Online courses directory (237)

This course has been designed to provide you with a clear, accessible introduction to discrete mathematics. Discrete mathematics describes processes that consist of a sequence of individual steps (as compared to calculus, which describes processes that change in a continuous manner). The principal topics presented in this course are logic and proof, induction and recursion, discrete probability, and finite state machines. As you progress through the units of this course, you will develop the mathematical foundations necessary for more specialized subjects in computer science, including data structures, algorithms, and compiler design. Upon completion of this course, you will have the mathematical know-how required for an in-depth study of the science and technology of the computer age.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

Build your earth science vocabulary and learn about cycles of matter and types of sedimentary rocks through the Education Portal course Earth Science 101: Earth Science. Our series of video lessons and accompanying self-assessment quizzes can help you boost your scientific knowledge ahead of the Excelsior Earth Science exam . This course was designed by experienced educators and examines both science basics, like experimental design and systems of measurement, and more advanced topics, such as analysis of rock deformation and theories of continental drift.

The laws of nature are expressed as differential equations. Scientists and engineers must know how to model the world in terms of differential equations, and how to solve those equations and interpret the solutions. This course focuses on the equations and techniques most useful in science and engineering.

Course Format

This course has been designed for independent study. It provides everything you will need to understand the concepts covered in the course. The materials include:

• Lecture Videos by Professor Arthur Mattuck.
• Course Notes on every topic.
• Practice Problems with Solutions.
• Problem Solving Videos taught by experienced MIT Recitation Instructors.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Interactive Java® Demonstrations called Mathlets to illustrate key concepts.
• A full set of Exams with Solutions, including practice exams to help you prepare.

Content Development

Topics covered in a first year course in differential equations.

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus playlist before starting here. What is a differential equation. Separable Differential Equations. Separable differential equations 2. Exact Equations Intuition 1 (proofy). Exact Equations Intuition 2 (proofy). Exact Equations Example 1. Exact Equations Example 2. Exact Equations Example 3. Integrating factors 1. Integrating factors 2. First order homegenous equations. First order homogeneous equations 2. 2nd Order Linear Homogeneous Differential Equations 1. 2nd Order Linear Homogeneous Differential Equations 2. 2nd Order Linear Homogeneous Differential Equations 3. 2nd Order Linear Homogeneous Differential Equations 4. Complex roots of the characteristic equations 1. Complex roots of the characteristic equations 2. Complex roots of the characteristic equations 3. Repeated roots of the characteristic equation. Repeated roots of the characteristic equations part 2. Undetermined Coefficients 1. Undetermined Coefficients 2. Undetermined Coefficients 3. Undetermined Coefficients 4. Laplace Transform 1. Laplace Transform 2. Laplace Transform 3 (L{sin(at)}). Laplace Transform 4. Laplace Transform 5. Laplace Transform 6. Laplace Transform to solve an equation. Laplace Transform solves an equation 2. More Laplace Transform tools. Using the Laplace Transform to solve a nonhomogeneous eq. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Laplace/Step Function Differential Equation. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob.

Differential equations with only first derivatives. What is a differential equation. Simple Differential Equations. Separable Differential Equations. Separable differential equations 2. Exact Equations Intuition 1 (proofy). Exact Equations Intuition 2 (proofy). Exact Equations Example 1. Exact Equations Example 2. Exact Equations Example 3. Integrating factors 1. Integrating factors 2. First order homegenous equations. First order homogeneous equations 2. What is a differential equation. Simple Differential Equations. Separable Differential Equations. Separable differential equations 2. Exact Equations Intuition 1 (proofy). Exact Equations Intuition 2 (proofy). Exact Equations Example 1. Exact Equations Example 2. Exact Equations Example 3. Integrating factors 1. Integrating factors 2. First order homegenous equations. First order homogeneous equations 2.

Transforms and the Laplace transform in particular. Convolution integrals. Laplace Transform 1. Laplace Transform 2. L{sin(at)}) - transform of sin(at). Part 2 of the transform of the sin(at). Laplace as linear operator and Laplace of derivatives. Laplace Transform of cos t and polynomials. "Shifting" transform by multiplying function by exponential. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Laplace Transform to solve an equation. Laplace Transform solves an equation 2. Using the Laplace Transform to solve a nonhomogeneous eq. Laplace/Step Function Differential Equation. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob. Laplace Transform 1. Laplace Transform 2. L{sin(at)}) - transform of sin(at). Part 2 of the transform of the sin(at). Laplace as linear operator and Laplace of derivatives. Laplace Transform of cos t and polynomials. "Shifting" transform by multiplying function by exponential. Laplace Transform of : L{t}. Laplace Transform of t^n: L{t^n}. Laplace Transform of the Unit Step Function. Inverse Laplace Examples. Dirac Delta Function. Laplace Transform of the Dirac Delta Function. Laplace Transform to solve an equation. Laplace Transform solves an equation 2. Using the Laplace Transform to solve a nonhomogeneous eq. Laplace/Step Function Differential Equation. Introduction to the Convolution. The Convolution and the Laplace Transform. Using the Convolution Theorem to Solve an Initial Value Prob.

