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Linear Algebra and Differential Equations for Engineers

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Science Education Specialist

- Khan Academy: Differential equation introduction
- Khan Academy: What is a differential equation
- Khan Academy: First order differential equations
- Khan Academy: Simple Differential Equations
- Khan Academy: Writing a differential equation
- Khan Academy: First order homogenous equations

- Khan Academy: Particular solution to differential equation example
- Khan Academy: Finding particular linear solution to differential equation
- Khan Academy: Verifying solutions to differential equations
- Khan Academy: Worked example: exponential solution to differential equation
- Khan Academy: Laplace transform to solve an equation
- Khan Academy: Solving the logistic differential equation part 1
- Khan Academy: Solving the logistic differential equation part 2
- Khan Academy: Worked example: Logistic model word problem
- Khan Academy: Simple Differential Equation Example
- Khan Academy: Exact equations example 1
- Khan Academy: Worked example: separable differential equations

- Khan Academy: Separable differential equations introduction
- Khan Academy: Worked example: separable differential equations
- Khan Academy: Worked example: identifying separable equations
- Khan Academy: Worked example: separable differential equation (with taking exp of both sides)
- Khan Academy: Worked example: separable differential equation (with taking log of both sides)
- Khan Academy: Worked example: separable equation with an implicit solution

- Khan Academy: Modeling population with simple differential equation |
- Khan Academy: Modeling population as an exponential function
- Khan Academy: Newton's Law of Cooling

- Khan Academy: Modeling population with simple differential equation
- Khan Academy: Modeling population as an exponential function

- Khan Academy: First order homogenous equations
- Khan Academy: First order homogeneous equations 2
- Khan Academy: 2nd order linear homogeneous differential equations 1
- Khan Academy: 2nd order linear homogeneous differential equations 2
- Khan Academy: 2nd order linear homogeneous differential equations 3
- Khan Academy: 2nd Order Linear Homogeneous Differential Equations 4

- Khan Academy: Complex roots of the characteristic equations 1
- Khan Academy: Complex roots of the characteristic equations 2
- Khan Academy: Complex roots of the characteristic equations 3
- Khan Academy: Example modeling asteroid velocity with differential equation

- Khan Academy: Repeated roots of the characteristic equation
- Khan Academy: Repeated roots of the characteristic equations part 2

- Khan Academy: 2nd order linear homogeneous differential equations 1
- Khan Academy: 2nd order linear homogeneous differential equations 2
- Khan Academy: 2nd order linear homogeneous differential equations 3
- Khan Academy: 2nd Order Linear Homogeneous Differential Equations 4

- Khan Academy: Undetermined coefficients 1
- Khan Academy: Undetermined coefficients 2
- Khan Academy: Undetermined coefficients 3
- Khan Academy: Undetermined coefficients 4

- Khan Academy: Fourier Series introduction

- Khan Academy: Linear Algebra Playlist

- Solving Systems of Equations
- Khan Academy: Introduction to matrices
- Khan Academy: Matrix equations and systems
- Khan Academy: Matrices to solve a system of equation
- Khan Academy: Introduction to the matrix

- Khan Academy: Matrices: Reduced row echelon form 1
- Khan Academy: Matrices: Reduced row echelon form 2
- Khan Academy: Matrices: Reduced row echelon form 3

- Khan Academy: Consistent and inconsistent systems
- Khan Academy: Inconsistent systems of equations

- Khan Academy: Defined and undefined matrix operations
- Khan Academy: Matrix addition and subtraction
- Khan Academy: More on matrix addition and scalar multiplication
- Khan Academy: Matrix multiplication introduction
- Khan Academy: Matrix multiplication (part 1)
- Khan Academy: Matrix multiplication (part 2)
- Khan Academy: Scalar multiplication
- Khan Academy: Multiplying a matrix by a column vector
- Khan Academy: Multiplying a matrix by a matrix

- Khan Academy: Associative property of matrix multiplication
- Khan Academy: Is matrix multiplication commutative
- Khan Academy: Distributive property of matrix products
- Khan Academy: Singular matrices

- Khan Academy: Introduction to linear independence
- Khan Academy: Span and linear independence example
- Khan Academy: More on linear independence
- Khan Academy: Relation of null space to linear independence of columns

- Khan Academy: Inverse of a 2x2 matrix
- Khan Academy: Idea behind inverting a 2x2 matrix
- Khan Academy: Example of finding matrix inverse
- Khan Academy: Deriving a method for determining inverses
- Khan Academy: Invertible and noninvertibles matrices
- Khan Academy: Inverting 3x3 part 1
- Khan Academy: Inverting 3x3 part 2
- Khan Academy: Showing that inverses are linear
- Khan Academy: Classic video on inverting a 3x3 matrix part 1
- Khan Academy: Classic video on inverting a 3x3 matrix part 2

- Khan Academy: Linear Algebra: Introduction to Vectors
- Khan Academy: Adding vectors
- Khan Academy: Vector intro for linear algebra
- Khan Academy: Vector intro for linear algebra
- Khan Academy: Normal vector from plane equation
- Khan Academy: Defining a plane in R3 with a point and normal vector
- Khan Academy: Visualizing a projection onto a plane
- Khan Academy: Point distance to plane
- Khan Academy: Multiplying a vector by a scalar

