A PowerPoint presentation on the Derivative as a Function. Includes example problems on finding the derivative using the definition, Power Rule, examining graphs of f(x) and f'(x), and local linearity.
These slides are a summary of the Well-Ordering Principle.
Video explains these slides is available in this link
https://youtu.be/EkleZiBtYyk
Reference books for these slides are
A Transition to Advanced Mathematics 8th Edition,
by Douglas Smith, Maurice Eggen, Richard St. Andre. ISBN-13: 978-1285463261, published by Cengage Learning (August 6, 2014).
https://www.cengagebrain.co.uk/shop/isbn/9781285463261
and
Discrete Mathematics with Applications, 3nd Edition, (1995)
By Susanna S. Epp, ISBN13: 9780534359454,
published by Thomson-Brooks/Cole Publishing Company.
Quadratic form and functional optimizationJunpei Tsuji
This slideshow describes a mathematics topic on quadratic form in English.
I made the slideshow to understand this topic on a deeper way.
I like linear algebra very much!!
A PowerPoint presentation on the Derivative as a Function. Includes example problems on finding the derivative using the definition, Power Rule, examining graphs of f(x) and f'(x), and local linearity.
These slides are a summary of the Well-Ordering Principle.
Video explains these slides is available in this link
https://youtu.be/EkleZiBtYyk
Reference books for these slides are
A Transition to Advanced Mathematics 8th Edition,
by Douglas Smith, Maurice Eggen, Richard St. Andre. ISBN-13: 978-1285463261, published by Cengage Learning (August 6, 2014).
https://www.cengagebrain.co.uk/shop/isbn/9781285463261
and
Discrete Mathematics with Applications, 3nd Edition, (1995)
By Susanna S. Epp, ISBN13: 9780534359454,
published by Thomson-Brooks/Cole Publishing Company.
Quadratic form and functional optimizationJunpei Tsuji
This slideshow describes a mathematics topic on quadratic form in English.
I made the slideshow to understand this topic on a deeper way.
I like linear algebra very much!!
Linear Equations Slide Share Version Exploded[1]keithpeter
GCSE Maths algebra linear equations revision, now tested by students and typos eliminated. Simple, two step, x on each side and bracket type equations but all examples have whole number answers.
Students learn to define and identify linear equations. They also learn the definition of Standard Form of a linear equation.
Students also learn to graph linear equations using x and y intercepts.
Math 235 - Summer 2015Homework 2Due Monday June 8 in cla.docxandreecapon
Math 235 - Summer 2015
Homework 2
Due Monday June 8 in class
Remember: In this course, you must always show reasoning for your answers. You can use any result we have
proved in class, in textbook reading, or in a previous homework.
Problem 1 For each of the following problems, you must justify your answer by finding the general solution
to the corresponding system of linear equations, or by showing that no solution exists.
(a) In the vector space P3(R), can −2x3 − 11x2 + 3x+ 2 be written as a linear combination of vectors in
{x3 − 2x2 + 3x− 1, 2x3 + x2 + 3x− 2}?
(b) In the vector space M2×2(R), can
(
1 0
0 1
)
be written as a linear combination of vectors
in
{(
1 0
−1 0
)
,
(
0 1
0 1
)
,
(
1 1
0 0
)}
?
Problem 2 Show that a subset W of a vector space V (over a field F ) is a subspace of V if and only if
span(W ) = W .
Problem 3 You are given a subset S of a vector space V . Determine whether S is linearly dependent or
linearly independent using exclusively methods developed in this course, and justify your answers.
(a) V = R3 and S = {(1, 2,−1), (2,−3, 1), (2, 3,−5)}.
(b) V = P3(R) and S = {1, 1 + 2t+ t2, 1− 2t+ t3, t2 + t3}.
(c) V = F(R,R) and S = {t, et, sin(t)}.
Problem 4 Prove that a subset S of a vector space V is linearly dependent if and only if there exists a
proper subset S′ ( S with the same span as S.
Problem 5 Exercise 1.6.13 from the textbook.
Problem 6 You are given a subspace S of M2×2(F ), the vector space of 2 × 2 matrices with entries in a
field F . You are required to find a basis for this subspace, and to find the dimension of this subspace.
For each problem, you DO NOT need to prove that S is a subspace, but you DO need to prove that your
conjectured basis is, in fact, a basis (that is, you need to show it is a linearly independent generating set for
S).
(a) S is the subspace of all diagonal 2× 2 matrices with entries in F .
(b) S is the subspace of all symmetric 2× 2 matrices with entries in F .
(c) S is the subspace of all skew-symmetric 2× 2 matrices with entries in F .
Problem 7 Let W1 and W2 be subspaces of a finite-dimensional vector space V . Prove that dim(W1∩W2) ≤
min{dim(W1),dim(W2)} and dim(W1 +W2) ≥ max{dim(W1),dim(W2)}.
Problem 8 Each of the maps below goes from one vector space to another (where both vectors spaces are
over the same field). For each map: prove that it is linear, determine whether it is one-to-one or not (prove
your answer), and determine whether it is onto or not (prove your answer).
(a) T : P3(R)→M2×2(R) defined by T (p) =
(
p(0) p′(0)
p′′(0) p′′′(0)
)
.
(b) T : M2×2(F ) → F defined by T (A) = tr(A), where F is a field. (Recall that for an n × n matrix,
tr(A) =
∑n
i=1Aii.)
1
(c) T : R2 → R3 defined by T ((a, b)) = (a, b, a+ b).
(Hint: You may find an analysis of rank and nullity useful here.)
Problem 9 Suppose that T : R2 → R2 is linear and that T ((1, 2)) = (3, 4) and T ((1, 3)) = (0, 1). Find
T ((1, 0)). Is T one-to-one? Justify your answer.
Problem 10 Let ...
I feel happy to make a presentation in odia language.
I am unable to make the alphabet for obtuse ,either it is "stu" or "stha" not exact one.Still I feel proud.
Adolescent should know that they are not one who faces the problems,all the adolescents have some common problems.They should develop certain life skills to grow smoothly.
The presentation is meant for Teachers.We as teachers think that due some lack of social skills students face self control problem but it may be due to learning disability
The pattern of question paper in the subject Mathematics has been changed in CBSE,India.I am uploading the paper with marking scheme so that students will be benefitted-Pratima Nayak,KVS
You have so many things in your life to be happy about. Appreciate those things, and suddenly your sadness will feel smaller and your happiness will grow larger
sometimes when you're in a really bad mood and you're not sure why?
A bad mood could be described as restless, dull, boredom, blah, dull, listless, melancholy or being just plain sad with no real explanation.
How to improve mood which is very important for success
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
4. Which of the following collections are well defined?
(1) The collection of male students in your class.
(2) The collection of numbers 2, 4, 6, 10 and 12.
(3) The collection of districts in Tamil Nadu.
(4) The collection of all good movies.
5. Sets are named with the capital letters A, B, C,
etc.
The elements of a set are
denoted by the small letters a, b, c, etc.
6. For example,
Consider the set A = {1, 3, 5, 9}
1 is an element of A, written as 1 A
3 is an element of A, written as 3 A
8 is not an element of A, written as 8 A
25. Venn Diagrams
We use diagrams or pictures in geometry to explain
a concept or a situation and sometimes we also
use them to solve problems. In mathematics, we
use diagrammatic representations called Venn
Diagrams to visualise the relationships between
sets and set operations.
48. Developed by
Pratima Nayak,PGT( Mathematics),
Kendriya Vidyalaya,Fort William,Kolkata
I acknowledge text books of different States of India
and NCERT.