This course is an introduction to the calculus of functions of several …
This course is an introduction to the calculus of functions of several variables. It begins with studying the basic objects of multidimensional geometry: vectors and vector operations, lines, planes, cylinders, quadric surfaces, and various coordinate systems. It continues with the elementary differential geometry of vector functions and space curves. After this, it extends the basic tools of differential calculus - limits, continuity, derivatives, linearization, and optimization - to multidimensional problems. The course will conclude with a study of integration in higher dimensions, culminating in a multidimensional version of the substitution rule.
This textbook covers multivariable Calculus. There are chapters on vectors and geometry …
This textbook covers multivariable Calculus. There are chapters on vectors and geometry in 2 and 3 dimensions, partial derivatives, and multivariable integrals.
This series of videos focusing on calculus covers minima, maxima, and critical …
This series of videos focusing on calculus covers minima, maxima, and critical points, rates of change, optimization, rates of change, L'Hopital's Rule, mean value theorem.
These thoroughly illustrated sheets make use of multiple representations and can be …
These thoroughly illustrated sheets make use of multiple representations and can be used for unit-end summaries in inquiry-based/modeling-style courses as well as for direct instruction in didactic courses.
This is a rigorous, open, and equitable Calculus I class. It follows …
This is a rigorous, open, and equitable Calculus I class. It follows the OpenStax Calculus I book and uses the MyOpenMath course created by Larry Green and the ZTC grant as homework and extra resources. As well as lecture notes and worksheets created in Microsoft Word.
The structure of the course is that it follows a flipped class model, where students are required to watch lecture video created off of the lecture notes. Then students work on sectional exercises embedded in Canvas from MyOpenMath and work by themselves on the hard worksheet before the last day of the class during the week. On that day of class students will have the opportunity to work in groups on the worksheet problems.
They will be motivated to work on the problems in their groups because they will then teach the professor their random problem received as well as their group mates have points associated with their group mates work. The way they do this is through a program called GoReact that is embedded in Canvas. The main thing about this program is that students can easily share a recorded video of them teaching the math to the professor and the professor in turn can give video feedback telling the student how much they rock or letting them know what went wrong. These Teach Me Video are the foundation of the course and are the only thing the professor grades for the week unless there is a test. They are fun for both the instructor and students and increase the teacher student relationship as well as the student to student relationship. It is also easy to bump the Teach Me Videos up to make students who didn't fully understand the problem by making them redo the video to get some points back.
Limits are the core tool that we build upon for calculus. Many …
Limits are the core tool that we build upon for calculus. Many times, a function can be undefined at a point, but we can think about what the function "approaches" as it gets closer and closer to that point (this is the "limit"). Other times, the function may be defined at a point, but it may approach a different limit. There are many, many times where the function value is the same as the limit at a point. Either way, this is a powerful tool as we start thinking about slope of a tangent line to a curve.
This series of videos focusing on calculus covers calculating derivatives, power rule, …
This series of videos focusing on calculus covers calculating derivatives, power rule, product and quotient rules, chain rule, implicit differentiation, derivatives of common functions.
This Project has been completed as part of a standard 10 weeks …
This Project has been completed as part of a standard 10 weeks Calculus 3 asynhronous online course with optional WebEx office hours during Summer 2022 semester at MassBay Community College, Wellesley Hills, MA.
This course analyzes the functions of a complex variable and the calculus …
This course analyzes the functions of a complex variable and the calculus of residues. It also covers subjects such as ordinary differential equations, partial differential equations, Bessel and Legendre functions, and the Sturm-Liouville theory.
This is an online textbook for a one semester calculus course aimed …
This is an online textbook for a one semester calculus course aimed at business students. The material covered is fairly standard: differentiation and integration without trigonometry, partial derivatives and optimization of functions of several variables. There are several characteristics that differentiate the text from other texts: Excel is used as the main computational engine throughout the text and the needed Excel skills are taught rather than assumed. Examples, exercises, and vocabulary are tailored to uses in a business curriculum. There is a modeling thread throughout the text. Webwork versions of exercises are available on request.
This course is a brief introduction to sequences and infinite series. We …
This course is a brief introduction to sequences and infinite series. We begin with a discussion of power series and develop tests for convergence and non-convergence. Taylor series are introduced and lead to an analysis of power series in general. This is a 1-credit course that can be taken any time after the student has completed Calculus I. All course content created by Javad Moulai. Content added to OER Commons by Julia Greider.
Open Source Calculus and Analysis - A comprehensive textbook introducing the main …
Open Source Calculus and Analysis - A comprehensive textbook introducing the main concepts from calculus and analysis
Features - Comprehensiveness: all from calculus and analysis that is needed in first year mathematics-oriented programmes - Mathematical rigour: formal definitions, extended theorems and proofs - Includes differential equations - Applicability: integrated symbolic (Mathematica or SymPy) and numerical computation (Python), review exercises, and so on - Accessibility: final solution to all exercises, QR codes to accompanying videos,… - Flexibility: using dedicated if-loops in the underlying Latex-code you can compile the version that suits your needs (Mathematica or Sympy, Calculus only or analysis as well, with or without differential equations,…)
This course covers differential, integral and vector calculus for functions of more …
This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.
Introduction to the theory and techniques of differential and integral calculus of …
Introduction to the theory and techniques of differential and integral calculus of elementary functions with emphasis on applications in business and finance, taught both online and in-person in Fall 2022 at Yavapai College. Note: Computer use and graphing calculator required (TI-83/84 recommended).This course makes use of an embedded OER textbook, but also uses Lumen OHM homework assignments; these require a subscription to Lumen, which in this instance was provided by the institution. In cases where that is not possible, the homework assignments will need to be replaced, or students will have to pay a fee to access the homework. Contact Lumen to find out more about student access to its homework platforms.
This course covers Limits and Continuity, Derivatives: definition and basic rules; Derivatives: …
This course covers Limits and Continuity, Derivatives: definition and basic rules; Derivatives: chain rule and other advanced topics; Applications of derivatives; Analyzing Functions; Integrals; Differential equations; and Applications of integrals.
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