How do electrical engineers find out all the currents and voltages in a network of connected components? How do civil engineers calculate the materials necessary to construct a curved dome over a new sports arena? How do space flight engineers launch an exploratory probe?
If questions like these pique your interest, this course is for you!
Calculus with differential equations is the universal language of engineers. In this course, “Engineering Calculus and Differential Equations,” we will introduce fundamental concepts of single-variable calculus and ordinary differential equations. We'll explore their applications in different engineering fields. In particular, you will learn how to apply mathematical skills to model and solve real engineering problems.
This course will enable you to develop a more profound understanding of engineering concepts and enhance your skills in solving engineering problems. In other words, youwill be able to construct relatively simple models of change and deduce their consequences. By studying these, youwill learn how to monitor and even controla given system to do what you want it to do.
Techniques widely used in engineering will be illustrated; such as Laplace transform for solving problems in vibrations and signal processing. We have designed animations and interactive visualizations to supplement complex mathematical theories and facilitate understanding of the dynamic nature of topics involving calculus.

Mathematics is the language of Science, Engineering and Technology. Calculus is an elementary mathematical course in any Science and Engineering Bachelor. Pre-university Calculus will prepare you for the Introductory Calculus courses by revising five important mathematical subjects that are assumed to be mastered by beginning Bachelor students: functions, equations, differentiation, integration and analytic geometry. After this course you will be well prepared to start your university calculus course. You will learn to understand the necessary definitions and mathematical concepts needed and you will be trained to apply those and solve mathematical problems. You will feel confident in using basic mathematical techniques for your first calculus course at university-level, building on high-school level mathematics. We aim to teach you the skills, but also to show you how mathematics will be used in different engineering and science disciplines.
Education method
This is a self-paced course consisting of 7 modules (or weeks) and 1 final exam. The modules consist of a collection of 3-5 minute lecture videos, inspirational videos on the use of mathematics in Science, Engineering and Technology, (interactive) exercises and homework.
The videos, practice exercises and homework are available free of charge in the audit track. In the ID-verified track, necessary if you pursue a certificate, you can additionally access the final exam.
This course has been awarded with the 2016 Open Education Award for Excellence in the category 'Open MOOC' by the Open Education Consortium.
Learn more about our High School and AP* Exam Preparation Courses
* Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.

Introduction to unconstrained nonlinear optimization, Newton’s algorithms and descent methods.

Systems of equations live at the heart of linear algebra. In this course you will explore fundamental concepts by exploring definitions and theorems that give a basis for this subject. At the start of this course we introduce systems of linear equations and a systematic method for solving them. This algorithm will be used for computations throughout the course as you investigate applications of linear algebra and more complex algorithms for analyzing them.
Later in this course you will later see how a system of linear equations can be represented in other ways, which can reduce problems involving linear combinations of vectors to approaches that involve systems of linear equations. Towards the end of the course we explore linear independence and linear transformations. They have an essential role throughout our course and in applications of linear algebra to many areas of industry, science, and engineering. __

Differential equations are the mathematical language we use to describe the world around us. Many phenomena are not modeled by differential equations, but by partial differential equations depending on more than one independent variable. In this course, we will use Fourier series methods to solve ODEs and separable partial differential equations (PDEs). You will learn how to describe any periodic function using Fourier series, and will be able to use resonance and to determine the behavior of systems with periodic input signals that can be described in terms of Fourier series. This course will use MATLAB to assist computations.
In this course we will explore:
How to process noisy sound files
The way a beam bends in response to external forces
How to design of ovens to create strong but lightweight composites
The motion of a violin string
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.
Violinist photo by user: DeshaCAM. Copyright © 2018 Adobe Systems Incorporated. Used with permission.

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)

This course is part one of the MathTrackX XSeries Program which has been designed to provide you with a solid foundation in mathematical fundamentals and how they can be applied in the real world.
This course will lay down the foundations of basic mathematical vocabulary and play a role in communicating key concepts throughout the MathTrackX Program. A central concept underpinning this course is the mathematical concept of function. Functions occur throughout mathematics and an understanding of them is essential.
Guided by experts from the School of Mathematics and the Maths Learning Centre at the University of Adelaide, this course will introduce functions, the algebra of numbers & polynomials and sets of numbers and intervals of the real number line.
Join us as we provide opportunities to develop your skills and confidence in these mathematical functions.