This document discusses first-order differential equations. It provides exercises related to modeling real-world phenomena using differential equations, including population growth, radioactive decay, learning rates, and exponential growth. It also covers equilibrium solutions and determining whether a solution is increasing or decreasing based on the sign of the derivative. Key concepts covered are modeling, equilibrium solutions, exponential functions, and interpreting solutions.
Stochastic Processes describe the system derived by noise.
Level of graduate students in mathematics and engineering.
Probability Theory is a prerequisite.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
Gamma Function mathematics and history.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
More presentations on different subjects can be found on my website at http://www.solohermelin.com.
A geometric progression is a sequence of numbers where each subsequent term is found by multiplying the previous term by a fixed ratio. The first term is denoted by a and the common ratio by r. The nth term is given by arn-1. The sum of the first n terms is given by (1 - rn) / (1 - r). The behavior of the sequence depends on the value of r, determining whether the terms grow, decay, or alternate in sign. Examples demonstrate calculating individual terms and sums of geometric progressions.
Below is given the summary from the 112th Congress of Senators whose terms en...Nadeem Uddin
This document summarizes data on US Senators from the 112th Congress whose terms expire in 2013, 2015, or 2017. It provides the numbers of Democratic and Republican Senators in each expiration year, and calculates the probabilities of various events based on this data. Specifically, it calculates: (a) the probability a randomly selected Senator is Democratic and their term expires in 2015, (b) the probability a randomly selected Senator is Republican or their term expires in 2013, and (c) the probability a Senator is Republican given their term expires in 2017. It also determines whether being Republican and having one's term expire in 2015 are independent events.
Combinatorics is a subfield of discrete mathematics that focuses on counting combinations and arrangements of discrete objects. It involves counting the number of ways to put things together into various combinations. Some key rules in combinatorics include the sum rule, which states that the number of ways to accomplish either of two independent tasks is the sum of the number of ways to accomplish each task individually. The product rule states that the number of ways to accomplish two independent tasks is the product of the number of ways to accomplish each task. Generating functions can be used to efficiently represent counting sequences by coding terms as coefficients of a variable in a formal power series. They allow problems involving counting and arrangements to be solved using operations with formal power series.
B.tech ii unit-5 material vector integrationRai University
This document discusses various vector integration topics:
1. It defines line, surface, and volume integrals and provides examples of evaluating each. Line integrals deal with vector fields along paths, surface integrals deal with vector fields over surfaces, and volume integrals deal with vector fields throughout a volume.
2. Green's theorem, Stokes' theorem, and Gauss's theorem are introduced as relationships between these types of integrals but their proofs are not shown.
3. Examples are provided to demonstrate evaluating line integrals of conservative and non-conservative vector fields, as well as a surface integral over a spherical surface.
This document discusses first-order differential equations. It provides exercises related to modeling real-world phenomena using differential equations, including population growth, radioactive decay, learning rates, and exponential growth. It also covers equilibrium solutions and determining whether a solution is increasing or decreasing based on the sign of the derivative. Key concepts covered are modeling, equilibrium solutions, exponential functions, and interpreting solutions.
Stochastic Processes describe the system derived by noise.
Level of graduate students in mathematics and engineering.
Probability Theory is a prerequisite.
For comments please contact me at solo.hermelin@gmail.com.
For more presentations on different subjects visit my website at http://www.solohermelin.com.
Gamma Function mathematics and history.
Please send comments and suggestions for improvements to solo.hermelin@gmail.com. Thanks.
More presentations on different subjects can be found on my website at http://www.solohermelin.com.
A geometric progression is a sequence of numbers where each subsequent term is found by multiplying the previous term by a fixed ratio. The first term is denoted by a and the common ratio by r. The nth term is given by arn-1. The sum of the first n terms is given by (1 - rn) / (1 - r). The behavior of the sequence depends on the value of r, determining whether the terms grow, decay, or alternate in sign. Examples demonstrate calculating individual terms and sums of geometric progressions.
