you give us proofs of theorems. Calculus II - MTH301 VU Video Lectures, Handouts, Power Point Slides, Solved Assignments, Solved Quizzes, Past Papers and Recommended Books. 2 Population Versus Sample 2 1. Business Calculus. To find the equation of a line in a two-dimensional plane, we need to know a point that the line passes through as well as the slope. Mathematics and Statistics Placement for Calculus and Precalculus. Ideas for my 2009/2010 Calculus Project Two years ago in calculus, when I only had one section and only 7 students were in that section, I had each student work on an individual project during the 4th quarter. Find materials for this course in the pages linked along the left. Application of concepts is stressed throughout the course. CALCULUS II LECTURE NOTES 3 1. This is exactly the way you defined the integral in one-variable calculus. We now call this sequence Applied Multivariable Calculus I, II, and III. Here's a simple example: the bucket at right integrates the flow from the tap over time. However, in multivariable calculus we want to integrate over regions other than boxes, and ensuring that we can do so takes a little work. Multivariable Calculus (Spring 16, 2 sections, course head) Junior Seminar on PDOs and the Nash-Moser Theorem (Fall 15) Differential Equations (Spring 15) Multivariable Calculus (Fall 14, 2 sections, course head) Real Analysis (Fall 13) Multivariable Calculus (Fall 12, 2 sections) Additional teaching at Princeton University. Multivariable Calculus The world is not one-dimensional, and calculus doesn't stop with a single independent variable. Limits and Continuity of Functions of Two or More Variables Introduction. Phi Beta Kappa Honor Society. MIT OpenCourseWare 511,398 views. Calculus & Analytic Geometry I An Online Course. There are German language college level textbooks by K¨utting and M¨oller and a high school level book by M¨uller which use this approach. Download Multivariable Calculus ebook for free in pdf and ePub Format. The setting is n-dimensional Euclidean space, with the material on diﬀerentiation culminat-ing in the Inverse Function Theorem and its consequences, and the material on integration culminating in the Generalized Fundamental Theorem of Inte-. 15 Vector Calculus 15. "), and then …. Why Study the Anatomy of Other Organisms? Homologous and analogous structures are often confusing topics to grasp in biology class. 02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates. Many colleges have enough economics and finance majors to support a multivariable calculus class designed on this basis. Optimization Vocabulary Your basic optimization problem consists of… •The objective function, f(x), which is the output you’re trying to maximize or minimize. 1 Introduction Data are information. These sessions are held throughout the. 35, MSRP) Out of Many ($121. Visit Mathway on the web. It is easy to understand and easy to implement. of 5 stars Calculus 6th edition by Edwards and Penney. They are abbreviated x n to refer to individuals or x to refer to them as a group. Come to Mathenomicon. Multivariable Calculus This presentation is not complete. Classwork and Key 1/28. I have tried to be somewhat rigorous about proving. We have numbered the videos for quick reference so it's. Math 1210 (Calculus 1) Lecture Videos These lecture videos are organized in an order that corresponds with the current book we are using for our Math1210, Calculus 1, courses (Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson). View Notes - 10 Multiple Integrals. 4 Contents Can one recover classical calculus from quantum calculus? There is the limit h → 0. My aim is to help students and faculty to download study materials at one place. Math 1210 (Calculus 1) Lecture Videos These lecture videos are organized in an order that corresponds with the current book we are using for our Math1210, Calculus 1, courses (Calculus, with Differential Equations, by Varberg, Purcell and Rigdon, 9th edition published by Pearson). I About 2/3 of calculus students have had some calculus in high school. They may not be sold or included in a commercial product or website without the permission of Greg Kelly, Hanford High School, Richland Washington Greg. The material is arranged in 6 chapters and delivered in the 6 weeks of the course. It is not comprehensive, and absolutely not intended to be a substitute for a one-year freshman course in differential and integral calculus. modern definition of a limit as follows: To say that the limit of f(x) as x approaches a is equal to L means that we can make the value of f(x) within a distance of epsilon units from L simply by making x within an appropriate distance of delta units from x. For You Explore. Courses in Year One. Notation During lectures I will use some notation/shorthand which you may not of seen before. Solving Equations With Multiplication And Division Ppt. Differential Calculus cuts something into small pieces to find how it changes. Studious includes more than 4000 video solutions to exercises from the Stewart textbook, plus hundreds of hours of lecture videos on key concepts in calculus, quizzes, interactive and printable flashcards, and more. Many calculus examples are based on physics.