Differential equations are the language of the models we use to describe the world around us. Most phenomena require not a single differential equation, but a system of coupled differential equations. In this course, we will develop the mathematical toolset needed to understand 2x2 systems of first order linear and nonlinear differential equations. We will use 2x2 systems and matrices to model: predator-prey populations in an ecosystem, competition for tourism between two states, the temperature profile of a soft boiling egg, automobile suspensions for a smooth ride, pendulums, and RLC circuits that tune to specific frequencies. The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Page to learn more and to enroll in the modules. Wolf photo by Arne von Brill on Flickr (CC BY 2.0) Rabbit photo by Marit & Toomas Hinnosaar on Flickr (CC BY 2.0)

**April 2016 update** The course has been redesigned from scratch with 2 more hours of material. Hope you guys enjoy! Over a 1000 students and counting with some great reviews already. See what some of my students have to say.. "Nice course structure. Additional diagrams drawn by the instructor make the material easier to understand. Option to type notes while watching the video is very convenient. Delivery of content is excellent and well paced which makes it easy to follow. Explanations are visually clear and the instructor does a good job of making his delivery engaging with a positive tone. He seems to know his stuff. Would highly recommend" "I really enjoyed this course. Everything was well presented and explained at just the right pace. If you need to brush up on basic maths skills, this is a great course to boost your confidence. Thanks Adi!" Welcome to Learn basic high school maths the easy way . After teaching maths to students for a better part of the decade, one thing that I've come to understand is how difficult a transition from primary school to high school can be for students. Have you ever wondered how some students are so far ahead in their learning? Are they all born Maths geniuses? Definitely not. It's because they have a really firm understanding of the fundamentals which allows them to progress a lot quicker when it comes to the more challenging topics, since every topic needs you to have a good base. How will this course help you? Every topic that I cover in this course will come up in some form in years to come. I go through every single topic in a step by step form so it's really easy for you to follow along. Not convinced? Then I suggest you check out the previews before you decide to enroll, to make sure my teaching style is easy to follow, I am very confident that it is. To go a step further, Udemy's 30-day money back guarantee should also make you feel at ease. Are you having a tough time keeping up in Maths at school? Do you think Algebra is just the worst or maybe indices is your green kryptonite? Then let me be your personal guide and teach you these topics in a way that will make you wonder why your teachers didn't just explain it to you like that. This course will not only help you catch up but also help you get ahead; if of course, you put in the required effort. I go through each chapter doing questions step by step using simple language. Something missing in the course? If you find I haven't covered a topic that you need at this level, let me know on the discussion board and I'll be happy to add it in :) **BONUS** I've provided worksheets (with answers) at the end of every chapter to test your knowledge from the lectures. I can guarantee that you'll be miles ahead of the competition if you take this course seriously and best part about knowing it all is - you can teach others as well. When you're willing to spend upwards of $50 an hour for a private tutor, it seems like a no brainer to at least give this a go, so that you have access to your very own private tutor any time you wish. I'm good with messages and emails so if you have questions, make sure to get in touch with me. And furthermore, I want you guys to make full use of the discussion board because one of the best ways to learn is by sharing your knowledge with others. Thanks guys, really hope you enjoy.

Basics of Statistical Inference and Modelling Using R is part one of the Statistical Analysis in R professional certificate. This course is directed at people with limited statistical background and no practical experience, who have to do data analysis, as well as those who are “out of practice”. While very practice oriented, it aims to give the students the understanding of why the method works (theory), how to implement it (programming using R) and when to apply it (and where to look if the particular method is not applicable in the specific situation).

How do populations grow? How do viruses spread? What is the trajectory of a glider? Many real-life problems can be described and solved by mathematical models. This course will introduce you to the modelling cycle which includes: analyzing a problem, formulating it as a mathematical model, calculating solutions and validating your results. All models are (systems of) ordinary differential equations, and you will learn more about those by watching videos and reading short texts, and more importantly, by completing well-crafted exercises. You will learn how to implement Euler's method in a (Python) program, and finally, you will learn how to write about your findings in a scientific way (with LaTeX). In the verified track of this course you will additionally: Consolidate the new theoretical skills with graded problem sets about five real-life applications. Work on your own modelling project (individually or in a team). Because mathematical modelling is only learned by doing it yourself, you complete your own modelling project on a self-defined real-life problem. You will be guided through the project by completing a list of smaller tasks. This course is aimed at Bachelor students from Mathematics, Engineering and Science disciplines. The course is for anyone who would to use mathematical modelling for solving real world problems, including business owners, researchers and students.