Below is given the summary from the 112th Congress of Senators whose terms en...Nadeem Uddin
This document summarizes data on US Senators from the 112th Congress whose terms expire in 2013, 2015, or 2017. It provides the numbers of Democratic and Republican Senators in each expiration year, and calculates the probabilities of various events based on this data. Specifically, it calculates: (a) the probability a randomly selected Senator is Democratic and their term expires in 2015, (b) the probability a randomly selected Senator is Republican or their term expires in 2013, and (c) the probability a Senator is Republican given their term expires in 2017. It also determines whether being Republican and having one's term expire in 2015 are independent events.
Combinatorics is a subfield of discrete mathematics that focuses on counting combinations and arrangements of discrete objects. It involves counting the number of ways to put things together into various combinations. Some key rules in combinatorics include the sum rule, which states that the number of ways to accomplish either of two independent tasks is the sum of the number of ways to accomplish each task individually. The product rule states that the number of ways to accomplish two independent tasks is the product of the number of ways to accomplish each task. Generating functions can be used to efficiently represent counting sequences by coding terms as coefficients of a variable in a formal power series. They allow problems involving counting and arrangements to be solved using operations with formal power series.
B.tech ii unit-5 material vector integrationRai University
This document discusses various vector integration topics:
1. It defines line, surface, and volume integrals and provides examples of evaluating each. Line integrals deal with vector fields along paths, surface integrals deal with vector fields over surfaces, and volume integrals deal with vector fields throughout a volume.
2. Green's theorem, Stokes' theorem, and Gauss's theorem are introduced as relationships between these types of integrals but their proofs are not shown.
3. Examples are provided to demonstrate evaluating line integrals of conservative and non-conservative vector fields, as well as a surface integral over a spherical surface.
The credit department of Lion’s Department Store in Anaheim.docxNadeem Uddin
The credit department of Lion’s Department Store in Anaheim, California, reported that30 percent of their sales are cash or check, 30 percent are paid with a credit card and 40 percent with a debit card. Twenty percent of the cash or check purchases, 90 percent of the credit card purchases, and 60 percent of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost$120. What is the probability that she paid cash or check?
Linear Combination, Span And Linearly Independent, Dependent SetDhaval Shukla
In this presentation, the topic of Linear Combination, Span and Linearly Independent and Linearly Dependent Sets have been discussed. The sums for each topic have been given to understand the concept clearly for viewers.
The LU factorization method decomposes a matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. It can be used to solve systems of linear equations of the form Ax=b. The document provides an example of using LU factorization to solve the system of equations: 8x - 3y + 2z = 20, 4x + 11y - z = 33, 6x + 3y + 12z = 36. The matrices L and U are calculated from the original coefficient matrix A. Then the system Ly=b is solved for y, and Ux=y is solved for x to obtain the solution x=3, y=2, z=1.
1. Define the Gamma and Beta functions.
2. Express integrals involving products of powers of x with sine and cosine functions in terms of Beta functions.
3. State properties of Gamma and Beta functions including their relationship and formulas for computing their values.
A relation is a set of ordered pairs that shows a relationship between elements of two sets. An ordered pair connects an element from one set to an element of another set. The domain of a relation is the set of first elements of each ordered pair, while the range is the set of second elements. Relations can be represented visually using arrow diagrams or directed graphs to show the connections between elements of different sets defined by the relation.
The answer for:
1)Give me a group of girls whose height is > than 156 cm is E,F,G.
2) The answers for Piano and Guitar question is:
n(U) =8,
n(A)=3,
n(B)=4
(A n B) = 1
( A U B)= 6
(A U B)' = 2
Only Piano ( A - B)=2
Only guitar(B-A) =3
Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp.
Content-
Venn diagram,
Set builder(Rule method),
List method(Roster method),
Universal set,
Union of sets,
Intersection of set
To multiply matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Each entry in a row of the first matrix is multiplied by the corresponding entry in a column of the second matrix and summed. This process is repeated for each row and column to populate the final matrix. The dimensions of the final matrix will be the number of rows in the first matrix and the number of columns in the second.