Linear differential equations that contain second derivatives. 2nd Order Linear Homogeneous Differential Equations 1. 2nd Order Linear Homogeneous Differential Equations 2. 2nd Order Linear Homogeneous Differential Equations 3. 2nd Order Linear Homogeneous Differential Equations 4. Complex roots of the characteristic equations 1. Complex roots of the characteristic equations 2. Complex roots of the characteristic equations 3. Repeated roots of the characteristic equation. Repeated roots of the characteristic equations part 2. Undetermined Coefficients 1. Undetermined Coefficients 2. Undetermined Coefficients 3. Undetermined Coefficients 4. 2nd Order Linear Homogeneous Differential Equations 1. 2nd Order Linear Homogeneous Differential Equations 2. 2nd Order Linear Homogeneous Differential Equations 3. 2nd Order Linear Homogeneous Differential Equations 4. Complex roots of the characteristic equations 1. Complex roots of the characteristic equations 2. Complex roots of the characteristic equations 3. Repeated roots of the characteristic equation. Repeated roots of the characteristic equations part 2. Undetermined Coefficients 1. Undetermined Coefficients 2. Undetermined Coefficients 3. Undetermined Coefficients 4.

This intermediate math course continues our free online maths suite of courses. It covers rules and applications of differentiation, straight line graphs, graphing circular functions, logs and indices, the Binomial theorem, inverse functions, and factors of polynomials. This course is ideal for second-level students, anyone studying for an exam, and those interested in re-igniting their knowledge of mathematics!<br />

ALISON.com's free online Diploma in Mathematics course gives you comprehensive knowledge and understanding of key subjects in mathematics. This course covers calculus, geometry, algebra, trigonometry, functions, vectors, data distributions, probability and probability and statistics. Math qualifications are in great demand from employers and this math course will greatly enhance your career prospects.<br />

Statistics and statistical methods play a major role in the work environment in areas such as business, science, finance, economics, engineering to mention just a few. It is very important that people are comfortable with reading statistics and using statistical methods. This free online Diploma in Statistics will give you the knowledge and understanding of basic statistical methods such as sampling and collecting data, probability, distributions, regression analysis. By completing this course you will gain the knowledge and understanding to confidently read statistics and apply statistical methods within your daily working environment.

This beginners math course is an ideal introduction to fractions. The tutorial uses an interactive multimedia format and relevant examples to thoroughly examine the topic. It is ideal as a study aid or as a complement to face-to-face classes.

The foundations of Geometry.

This free online course in Geometry is for high school and secondary school students. The course will guide you through several different areas of Geometry such as points, lines, angles, triangles, quadrilaterals and circles, as well as transformations and area. The course is divided into ten modules and each module is divided into several lessons. Under each lesson you will find theory, examples and video lessons. This course is ideal for learners who want to gain a comprehensive knowledge and understanding of topics in Geometry which they can build on in later courses.

<p>This free online Geometry course provides a comprehensive introduction to geometrical methods and techniques, covering angles, triangles, quadrilaterals, polygons, and more. </p><br /> <p>It is ideal for complementing face-to-face classes, as a study guide, or for those who would like to refresh their knowledge of mathematics. </p>

This topic continues our journey through the world of Euclid by helping us understand angles and how they can relate to each other. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. Proof - Sum of Measures of Angles in a Triangle are 180. Triangle Angle Example 1. Triangle Angle Example 2. Triangle Angle Example 3. Challenging Triangle Angle Problem. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate. Angle basics. Measuring angles in degrees. Using a protractor. Measuring angles. Measuring angles. Acute right and obtuse angles. Angle types. Vertical, adjacent and linearly paired angles. Exploring angle pairs. Introduction to vertical angles. Vertical angles. Using algebra to find the measures of vertical angles. Vertical angles 2. Proof-Vertical Angles are Equal. Angles Formed by Parallel Lines and Transversals. Identifying Parallel and Perpendicular Lines. Figuring out angles between transversal and parallel lines. Congruent angles. Parallel lines 1. Using algebra to find measures of angles formed from transversal. Parallel lines 2. CA Geometry: Deducing Angle Measures. Proof - Sum of Measures of Angles in a Triangle are 180. Triangle Angle Example 1. Triangle Angle Example 2. Triangle Angle Example 3. Challenging Triangle Angle Problem. Proof - Corresponding Angle Equivalence Implies Parallel Lines. Finding more angles. Angles 1. Angles 2. Sum of Interior Angles of a Polygon. Angles of a polygon. Sum of the exterior angles of convex polygon. Introduction to angles (old). Angles (part 2). Angles (part 3). Angles formed between transversals and parallel lines. Angles of parallel lines 2. The Angle Game. Angle Game (part 2). Acute right and obtuse angles. Complementary and supplementary angles. Complementary and supplementary angles. Example using algebra to find measure of complementary angles. Example using algebra to find measure of supplementary angles. Angle addition postulate.

Finding measurements and applying and proving circle theorems. Language and Notation of the Circle. Circles: Radius, Diameter and Circumference. Parts of a Circle. Three Points Defining a Circle. Area of a Circle. Pi Is (still) Wrong.. Right Triangles Inscribed in Circles (Proof). Right Triangles Inscribed in Circles (Proof). Perpendicular Radius Bisects Chord. Incenter and incircles of a triangle. Inradius Perimeter and Area.