In this course, we go beyond the calculus textbook, working with practitioners in social, life and physical sciences to understand how calculus and mathematical models play a role in their work. Through a series of case studies, you’ll learn: How standardized test makers use functions to analyze the difficulty of test questions; How economists model interaction of price and demand using rates of change, in a historical case of subway ridership; How an x-ray is different from a CT-scan, and what this has to do with integrals; How biologists use differential equation models to predict when populations will experience dramatic changes, such as extinction or outbreaks; How the Lotka-Volterra predator-prey model was created to answer a biological puzzle; How statisticians use functions to model data, like income distributions, and how integrals measure chance; How Einstein’s Energy Equation, E=mc2 is an approximation to a more complicated equation. With real practitioners as your guide, you’ll explore these situations in a hands-on way: looking at data and graphs, writing equations, doing calculus computations, and making educated guesses and predictions. This course provides a unique supplement to a course in single-variable calculus. Key topics include application of derivatives, integrals and differential equations, mathematical models and parameters. This course is for anyone who has completed or is currently taking a single-variable calculus course (differential and integral), at the high school (AP or IB) or college/university level. You will need to be familiar with the basics of derivatives, integrals, and differential equations, as well as functions involving polynomials, exponentials, and logarithms. This is a course to learn applications of calculus to other fields, and NOT a course to learn the basics of calculus. Whether you’re a student who has just finished an introductory Calculus course or a teacher looking for more authentic examples for your classroom, there is something for you to learn here, and we hope you’ll join us!

Matrix Algebra underlies many of the current tools for experimental design and the analysis of high-dimensional data. In this introductory online course in data analysis, we will use matrix algebra to represent the linear models that commonly used to model differences between experimental units. We perform statistical inference on these differences. Throughout the course we will use the R programming language to perform matrix operations. Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. You will need to know some basic stats for this course. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts. These courses make up two Professional Certificates and are self-paced: Data Analysis for Life Sciences: PH525.1x: Statistics and R for the Life Sciences PH525.2x: Introduction to Linear Models and Matrix Algebra PH525.3x: Statistical Inference and Modeling for High-throughput Experiments PH525.4x: High-Dimensional Data Analysis Genomics Data Analysis: PH525.5x: Introduction to Bioconductor PH525.6x: Case Studies in Functional Genomics PH525.7x: Advanced Bioconductor This class was supported in part by NIH grant R25GM114818.

Introduction to the mathematical concept of networks, and to two important optimization problems on networks: the transshipment problem and the shortest path problem. Short introduction to the modeling power of discrete optimization, with reference to classical problems. Introduction to the branch and bound algorithm, and the concept of cuts.

Differential equations are the mathematical language we use to describe the world around us. Most phenomena can be modeled not by single differential equations, but by systems of interacting differential equations. These systems may consist of many equations. In this course, we will learn how to use linear algebra to solve systems of more than 2 differential equations. We will also learn to use MATLAB to assist us. We will use systems of equations and matrices to explore: The original page ranking systems used by Google, Balancing chemical reaction equations, Tuned mass dampers and other coupled oscillators, Threeor more species competing for resources in an ecosystem, The trajectory of a rider on a zipline. The five modules in this seriesare being offered as an XSeries on edX. Please visit the Differential EquationsXSeries Program Page to learn more and to enroll in the modules. *Zipline photo by teanitiki on Flickr (CC BY-SA 2.0)

More than 2000 years ago, long before rockets were launched into orbit or explorers sailed around the globe, a Greek mathematician measured the size of the Earth using nothing more than a few facts about lines, angles, and circles. This course will start at the very beginnings of geometry, answering questions like "How big is an angle?" and "What are parallel lines?" and proceed up through advanced theorems and proofs about 2D and 3D shapes. Along the way, you'll learn a few different ways to find the area of a triangle, you'll discover a shortcut for counting the number of stones in the Great Pyramid of Giza, and you'll even come up with your own estimate for the size of the Earth. In this course, you'll be able to choose your own path within each lesson, and you can jump between lessons to quickly review earlier material. GeometryX covers a standard curriculum in high school geometry, and CCSS (common core) alignment is indicated where applicable. Learn more about our High School and AP* Exam Preparation Courses This course was funded in part by the Wertheimer Fund.

Preparing for the AP Calculus AB exam requires a deep understanding of many different topics in calculus as well as an understanding of the AP exam and the types of questions it asks. This course is Part 1 of our XSeries: AP Calculus AB and it is designed to prepare you for the AP exam. In Part 2, you will use and apply the meaning and interpretations of derivatives from Part 1 to the integral, antiderivatives and differential equations. You will learn some applications of integrals including finding volumes of solids and solids of revolution, volumes with known cross sections and applications to Velocity-Time graphs. We will close with an introduction to differential equations and see how they are used. As you work through this course, you will find lecture videos taught by expert AP calculus teachers, practice multiple choice questions and free response questions that are similar to what you will encounter on the AP exam and tutorial videos that show you step-by-step how to solve problems. By the end of the course, you should be ready to take on the AP exam!