This document contains a series of math quizzes covering various topics like multiplication, factoring, exponents, algebra, angles, and more. It includes over 50 questions testing skills like finding products, factoring numbers, solving equations, calculating angles of circles, and evaluating expressions. The quizzes start with simpler questions and increase in difficulty, containing up to 6 possible answer choices. After each short quiz, the number of correct answers is reported out of the total number of questions. At the end of the document, the participant is congratulated for getting all questions correct across every quiz.
The document provides 10 examples of solving mixture and alligation problems using the rule of alligation. The rule states that if two items are mixed in a ratio, the ratio of the difference between the mean price and dearer price to the difference between the mean price and cheaper price is equal to the ratio of the quantities of the cheaper and dearer items. Each example applies this rule to find unknown quantities, prices, or percentages when items of different values or concentrations are mixed.
This document discusses sequences and their properties. It defines a sequence as a list of numbers written in a definite order. The nth term of a sequence is denoted as an. It provides examples of describing sequences using notation, defining formulas, and listing terms. It defines convergent and divergent sequences and gives examples testing for convergence or divergence. It also discusses bounded sequences and decreasing sequences, giving examples and proofs.
The document discusses the gamma function, which generalizes the factorial function to real and complex numbers. It provides a brief history of the gamma function, noting it was first introduced by Euler to extend the factorial to non-integer values. The document defines the gamma function, provides some of its key properties like its relationship to the factorial of integers, and discusses other related functions like the beta function. It also gives some examples of applications of the gamma function, such as using it to calculate volumes of n-dimensional balls and in computing infinite sums.
The binomial theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms of the expansion are determined by binomial coefficients. Pascal's triangle is a mathematical arrangement that shows the binomial coefficients and can be used to determine the coefficients in a binomial expansion. The proof of the binomial theorem uses mathematical induction to show that the formula holds true for any positive integer value of n.
The document provides steps for solving equations with fractions that involve the same variable on both sides. It explains that these types of equations cannot be solved using traditional back-tracking methods. The extra steps include: 1) cross multiplying using brackets to remove fractions, 2) identifying the smaller letter term on both sides, and 3) applying the opposite operation to this term on both sides before simplifying and solving as normal. It then works through examples demonstrating these steps, such as solving the equation n-3=n+6/2/3.
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Spectral methods for solving differential equationsRajesh Aggarwal
This project report describes Rajesh Aggarwal's summer research fellowship project on spectral methods for solving differential equations under the guidance of Dr. Pravin Kumar Gupta at IIT Roorkee from June 11, 2014 to August 6, 2014. The report provides background on analytical and numerical methods for solving differential equations, specifically conventional finite difference methods and spectral finite difference methods. It then describes the methodology, codes, and results of applying both methods to solve sample differential equations on a half-space and layered earth problems. Tables and graphs comparing the accuracy of the two methods are presented.
Singular Value Decompostion (SVD): Worked example 2Isaac Yowetu
This document provides an example of calculating the singular value decomposition (SVD) of a 3x3 matrix A. It finds the matrices U, Σ, and V such that A = UΣV^T. It first calculates the eigenvalues and eigenvectors of A^TA to construct Σ and V. It then uses A and the eigenvectors to calculate the columns of U. The final SVD of A is presented.
Singular Value Decompostion (SVD): Worked example 3Isaac Yowetu
Singular Value Decomposition (SVD) decomposes a matrix A into three matrices: U, Σ, and V. The document provides an example of using SVD to decompose the matrix A = [[3, 1, 1], [-1, 3, 1]]. It finds the singular values and constructs the U, Σ, and V matrices. The SVD of A is written as A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix containing the singular values of A.
