# Courses tagged with "Mathematics" (77)

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### Algebra: Rational expressions

Khan Academy Free Closed [?] Mathematics Algebra College algebra Rational expressions

### Algebra: Ratios & proportions

Khan Academy Free Closed [?] Mathematics Algebra College algebra Ratios & proportions

Solving and writing algebraic ratios and proportions. Solving rational equations. Introduction to Ratios (new HD version). Understanding Proportions. Ratios as Fractions in Simplest Form. Simplifying Rates and Ratios. Find an Unknown in a Proportion. Ratio and Proportion. Find an Unknown in a Proportion 2. Another Take on the Rate Problem. Finding Unit Rates. Finding Unit Prices. Writing Proportions. Ratio problem with basic algebra (new HD). More advanced ratio problem--with Algebra (HD version). Alternate Solution to Ratio Problem (HD Version). Advanced ratio problems. Unit conversion. Conversion between metric units. Converting within the metric system. Converting pounds to ounces. Converting Gallons to quarts pints and cups. Converting Farenheit to Celsius. Comparing Celsius and Farenheit temperature scales. Applying the Metric System. U.S. Customary and Metric units. Converting Yards into Inches. Unit Conversion with Fractions. Performing arithmetic calculations on units of volume. Application problems involving units of weight. Solving application problems involving units of volume. Unit Conversion Example: Drug Dosage. Perimeter and Unit Conversion. Rational Equations. Solving Rational Equations 1. Solving Rational Equations 2. Solving Rational Equations 3. Applying Rational Equations 1. Applying Rational Equations 2. Applying Rational Equations 3. Extraneous Solutions to Rational Equations. Rational Inequalities 2.

### Algebra: Ratios and proportions

Khan Academy Free Closed [?] Mathematics Algebra College algebra Ratios and proportions

What ratios and proportions are. Using them to solve problems in the real world. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem. Ratio problem with basic algebra (new HD). Writing proportions. Writing proportions. Find an Unknown in a Proportion. Find an Unknown in a Proportion 2. Proportions 1. Proportions 2 exercise examples. Proportions 2. Constructing proportions to solve application problems. Constructing proportions to solve application problems. The Golden Ratio. Advanced ratio problems. More advanced ratio problem--with Algebra (HD version). Another Take on the Rate Problem. Alternate Solution to Ratio Problem (HD Version). Mountain height word problem.

### Algebra: Systems of equations and inequalities

Khan Academy Free Closed [?] Mathematics Algebra College algebra Systems of equations and inequalities

### Arithmétique: en route pour la cryptographie

Canvas.net Free Closed [?] Mathematics

This course is taught in French Vous voulez comprendre l'arithmétique ? Vous souhaitez découvrir une application des mathématiques à la vie quotidienne ? Ce cours est fait pour vous ! De niveau première année d'université, vous apprendrez les bases de l'arithmétique (division euclidienne, théorème de Bézout, nombres premiers, congruence). Vous vous êtes déjà demandé comment sont sécurisées les transactions sur Internet ? Vous découvrirez les bases de la cryptographie, en commençant par les codes les plus simples pour aboutir au code RSA. Le code RSA est le code utilisé pour crypter les communications sur internet. Il est basé sur de l'arithmétique assez simple que l'on comprendra en détail. Vous pourrez en plus mettre en pratique vos connaissances par l'apprentissage de notions sur le langage de programmation Python. Vous travaillerez à l'aide de cours écrits et de vidéos, d'exercices corrigés en vidéos, des quiz, des travaux pratiques. Le cours est entièrement gratuit !

### Calculus I (Differential Calculus)

Udemy Free Closed [?] Mathematics Calculus Calculus I Math Math and Science

Videos on a first course in calculus (Differential Calculus).

### Calculus II (Integral Calculus)

Udemy \$10 Closed [?] Mathematics Calculus Calculus II Math Math & Science Math and Science

Videos on a second course in calculus (Integral Calculus).

### Core Science - Numerical Methods and Programing

Udemy Free Closed [?] Mathematics Math and Science Numerical Methods

Lectures by P.B.Sunil Kumar, Department of Physics, IIT Madras

### CS106/MA121: Introduction to Statistics

Saylor.org Free Closed [?] Mathematics Computer Science Math and Science Statistics Statistics and Data Analysis

In this course, you will look at the properties behind the basic concepts of probability and statistics and focus on applications of statistical knowledge.  You will learn about how statistics and probability work together.  The subject of statistics involves the study of methods for collecting, summarizing, and interpreting data.  Statistics formalizes the process of making decisions, and this course is designed to help you use statistical literacy to make better decisions.  Note that this course has applications for the natural sciences, economics, computer science, finance, psychology, sociology, criminology, and many other fields. We read data in articles and reports every day.  After finishing this course, you should be comfortable evaluating an author's use of data.  You will be able to extract information from articles and display that information effectively.  You will also be able to understand the basics of how to draw statistical conclusions. This course will begin with descriptive statistic…

### Differential Equations (Fall 2011)

MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

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.