- Khan Academy: Vectors and spaces

- Dot Products
- Dot Products
- Cross Product of Two Vectors
- Khan Academy: Vector dot product and vector length
- Khan Academy: Cross product introduction
- Khan Academy: Dot vs. cross product
- Khan Academy: Dot and cross product comparison/intuition

- Khan Academy: Vector dot product and vector length

- Khan Academy: Basis of a subspace

- Khan Academy: Dimension of the column space or rank
- Khan Academy: Dimension of the null space or nullity
- Khan Academy: Dimensions of identity matrix

- Khan Academy; Vectors and spaces

- Khan Academy: Linear subspace
- Khan Academy: Basis of a subspace
- Khan Academy: Projections onto subspaces
- Khan Academy: Subspace projection matrix example
- Khan Academy: Projection is closest vector in subspace

- Khan Academy: Coordinates with respect to a basis
- Khan Academy: Span and linear independence example
- Khan Academy: Span and linear independence example
- Khan Academy: Coordinates with respect to orthonormal bases

- Khan Academy: Introduction to orthonormal bases

- Khan Academy: Linear transformations
- Khan Academy: Linear transformations as matrix vector products
- Khan Academy: Linear transformations as matrix vector products
- Khan Academy: Linear transformation examples: Rotations in R2
- Khan Academy: Linear transformation examples: Rotations in R2
- Khan Academy: Compositions of linear transformations 1
- Khan Academy: Compositions of linear transformations 2

- Khan Academy: Introduction to eigenvalues and eigenvectors
- Khan Academy: Example solving for the eigenvalues of a 2x2 matrix

- Khan Academy: Finding the determinant of a 2x2 matrix
- Khan Academy: 3 x 3 determinant
- Khan Academy: Simpler 4x4 determinant
- Khan Academy: Determinants along other rows/cols
- Khan Academy: Determinant after row operations
- Khan Academy: Determinant when multiplying a matrix by a constant
- Khan Academy: Determinant when row multiplied by scalar
- Khan Academy: Determinant when row multiplied by scalar
- Khan Academy: Complex determinant example

- Khan Academy: Eigenvalues of a 3x3 matrix

- Khan Academy: Finding eigenvectors and eigenspaces example
- Khan Academy: Eigenvectors and eigenspaces for a 3x3 matrix

- Khan Academy: Linear transformations

- OSU Library CatalogSearch for books and other items available at OSU - includes ebooks
- OhioLINK CatalogSearch for books statewide.

- Electronic Book Center (OhioLINK) [Full Text] This link opens in a new windowElectronic Book Center included ebooks on all subjects, including many encyclopedias, handbooks, biographical collections, and guides.

The OSU Library Catalog has subject headings. If you had found a good book on your topic, examine the subject headings for that book below the location/call number box. You can click on these to see other items with that subject ot you can search subject directly as follows.

Examples:

"History" is a subdivision of a subject that can be added after any other term. Examples: Format: branch--history. Clickable examples:

For mathematics history in a country, region, use for format mathematics--country/region--history Examples:

**MathSciNet **is the major database to find content in the mathematics and statistics literature.

**MathSciNet has been Redesigned!**

This redesign has made significant changes to the way you search MathSciNet. The following tutorials will walk you through these changes:

- MathSciNet: Basic Search
- MathSciNet: Using Field Codes
- MathSciNet: Using Filters
- MathSciNet: Citing
- Example: Using MathSciNet's Updated Features to Explore Arithmetic Progressions

You can still use the previous interface, see the *Show Classic Interface* link above the magnifying glass search button, to the upper right of the search box.

Citation databases allow you to see for each article the items it cited and also the items that have cited it. If you find a great article, use these databases to move both back and forward in time from that article.

- Scopus This link opens in a new windowCitation searching across most disciplines. Contains most of the content from Compendex (engineering and computer science) and GEOBASE (geography).
- Web of Science Core Collection This link opens in a new windowArticles from all disciplines, back to 1900 (1975 for arts/humanities).

- Computers and Applied Sciences Complete [Selected Articles in Full Text] This link opens in a new windowSearches articles in multiple applied science areas

- JSTOR [Selected Articles in Full Text] This link opens in a new windowA collection of major journals in multiple disciplines. Most titles limited to contest older than 3-5 years.
- Academic Search Complete [Selected Articles in Full Text] This link opens in a new windowA general database covering multiple areas

*Google Scholar covers a wide range of topics.*

* Use the above link to you can make sure Google Scholar works best for you on or off campus.* In order to better use it, connect it to OSU by going to

You'll see some important buttons while using the OSU Libraries resouces. Especially important are these 4:

Where: OSU Library Catalog.

What: Have an item sent to another location for pickup or recall an item checked out.

Where: OSU Library Catalog.

What: Check for access of an individual item via OhioLINK - such as an item checked out at OSU. Also repeats searches in the OhioLINK catalog to see additional options for your need.

Where: OhioLINK Catalog

What: Click to have an item delivered to OSU from an OhioLINK library.

Where: Library Databases

What: Check for online access to journal articles, conference papers, and more. Also gives interlibrary loan option if item is not available online.

- Choosing & Usng SourcesTutorials on finding and using info.
- Article Express / Interlibrary LoanRequest articles, conference papers, and even books (check OhioLINK first) when unavailable at OSU. Request scans of print-only journal articles available at OSU.