This exercise book contains a wide variety of problems in integral calculus, linear algebra, and linear regression, with applications to differential equations, probability, and life sciences. Every problem has a very detailed solution, and the book is self-contained, as the summary for every concept is provided. The book aims to help students learn the material more efficiently and get better results.

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

KiteModeler was developed in an effort to foster hands-on, inquiry-based learning in science and math. KiteModeler is a simulator that models the design, trimming, and flight of a kite. The program works in three modes: Design Mode, Trim Mode, or Flight Mode. In the Design Mode (shown below), you pick from five basic types of kite designs. You can then change design variables including the length and width of various sections of the kite. You can also select different materials for each component. When you have a design that you like, you switch to the Trim Mode where you set the length of the bridle string and tail and the location of the knot attaching the bridle to the control line. Based on your inputs, the program computes the center of gravity and pressure, the magnitude of the aerodynamic forces and the weight, and determines the stability of your kite. With a stable kite design, you are ready for Flight Mode. In Flight Mode you set the wind speed and the length of control line. The program then computes the sag of the line caused by the weight of the string and the height and distance that your kite would fly. Using all three modes, you can investigate how a kite flies, and the factors that affect its performance.

This Project has been completed as part of a standard 10 weeks Calculus 1 asynchronous online course with optional WebEx sessions during Summer 2021 Semester at MassBay Community College, Wellesley Hills, MA.

An Open Education Resource

Short Description:
Mathematical modelling plays an increasingly important role in almost any area of life sciences, and this interactive textbook focuses on the areas of population ecology, infectious diseases, immunology and cell dynamics, gene networks and pharmacokinetics. It is aimed at anyone who is interested in learning about how to model biological systems, including undergraduate and postgraduate mathematics students who have not studied mathematical biology before, life-sciences students with an interest in modelling, and post-16 mathematics students interested in university-level material. Some mathematical knowledge is assumed, and the mathematical models used are all in the form of ordinary differential equations.

Word Count: 41598

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

To Interpret the meaning of areas associated with the graph of a rate of change in context.

Analysis I (18.100) 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 textbook, or really a “coursebook” for a college freshman-level class, has been updated for Spring 2014 and provides an introduction to programming and problem solving using both Matlab and Mathcad. We provide a balanced selection of introductory exercises and real-world problems (i.e. no “contrived” problems). We include many examples and screenshots to guide the reader. We assume no prior knowledge of Matlab or Mathcad.

This is a text for a two-term course in introductory real analysis for junior or senior mathematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathematical maturity that can be gained from an introductory real analysis course.

The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calculus sequence is the only specific prerequisite for Chapters 1–5, which deal with real-valued functions. (However, other analysis oriented courses, such as elementary differential equation, also provide useful preparatory experience.) Chapters 6 and 7 require a working knowledge of determinants, matrices and linear transformations, typically available from a first course in linear algebra. Chapter 8 is accessible after completion of Chapters 1–5.

A Standards-Based Approach to the Foundations of Calculus

Word Count: 17914

(Note: This resource's metadata has been created automatically as part of a bulk import process by reformatting and/or combining the information that the author initially provided. As a result, there may be errors in formatting.)

This is an open-access textbook for calculus-based introductory physics courses. Anyone that complies with the license is welcome to modify and use this work for their own use, and we hope that you will choose to contribute. The textbook is specifically intended for a flipped-classroom approach, wherein students complete readings at home and the material is then discussed in class. The textbook thus contains questions and activities to engage readers. This text also includes a curriculum in experimental physics, detailing the scientific method and process, suggesting experiments to perform at home and in the lab, and has chapters that cover: writing and reviewing proposals, writing and reviewing reports, analyzing data, as well as an introduction to python. Finally, this textbook was written with many contributions from students! We hope that you may find it useful, and we are interested to know if you are using it!

Le frazioni che hanno al denominatore 10, 100, 100, 10000 sono dette frazioni decimali.Tutte le frazioni decimali possono essere scritte sotto forma di numeri decimali.Come possiamo procedere?-Poichè la frazione corrisponde ad una divisione, possiamo dividere il numeratore per il denominatore.es:12/10= 12:10 = 1,27/100 = 7:100 = 0,0715/1000 = 15:1000 = 0,015-Oppure possiamo scrivere il numeratore ed inserire la virgola in modo che vi siano tante cifre decimali quanti sono gli zeri del denominatore.Es:1545/100 = 15,451467/10 = 146,7 -Viceversa, per trasformare un numero decimale in frazione decimale si scrive una frazione che ha al numeratore il numero senza virgola, mentre il denominatore sarà 10, 100, 1000 a seconda delle cifre decimali del numero di partenza.Es:1,6 = 16/1014,45 = 1445/1002,347 = 2347/1000ESEGUI GLI ESERCIZI

This Project has been completed as part of a standard 10 weeks Calculus 3 asynhronous online course with optional office hours during Summer 2022 semester at MassBay Community College, Wellesley Hills, MA. 

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.

Precalculus Course with newly added video content in Spanish in weeks 01 and 02, more to come.

Math of Biological/Management/Social Sciences presents intuitive development of the calculus of polynomial, exponential and logarithmic functions, and extrema theory and applications.

Course Outcomes:
1. Apply calculus to solve problems with confidence, persistence, and openness to alternate approaches.
2. Interpret and communicate the concepts of rates of change and derivatives.
3. Connect the graphical behavior, numerical patterns and symbolic representations of function and derivatives.
4. Collaborate to solve calculus problems related to their field of study.
5. Recognize when and how to proficiently apply calculus tools to solve problems in business management, social sciences and and biological sciences.
6. Use a graphing calculator and/or other technology to solve applied problems.

A Google Drive folder created by Kevin Fink of materials for Math 2231 - Calculus with Analytical Geometry at the College of DuPage. This is intended to be a foundation for anyone wanting to teach Math 2231 where students would need to spend little to no money for materials during the semester. Includes links to a textbook on openstax, a myopenmath shell template, links to lecture videos, supplemental homework assignments and answers, and the materials for an Area project about approximating area under curves.This resource will be updated as needed. For the google drive folder and the most recent version, visit: https://drive.google.com/drive/folders/1KhhTIXOT2a0oEX1hqMIhDsNi4DaO6NSk?usp=sharing