Haynes Miller
Jeremy Orloff
Dr. John Lewis
Arthur Mattuck

## Other OCW Versions

OCW has published multiple versions of this subject. ## Related Content

### Differential Equations

Udemy Free Closed [?] Mathematics Differential Equations Math and Science

Topics covered in a first year course in differential equations.

### Differential Equations

Khan Academy Free Closed [?] Mathematics Differential Equations Math and Science

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.

### Electronics - Digital Signal Processing

Udemy Free Closed [?] Engineering Artificial Intelligence Math and Science Mathematics Signal processing

Lecture Series by Prof. S.C Dutta Roy, Department of Electrical Engineering, IIT Delhi

### Electronics - Electronics For Analog Signal Processing - I

Udemy Free Closed [?] Engineering Artificial Intelligence Math and Science Mathematics Signal processing

Lecture Series on Electronics For Analog Signal Processing by Prof.K.Radhakrishna Rao, Department of Electrical Engineer

### Linear Algebra (Fall 2011)

MIT OpenCourseWare (OCW) Free Mathematics MIT OpenCourseWare Undergraduate

This course covers matrix theory and linear algebra, emphasizing topics useful in other disciplines such as physics, economics and social sciences, natural sciences, and engineering. It parallels the combination of theory and applications in Professor Strang’s textbook Introduction to Linear Algebra.

#### 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:

• A complete set of Lecture Videos by Professor Gilbert Strang.
• Summary Notes for all videos along with suggested readings in Prof. Strang's textbook Linear Algebra.
• Problem Solving Videos on every topic taught by an experienced MIT Recitation Instructor.
• Problem Sets to do on your own with Solutions to check your answers against when you're done.
• A selection of Java® Demonstrations to illustrate key concepts.
• A full set of Exams with Solutions, including review material to help you prepare.