The credit department of Lion’s Department Store in Anaheim.docxNadeem Uddin
The credit department of Lion’s Department Store in Anaheim, California, reported that30 percent of their sales are cash or check, 30 percent are paid with a credit card and 40 percent with a debit card. Twenty percent of the cash or check purchases, 90 percent of the credit card purchases, and 60 percent of the debit card purchases are for more than $50. Ms. Tina Stevens just purchased a new dress that cost$120. What is the probability that she paid cash or check?
Linear Combination, Span And Linearly Independent, Dependent SetDhaval Shukla
In this presentation, the topic of Linear Combination, Span and Linearly Independent and Linearly Dependent Sets have been discussed. The sums for each topic have been given to understand the concept clearly for viewers.
The LU factorization method decomposes a matrix A into the product of a lower triangular matrix L and an upper triangular matrix U. It can be used to solve systems of linear equations of the form Ax=b. The document provides an example of using LU factorization to solve the system of equations: 8x - 3y + 2z = 20, 4x + 11y - z = 33, 6x + 3y + 12z = 36. The matrices L and U are calculated from the original coefficient matrix A. Then the system Ly=b is solved for y, and Ux=y is solved for x to obtain the solution x=3, y=2, z=1.
1. Define the Gamma and Beta functions.
2. Express integrals involving products of powers of x with sine and cosine functions in terms of Beta functions.
3. State properties of Gamma and Beta functions including their relationship and formulas for computing their values.
A relation is a set of ordered pairs that shows a relationship between elements of two sets. An ordered pair connects an element from one set to an element of another set. The domain of a relation is the set of first elements of each ordered pair, while the range is the set of second elements. Relations can be represented visually using arrow diagrams or directed graphs to show the connections between elements of different sets defined by the relation.
The answer for:
1)Give me a group of girls whose height is > than 156 cm is E,F,G.
2) The answers for Piano and Guitar question is:
n(U) =8,
n(A)=3,
n(B)=4
(A n B) = 1
( A U B)= 6
(A U B)' = 2
Only Piano ( A - B)=2
Only guitar(B-A) =3
Sets [Algebra] in an easier and interesting way to learn! Specially suited for young children and for those who find Sets difficult to grasp.
Content-
Venn diagram,
Set builder(Rule method),
List method(Roster method),
Universal set,
Union of sets,
Intersection of set
To multiply matrices, the number of columns in the first matrix must equal the number of rows in the second matrix. Each entry in a row of the first matrix is multiplied by the corresponding entry in a column of the second matrix and summed. This process is repeated for each row and column to populate the final matrix. The dimensions of the final matrix will be the number of rows in the first matrix and the number of columns in the second.
This document contains a series of math quizzes covering various topics like multiplication, factoring, exponents, algebra, angles, and more. It includes over 50 questions testing skills like finding products, factoring numbers, solving equations, calculating angles of circles, and evaluating expressions. The quizzes start with simpler questions and increase in difficulty, containing up to 6 possible answer choices. After each short quiz, the number of correct answers is reported out of the total number of questions. At the end of the document, the participant is congratulated for getting all questions correct across every quiz.
The document provides 10 examples of solving mixture and alligation problems using the rule of alligation. The rule states that if two items are mixed in a ratio, the ratio of the difference between the mean price and dearer price to the difference between the mean price and cheaper price is equal to the ratio of the quantities of the cheaper and dearer items. Each example applies this rule to find unknown quantities, prices, or percentages when items of different values or concentrations are mixed.
This document discusses sequences and their properties. It defines a sequence as a list of numbers written in a definite order. The nth term of a sequence is denoted as an. It provides examples of describing sequences using notation, defining formulas, and listing terms. It defines convergent and divergent sequences and gives examples testing for convergence or divergence. It also discusses bounded sequences and decreasing sequences, giving examples and proofs.
The document discusses the gamma function, which generalizes the factorial function to real and complex numbers. It provides a brief history of the gamma function, noting it was first introduced by Euler to extend the factorial to non-integer values. The document defines the gamma function, provides some of its key properties like its relationship to the factorial of integers, and discusses other related functions like the beta function. It also gives some examples of applications of the gamma function, such as using it to calculate volumes of n-dimensional balls and in computing infinite sums.
