Welcome to applied calculus for computing. Calculation intended to be a general method of solving quantifiable problems. In the application of the calculation method, or as it is known the”infinitesimal” method, a problem is”divided into infinitesimal parts”(differentiation), analysed in its relations with the neighbouring parts and then”added”(integration) until the solution method. The two parts of this the analysis and synthesis form a model for more sophisticated methods based on calculation, used in applied science concepts you learn in calculus allow statistical , physicists and engineers create mathematical models of real situations and real problems and simulate their resolutions under different operating conditions.
In the EL Education model, differentiation is a philosophical belief and an instructional approach through which teachers proactively plan instruction to capitalize on students’ varied assets and meet students’ varied needs based upon ongoing assessment. Teachers differentiate for students with disabilities, for advanced learners, for English language learners (see also Core Practice 20: Teaching English Language Learners), and for students whose differences are not formally evaluated but have been identified through informal learning and interest inventories. In whole group general education instruction, teachers use flexible groupings of students and design respectful tasks that allow for different approaches to the same goals. Teachers build a culture that honors diverse assets and needs and holds all students accountable to the same long-term learning targets, putting equity at the center of the school’s commitment and vision. At the same time, general education teachers make accommodations and modifications for students who have identified exceptionalities and collaborate with a team of school professionals to provide additional supports or extensions.
This course begins with a review of algebra specifically designed to help and prepare the student for the study of calculus, and continues with discussion of functions, graphs, limits, continuity, and derivatives. The appendix provides a large collection of reference facts, geometry, and trigonometry that will assist in solving calculus problems long after the course is over. Upon successful completion of this course, the student will be able to: calculate or estimate limits of functions given by formulas, graphs, or tables by using properties of limits and LĺÎĺ_ĺĚĺ_hopitalĺÎĺ_ĺĚĺ_s Rule; state whether a function given by a graph or formula is continuous or differentiable at a given point or on a given interval and justify the answer; calculate average and instantaneous rates of change in context, and state the meaning and units of the derivative for functions given graphically; calculate derivatives of polynomial, rational, common transcendental functions, and implicitly defined functions; apply the ideas and techniques of derivatives to solve maximum and minimum problems and related rate problems, and calculate slopes and rates for function given as parametric equations; find extreme values of modeling functions given by formulas or graphs; predict, construct, and interpret the shapes of graphs; solve equations using NewtonĺÎĺ_ĺĚĺ_s Method; find linear approximations to functions using differentials; festate in words the meanings of the solutions to applied problems, attaching the appropriate units to an answer; state which parts of a mathematical statement are assumptions, such as hypotheses, and which parts are conclusions. This free course may be completed online at any time. It has been developed through a partnership with the Washington State Board for Community and Technical Colleges; the Saylor Foundation has modified some WSBCTC materials. (Mathematics 005)
CK-12 Foundation's Single Variable Calculus FlexBook introduces high school students to the topics covered in the Calculus AB course. Topics include: Limits, Derivatives, and Integration.
CK-12 Calculus Teacher's Edition covers tips, common errors, enrichment, differentiated instruction and problem solving for teaching CK-12 Calculus Student Edition. The solution guide is available upon request.
Seminar covering topics of current interest in biology. Includes reading and analysis of research papers and student presentations. Contact Biology Education Office for topics. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. In 1971, President Nixon declared the "War on Cancer," but after three decades the war is still raging. How much progress have we made toward winning the war and what are we doing to improve the fight? Understanding the molecular and cellular events involved in tumor formation, progression, and metastasis is crucial to the development of innovative therapy for cancer patients. Insights into these processes have been gleaned through basic research using biochemical, molecular, and genetic analyses in yeast, C. elegans, mice, and cell culture models. We will explore the laboratory tools and techniques used to perform cancer research, major discoveries in cancer biology, and the medical implications of these breakthroughs. A focus of the class will be critical analysis of the primary literature to foster understanding of the strengths and limitations of various approaches to cancer research. Special attention will be made to the clinical implications of cancer research performed in model organisms and the prospects for ending the battle with this devastating disease.
This course will serve as both an introduction to contemporary political philosophy and a way to explore issues of pluralism and multiculturalism. Racial and ethnic groups, national minorities, aboriginals, women, sexual minorities, and other groups have organized to highlight injustice and demand recognition and accommodation on the basis of their differences. In practice, democratic states have granted a variety of group-differentiated rights, such as exemptions from generally applicable laws, special representation rights, language rights, or limited self-government rights, to different types of groups. This course will examine how different theories of citizenship address the challenges raised by different forms of pluralism. We will focus in particular on the following questions: - Does justice require granting group-differentiated rights? - Do group-differentiated rights conflict with liberal and democratic commitments to equality and justice for all citizens? - What, if anything, can hold a multi-religious, multicultural society together? Why should the citizens of such a society want to hold together?