## Other OCW Versions

OCW has published multiple versions of this subject. ## Related Content

### Linear Algebra

Khan Academy Free Closed [?] Mathematics Linear Algebra

Matrices, vectors, vector spaces, transformations. Covers all topics in a first year college linear algebra course. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra. Introduction to matrices. Matrix multiplication (part 1). Matrix multiplication (part 2). Idea Behind Inverting a 2x2 Matrix. Inverting matrices (part 2). Inverting Matrices (part 3). Matrices to solve a system of equations. Matrices to solve a vector combination problem. Singular Matrices. 3-variable linear equations (part 1). Solving 3 Equations with 3 Unknowns. Introduction to Vectors. Vector Examples. Parametric Representations of Lines. Linear Combinations and Span. Introduction to Linear Independence. More on linear independence. Span and Linear Independence Example. Linear Subspaces. Basis of a Subspace. Vector Dot Product and Vector Length. Proving Vector Dot Product Properties. Proof of the Cauchy-Schwarz Inequality. Vector Triangle Inequality. Defining the angle between vectors. Defining a plane in R3 with a point and normal vector. Cross Product Introduction. Proof: Relationship between cross product and sin of angle. Dot and Cross Product Comparison/Intuition. Matrices: Reduced Row Echelon Form 1. Matrices: Reduced Row Echelon Form 2. Matrices: Reduced Row Echelon Form 3. Matrix Vector Products. Introduction to the Null Space of a Matrix. Null Space 2: Calculating the null space of a matrix. Null Space 3: Relation to Linear Independence. Column Space of a Matrix. Null Space and Column Space Basis. Visualizing a Column Space as a Plane in R3. Proof: Any subspace basis has same number of elements. Dimension of the Null Space or Nullity. Dimension of the Column Space or Rank. Showing relation between basis cols and pivot cols. Showing that the candidate basis does span C(A). A more formal understanding of functions. Vector Transformations. Linear Transformations. Matrix Vector Products as Linear Transformations. Linear Transformations as Matrix Vector Products. Image of a subset under a transformation. im(T): Image of a Transformation. Preimage of a set. Preimage and Kernel Example. Sums and Scalar Multiples of Linear Transformations. More on Matrix Addition and Scalar Multiplication. Linear Transformation Examples: Scaling and Reflections. Linear Transformation Examples: Rotations in R2. Rotation in R3 around the X-axis. Unit Vectors. Introduction to Projections. Expressing a Projection on to a line as a Matrix Vector prod. Compositions of Linear Transformations 1. Compositions of Linear Transformations 2. Matrix Product Examples. Matrix Product Associativity. Distributive Property of Matrix Products. Introduction to the inverse of a function. Proof: Invertibility implies a unique solution to f(x)=y. Surjective (onto) and Injective (one-to-one) functions. Relating invertibility to being onto and one-to-one. Determining whether a transformation is onto. Exploring the solution set of Ax=b. Matrix condition for one-to-one trans. Simplifying conditions for invertibility. Showing that Inverses are Linear. Deriving a method for determining inverses. Example of Finding Matrix Inverse. Formula for 2x2 inverse. 3x3 Determinant. nxn Determinant. Determinants along other rows/cols. Rule of Sarrus of Determinants. Determinant when row multiplied by scalar. (correction) scalar multiplication of row. Determinant when row is added. Duplicate Row Determinant. Determinant after row operations. Upper Triangular Determinant. Simpler 4x4 determinant. Determinant and area of a parallelogram. Determinant as Scaling Factor. Transpose of a Matrix. Determinant of Transpose. Transpose of a Matrix Product. Transposes of sums and inverses. Transpose of a Vector. Rowspace and Left Nullspace. Visualizations of Left Nullspace and Rowspace. Orthogonal Complements. Rank(A) = Rank(transpose of A). dim(V) + dim(orthogonal complement of V)=n. Representing vectors in Rn using subspace members. Orthogonal Complement of the Orthogonal Complement. Orthogonal Complement of the Nullspace. Unique rowspace solution to Ax=b. Rowspace Solution to Ax=b example. Showing that A-transpose x A is invertible. Projections onto Subspaces. Visualizing a projection onto a plane. A Projection onto a Subspace is a Linear Transforma. Subspace Projection Matrix Example. Another Example of a Projection Matrix. Projection is closest vector in subspace. Least Squares Approximation. Least Squares Examples. Another Least Squares Example. Coordinates with Respect to a Basis. Change of Basis Matrix. Invertible Change of Basis Matrix. Transformation Matrix with Respect to a Basis. Alternate Basis Transformation Matrix Example. Alternate Basis Transformation Matrix Example Part 2. Changing coordinate systems to help find a transformation matrix. Introduction to Orthonormal Bases. Coordinates with respect to orthonormal bases. Projections onto subspaces with orthonormal bases. Finding projection onto subspace with orthonormal basis example. Example using orthogonal change-of-basis matrix to find transformation matrix. Orthogonal matrices preserve angles and lengths. The Gram-Schmidt Process. Gram-Schmidt Process Example. Gram-Schmidt example with 3 basis vectors. Introduction to Eigenvalues and Eigenvectors. Proof of formula for determining Eigenvalues. Example solving for the eigenvalues of a 2x2 matrix. Finding Eigenvectors and Eigenspaces example. Eigenvalues of a 3x3 matrix. Eigenvectors and Eigenspaces for a 3x3 matrix. Showing that an eigenbasis makes for good coordinate systems. Vector Triple Product Expansion (very optional). Normal vector from plane equation. Point distance to plane. Distance Between Planes.

### MA001: Beginning Algebra

Saylor.org Free Closed [?] Mathematics

In this course, you will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve real-world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in pre-algebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction. This course provides students the opportuni…

### MA002: Precalculus I

Saylor.org Free Closed [?] Mathematics Math Precalculus Precalculus Algebra

Precalculus I is designed to prepare you for Precalculus II, Calculus, Physics, and higher math and science courses. In this course, the main focus is on five types of functions: linear, polynomial, rational, exponential, and logarithmic. In accompaniment with these functions, you will learn how to solve equations and inequalities, graph, find domains and ranges, combine functions, and solve a multitude of real-world applications. In this course, you will not only be learning new algebraic techniques that are necessary for other math and science courses, but you will be learning to become a critical thinker. You will be able to determine what is the best approach to take such as numerical, graphical, or algebraic to solve a problem given particular information. Then you will investigate and solve the problem, interpret the answer, and determine if it is reasonable. A few examples of applications in this course are determining compound interest, growth of bacteria, decay of a radioactive substance, and the…