The binomial theorem provides a formula for expanding binomial expressions of the form (a + b)^n. It states that the terms of the expansion are determined by binomial coefficients. Pascal's triangle is a mathematical arrangement that shows the binomial coefficients and can be used to determine the coefficients in a binomial expansion. The proof of the binomial theorem uses mathematical induction to show that the formula holds true for any positive integer value of n.
The document provides steps for solving equations with fractions that involve the same variable on both sides. It explains that these types of equations cannot be solved using traditional back-tracking methods. The extra steps include: 1) cross multiplying using brackets to remove fractions, 2) identifying the smaller letter term on both sides, and 3) applying the opposite operation to this term on both sides before simplifying and solving as normal. It then works through examples demonstrating these steps, such as solving the equation n-3=n+6/2/3.
1. The document discusses the gamma and beta functions, which are defined in terms of improper definite integrals and belong to the category of special transcendental functions.
2. Several properties and examples involving the gamma and beta functions are provided, including their relationship via the equation β(m,n)= Γ(m)Γ(n)/Γ(m+n).
3. Dirichlet's integral and its extension to calculating areas and volumes are covered. Four examples demonstrating the application of gamma and beta functions are worked out.
Spectral methods for solving differential equationsRajesh Aggarwal
This project report describes Rajesh Aggarwal's summer research fellowship project on spectral methods for solving differential equations under the guidance of Dr. Pravin Kumar Gupta at IIT Roorkee from June 11, 2014 to August 6, 2014. The report provides background on analytical and numerical methods for solving differential equations, specifically conventional finite difference methods and spectral finite difference methods. It then describes the methodology, codes, and results of applying both methods to solve sample differential equations on a half-space and layered earth problems. Tables and graphs comparing the accuracy of the two methods are presented.
Singular Value Decompostion (SVD): Worked example 2Isaac Yowetu
This document provides an example of calculating the singular value decomposition (SVD) of a 3x3 matrix A. It finds the matrices U, Σ, and V such that A = UΣV^T. It first calculates the eigenvalues and eigenvectors of A^TA to construct Σ and V. It then uses A and the eigenvectors to calculate the columns of U. The final SVD of A is presented.
Singular Value Decompostion (SVD): Worked example 3Isaac Yowetu
Singular Value Decomposition (SVD) decomposes a matrix A into three matrices: U, Σ, and V. The document provides an example of using SVD to decompose the matrix A = [[3, 1, 1], [-1, 3, 1]]. It finds the singular values and constructs the U, Σ, and V matrices. The SVD of A is written as A = UΣV^T, where U and V are orthogonal matrices and Σ is a diagonal matrix containing the singular values of A.
Se resuelven exámenes o relaciones de ejercicios de Bachillerato para las asignaturas de Matemáticas, Matemáticas Aplicadas a las Ciencias Sociales, Física y Química; y de nivel universitario para Estadística, Bioestadistica, Calculo y Álgebra.
A cargo de un Ingeniero de Caminos, Canales y Puertos y de un Licenciado en Matemáticas.
Envios por correo en PDF.
Pagos por transferencia o Paypal.
Precios de acuerdo al numero de ejercicios y dificultad de la materia.
Contacto en granada.clases.particulares@gmail.com
http://granada-clases-matematicas.blogspot.com/
Mathematikunterricht in 1zu1 Ausstattungen.pptxFlippedMathe
Wie geht guter Mathematikunterricht? Und jetzt auch noch mit Tablet/Laptop? In dieser Fortbildung soll es genau darum gehen.