How does a regenerating animal "know" what's missing? How are stem cells or differentiated cells used to create new tissues during regeneration? In this class we will take a comparative approach to explore this fascinating problem by critically examining classic and modern scientific literature about the developmental and molecular biology of regeneration. We will learn about conserved developmental pathways that are necessary for regeneration, and we will discuss the relevance of these findings for regenerative medicine. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching.
This article includes a menu of post-reading activities for use with any nonfiction text. Students spend $50 on their choice of activities.
- Environmental Science
- Material Type:
- Lesson Plan
- Ohio State University College of Education and Human Ecology
- Provider Set:
- Beyond Penguins and Polar Bears: An Online Magazine for K-5 Teachers
- Clarissa Reeson
- Tracey Allen
- Date Added:
This site explains how teachers can tier activities in their World Language classrooms. It includes background information about tiering, steps for teachers to develop tiered activities, and examples of tiered activities.
In a multi-grade class of fourth, fifth, and sixth graders, students learn to work and communicate in teams. Through projects and a class structure that supports differentiation, Ms. Ehrke is able to keep students challenged and engaged. Her strategies for differentiation and communication can be used in any classroom.
" During development, the genetic content of each cell remains, with a few exceptions, identical to that of the zygote. Most differentiated cells therefore retain all of the genetic information necessary to generate an entire organism. It was through pioneering technology of somatic cell nuclear transfer (SCNT) that this concept was experimentally proven. Only 10 years ago the sheep Dolly was the first mammal to be cloned from an adult organism, demonstrating that the differentiated state of a mammalian cell can be fully reversible to a pluripotent embryonic state. A key conclusion from these experiments was that the difference between pluripotent cells such as embryonic stem (ES) cells and unipotent differentiated cells is solely a consequence of reversible changes. These changes, which have proved to involve reversible alterations to both DNA and to proteins that bind DNA, are known as epigenetic, to distinguish them from genetic alterations to DNA sequence. In this course we will explore such epigenetic changes and study different approaches that can return a differentiated cell to an embryonic state in a process referred to as epigenetic reprogramming, which will ultimately allow generation of patient-specific stem cells and application to regenerative therapy. This course is one of many Advanced Undergraduate Seminars offered by the Biology Department at MIT. These seminars are tailored for students with an interest in using primary research literature to discuss and learn about current biological research in a highly interactive setting. Many instructors of the Advanced Undergraduate Seminars are postdoctoral scientists with a strong interest in teaching."
This resource is intended to provide all educators with an overview of the process of designing a Language Dive. The suggestions should be modified to meet the needs of your ELLs across K-12 in all content areas.
Analysis I in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space. MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.
This course is offered to undergraduates and introduces students to the formulation, methodology, and techniques for numerical solution of engineering problems. Topics covered include: fundamental principles of digital computing and the implications for algorithm accuracy and stability, error propagation and stability, the solution of systems of linear equations, including direct and iterative techniques, roots of equations and systems of equations, numerical interpolation, differentiation and integration, fundamentals of finite-difference solutions to ordinary differential equations, and error and convergence analysis. The subject is taught the first half of the term. This class was originally listed in Course 13 (Ocean Engineering) as 13.002J.
This website guides teachers through establishing a routine for running centers or stations in their World Language classrooms. This includes an overview of different centers models, how to select student groups, how to select activities for centers, how to organize procedures, as well as links to resources.
Explores the difference between service and manufacturing operations, and the degree of distinct management skills and tools required. Analyzes cases selected from a variety of service operations with a particular focus on e-commerce. Guest speakers from specific service industries discuss the essence of managing those operations. This course covers organizational, strategic and operational aspects of managing Supply Networks (SNs) from domestic and international perspectives. Topics include alternative SN structures, strategic alliances, design of delivery systems and the role of third party logistics providers. Many of the activities exchanged among enterprises in a SN are of a service nature, and the final output is often a combination of tangible products and services which the end-customer purchases. A series of concepts, frameworks and analytic tools are provided to better understand the management of service operations. Guest speakers share their experiences in managing SNs and services. Restricted to MIT Sloan Fellows in Innovation and Global Leadership.
Mathematics explained: Here you find videos on various math topics:
Pre-university Calculus (functions, equations, differentiation and integration)
Vector calculus (preparation for mechanics and dynamics courses)
Differential equations, Calculus
Functions of several variables, Calculus
Probability and Statistics
This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material.