This graduate-level course covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.
Methods of Calculus eText
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include Vectors and Matrices, Partial Derivatives, Double and Triple Integrals, and Vector Calculus in 2 and 3-space.
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space.
MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.
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.
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.
The materials have been organized to support independent study. The website includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:
Lecture Videos recorded on the MIT campus
Recitation Videos with problem-solving tips
Examples of solutions to sample problems
Problems for you to solve, with solutions
Exams with solutions
Interactive Java Applets ("Mathlets") to reinforce key concepts
Content Development
Denis Auroux
Arthur Mattuck
Jeremy Orloff
John Lewis
Heidi Burgiel
Christine Breiner
David Jordan
Joel Lewis
This course is a continuation of 18.014 Calculus with Theory. It covers the same material as 18.02 Multivariable Calculus, but at a deeper level, emphasizing careful reasoning and understanding of proofs. There is considerable emphasis on linear algebra and vector integral calculus.
(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)
El módulo 1 prepara el escenario para ampliar la comprensión de los estudiantes de las transformaciones explorando la noción de linealidad. Esto conduce al estudio de números complejos y transformaciones lineales en el plano complejo. Los materiales del maestro consisten en las páginas del maestro que incluyen boletos de salida, soluciones de boletos de salida y todos los materiales del alumno con soluciones para cada lección en el módulo 1.
English Description:
Module 1 sets the stage for expanding students' understanding of transformations by exploring the notion of linearity. This leads to the study of complex numbers and linear transformations in the complex plane. The teacher materials consist of the teacher pages including exit tickets, exit ticket solutions, and all student materials with solutions for each lesson in Module 1.
A visual demo of Newton's Method for pre-calculus students.
The following notes and practice problems are ancillary materials for OpenStax Calculus Volume 1. Topics include:
Limit of a Function
Continuity
Derivatives
Differentiation
A first one-semester course on differential equations aimed at engineers.
This book covers the material normally presented in a two-term course on numerical analysis, starting with the basic concept and ending with topics that are more appropriate for a course in numerical analysis for differential equations: numerical solution of systems of linear and nonlinear equations, polynomial interpolation, numerical approximation of functions, numerical computation of eigenvalues, numerical derivation and integration, numerical solution of ordinary and partial differential equations.
With a focus on algorithms, it can be used as an introduction to numerical analysis for engineering and applied science students. With a focus on theory, it can be used as an introduction to numerical analysis for students in mathematics or physics. Most of the numerical methods presented in this book are accompanied by a MATLAB code.
This is a path for those of you who want to complete the Data Science undergraduate curriculum on your own time, for free, with courses from the best universities in the World. In our curriculum, we give preference to MOOC (Massive Open Online Course) style courses because these courses were created with our style of learning in mind. OSSU Data Science uses the report Curriculum Guidelines for Undergraduate Programs in Data Science (https://www.amstat.org/asa/files/pdfs/EDU-DataScienceGuidelines.pdf) as our guide for course recommendation.
It is possible to finish within about 2 years if you plan carefully and devote roughly 20 hours/week to your studies. Learners can use this spreadsheet (linked in resource) to estimate their end date. Make a copy and input your start date and expected hours per week in the Timeline sheet. As you work through courses you can enter your actual course completion dates in the Curriculum Data sheet and get updated completion estimates.
Python and R are heavily used in Data Science community and our courses teach you both. Remember, the important thing for each course is to internalize the core concepts and to be able to use them with whatever tool (programming language) that you wish.
The Data Science curriculum assumes the student has taken high school math and statistics.
This Open Educational Resources site will complement textbooks and lectures with obvious information gaps. An extension of regular learning content. For example, you can accompany the text with multimedia materials such as videos. By presenting information in multiple formats, students can more easily learn the material being taught.
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 sample shell is produced by the California Community Colleges CVC-OEI to support faculty in the use of Open Educational Resources and development of courses aligned to the OEI Course Design Rubric. The shell may be used for online, hybrid, &/or face-to-face classes. The shell is available for all faculty, not just those faculty in the CCC system. The team producing this shell includes Helen Graves, Liezl Madrona, Cyrus Helf, Nicole Woolley & Barbara Illowsky. If you are having challenges importing the shell, here are some steps to take. (1) Create an empty shell in your sandbox. (2) Import the Canvas Commons course into your shell. (3) Adapt the content as you wish. (4) If all else fails, contact your college IT person or Canvas administrator.
This sample shell is produced by the California Community Colleges CVC-OEI to support faculty in the use of Open Educational Resources and development of courses aligned to the OEI Course Design Rubric. The shell may be used for online, hybrid, &/or face-to-face classes. The shell is available for all faculty, not just those faculty in the CCC system. The team producing this shell includes Helen Graves, Liezl Madrona, Cyrus Helf, Nicole Woolley & Barbara Illowsky. If you are having challenges importing the shell, here are some steps to take. (1) Create an empty shell in your sandbox. (2) Import the Canvas Commons course into your shell. (3) Adapt the content as you wish. (4) If all else fails, contact your college IT person or Canvas administrator.
Calculus is designed for the typical two- or three-semester general calculus course, incorporating innovative features to enhance student learning. The book guides students through the core concepts of calculus and helps them understand how those concepts apply to their lives and the world around them. Due to the comprehensive nature of the material, we are offering the book in three volumes for flexibility and efficiency. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and second-order differential equations.
These OpenStax Calculus I ancillary materials, including guided notes and questions using Edfinity, were developed as a result of a Round 17 Affordable Materials Grant.