Sebastian Schmidt kennt vielleicht nicht Ihre persönliche Antwort auf guten (digitalen) Mathematikunterricht, aber er hat seit 2013 versucht, mit digitalen Hilfsmitteln seinen Unterricht kompetenzorientierter zu gestalten. Die Digitalisierung von Unterricht hat immer die Problematik, das Lernen der Schülerinnen und Schülern aus dem Fokus zu verlieren. Diese sollen digital mündig werden und gleichzeitig Mathematik besser verstehen.
In dieser eSession werden zahlreiche Methoden, Konzepte und auch Tools vorgestellt, die im Mathematikunterricht des Referenten erfolgreich eingesetzt werden konnten. Nicht alles kann am nächsten Tag im Unterricht eingesetzt werden, aber man erhält einen Überblick, was möglich ist. Sie entscheiden dann selbst, worauf Sie Ihren Fokus legen und wie Sie selbst in die 1:1-Ausstattung starten.
Lassen Sie sich überraschen und nehmen Sie mit, was für Sie sinnvoll erscheint. Auf der Homepage von Sebastian Schmidt gibt es neben Links und Materialien zur Fortbildungen auch Workshops fürs eigene Ausprobieren. https://www.flippedmathe.de/fortbildung/mathe-ws/
Teaching and Learning Experience Design – der Ruf nach besserer Lehre: aber wie?Isa Jahnke
Der Ruf danach, dass es bessere Lehre geben muss oder das Lehre verbessert werden sollte, ist nicht neu. Es gibt auch schon seit längerer Zeit Rufe danach, dass Lehre der Forschung in Universitäten gleichgestellt werden soll. (Und in den letzten Jahren ist in Deutschland auch einiges an positiven Entwicklungen geschehen, z.B. durch die Aktivitäten des Stifterverbands). Wie kann die Verbesserung der Lehre weitergehen? Fehlt etwas in dieser Entwicklung? Ja, sagt dieser Beitrag, der zum Nachdenken und Diskutieren anregen soll. In diesem Beitrag wird ein forschungsbasierter Ansatz zur Diskussion gestellt. Es wird argumentiert, dass Lehre nur dann besser wird, wenn es mit den Prinzipen der Wissenschaft und Forschung angegangen wird (d.h. gestalten, Daten erheben, auswerten, verbessern). Es benötigt neue Verhaltensregeln oder -prinzipien bei der Gestaltung von Lehrveranstaltungen. Das bedeutet zum Beispiel das Prinzipien der Evidenzbasierung und wissenschaftliche Herangehensweisen im Lehr-Lerndesign als zentrales Fundament etabliert werden sollte. Evidenzbasierung hier meint, folgt man der Logik der Forschung, dass Lehrveranstaltungen als Intervention verstanden werden. Mit dieser Intervention werden Studierende befähigt, bestimmte vorab festgelegte Kompetenzen zu entwickeln. Und die Frage, die sich bei jeder Lehr-Lernveranstaltung dann stellt, ist, ob diese Objectives bzw. Learning Outcomes auch erreicht wurden. Klar ist, dass die subjektive Lehrevaluation der Studierenden oder auch die Notengebnung nicht ausreichen, um diese Frage zu beantworten. Hierfür gibt es eine Reihe von Methoden, die genutzt werden können, z.B. aus dem Bereich des User- / Learning Experience Design. Diese Methoden umfassen unter anderem Usability-Tests, Learner Experience Studies, Pre-/Post-Tests, und Follow-up Interviews. Diese können zur Gestaltung und Erfassung von effektiven, effizienten und ansprechenden digitalen Lerndesigns verwendet (Reigeluth 1983, Honebein & Reigeluth, 2022).
Der Beitrag will die Entwicklung zur Verbesserung von Lehre weiter pushen. Neue Ideen in die Bewegung bringen. Als Gründungsvizepräsidentin der UTN hab ich die Chance, hier ein neues Fundament für eine gesamte Uni zu legen. Wird das Gelingen? Ist dieser Ansatz, den ich hier vorstelle, eine erfolgsversprechende Option dafür? Hier können sich die TeilnehmerInnen an dieser Entwicklung beteiligen.