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Fundamentals of Mathematics for Engineers

Mathematical Sciences Librarian

Science Education Specialist

- 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.

- Area Between Upper and Lower Curves
- Khan Academy: Area between curves
- Khan Academy: Area between curves
- Khan Academy: Area between curves with multiple boundaries

- Khan Academy: Volume with cross sections: intro
- Khan Academy: Volume with cross sections: semicircle
- Khan Academy: Slice a rectangular pyramid
- Khan Academy: Volume with cross sections: triangle
- Khan Academy: Volume with cross sections: squares and rectangles
- Khan Academy: Interpreting graphs with slices

- Khan Academy: Shell method for rotating around vertical line
- Khan Academy: Shell method for rotating around horizontal line
- Khan Academy: Shell method with two functions of y
- Khan Academy: Shell method with two functions of x

- Arc Length of y=f(x)
- Khan Academy: Arc length intro
- Khan Academy: Worked example: arc length
- Khan Academy: Another arc length integration example

- Integration techniques
- Khan Academy: Introduction to integral calculus

- Integration by Parts
- Khan Academy: Integration by parts intro
- Khan Academy:Integration by parts Example 1
- Khan Academy: Integration by parts Example 2
- Khan Academy: Integration by parts: definite integrals
- Khan Academy:Integration by parts of (e^x)(cos x)

- Trigonometric Substitution Setup
- Trigonometric Substitution with Sine
- Trigonometric Substitution with Sine Example 2
- Trigonometric Substitution with Tangent
- Trigonometric Substitution with Tangent Example 2
- Khan Academy: Introduction to trigonometric substitution
- Khan Academy: Introduction to trig substitution
- Khan Academy: Trig substitution with tangent
- Khan Academy:Integrals: Trig Substitution 1
- Khan Academy: Integrals: Trig Substitution 2
- Khan Academy: Integrals: Trig Substitution 3 (long problem)

- Repeated Linear Factors Calculus-Integrals: Partial Fractions
- Repeated Quadratic Factors Calculus-Integrals: Partial Fractions
- Repeated Quadratic Factors. Calculus-Integrals: Partial Fractions Example 2
- Distinct Quadratic Factors. Calculus-Integrals: Partial Fractions Example 2
- Distinct Quadratic Factors. Calculus-Integrals: Partial Fractions Example 3
- Distinct Linear Factors. Calculus-Integrals: Partial Fractions Example 2
- Distinct Linear Factors. Calculus-Integrals: Partial Fractions Example 3
- Khan Academy: Integration with partial fractions
- Khan Academy: Partial fraction expansion to evaluate integral

- Khan Academy:: Introduction to improper integrals
- Khan Academy:: Divergent improper integral
- Khan Academy:: Improper integral with two infinite bounds

- Geometric Series for Repeating Decimals
- Sum of a Telescoping Series
- Limit vs. Sum of the Series
- Maclaurin Series
- Sum of the Geometric Series
- Interval of Convergence: Limits and sums, radius and interval of convergence
- Khan Academy: Sequences and Series (part 1)
- Khan Academy: Sequences and series (part 2)

- Khan Academy: Introduction to arithmetic sequences
- Khan Academy: Introduction to geometric sequence
- Khan Academy: Explicit and recursive definitions of sequences
- Khan Academy: Convergent and divergent sequences
- Khan Academy: Proving a sequence converges using the formal definition
- Khan Academy: Formal definition for limit of a sequence
- Khan Academy: Worked example: sequence explicit formula
- Khan Academy: Worked example: sequence convergence/divergence

- Integral Test Calculus-Sequences & Series: Integral Test
- Khan Academy: Integral test
- Khan Academy: Worked example: Integral test
- Khan Academy: Worked example: sequence convergence/divergence
- Khan Academy: Proof: harmonic series diverges
- Khan Academy: Worked example: divergent geometric series

- Ratio Test
- Ratio Test with Factorials
- Root Test
- Comparison Test
- Limit Comparison Test
- Khan Academy: Ratio test
- Khan Academy: Radius of convergence using Ratio Test
- Khan Academy: Direct comparison test
- Khan Academy: Worked example: direct comparison test
- Khan Academy:Limit comparison test
- Khan Academy: Worked example: limit comparison test

- Khan Academy: Polynomial approximation of functions (part 1)
- Khan Academy: Polynomial approximation of functions (part 2)
- Khan Academy: Approximating functions with polynomials (part 3)
- Khan Academy: Polynomial approximation of functions (part 4)
- Khan Academy: Polynomial approximations of functions (part 5)
- Khan Academy: Polynomial approximation of functions (part 6)
- Khan Academy: Polynomial approximation of functions (part 7)

- Taylor Series
- Taylor's Inequality
- Khan Academy: Taylor Polynomials
- Khan Academy:Visualizing Taylor series approximations
- Khan Academy: Worked example: recognizing function from Taylor series

- Eliminating the Parameter
- Volume of Revolution of a Parametric Curve
- Surface Area of Revolution: Vertical Axis
- Surface Area of revolution of a Parametric Curve, Horizontal Axis
- Tangent Line to the Parametric Curve
- Khan Academy: Parametric curves
- Khan Academy: Derivative of a parametric function
- Khan Academy: Partial derivative of a parametric surface, part 1
- Khan Academy: Partial derivative of a parametric surface, part 2
- Khan Academy: Second derivatives (parametric functions)

- Polar Coordinates
- Converting Rectangular Equations: Introduction to Polar Curves
- Sketching Polar Curves
- Converting Polar Equations
- Complex Numbers in Polar Form
- Product of Complex Numbers in Polar Form
- Khan Academy: Polar coordinates 1
- Khan Academy: Polar coordinates 2
- Khan Academy: Polar coordinates 3

- Area Between Polar Curves
- Arc Length of a Polar Curve
- Arc Length of a Polar Curve
- Area Bounded by One loop of a Polar Curve
- Area Inside a Polar Curve
- Khan Academy: Polar functions derivatives
- Khan Academy: Worked example: Area between two polar graphs
- Khan Academy:Worked example: differentiating polar functions
- Khan Academy: Area bounded by polar curve

- 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: 3d vector fields, introduction
- Khan Academy: 3d vector field example
- Khan Academy: Representing points in 3d

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

- Khan Academy: Position vector valued functions

- Partial Derivatives in Two Variables
- Partial Derivatives in Three or More Variables
- Higher Order Partial Derivatives Calculus-Partial Derivatives
- Khan Academy: Partial derivatives, introduction
- Khan Academy: Formal definition of partial derivatives
- Khan Academy: Partial derivatives and graphs
- Khan Academy: Partial derivatives
- Khan Academy: Partial derivatives 2
- Khan Academy: Partial derivatives of vector-valued functions
- Khan Academy: Partial derivatives of vector fields
- Khan Academy: Computing the partial derivative of a vector-valued function
- Khan Academy: Partial derivatives of vector fields, component by component

- Khan Academy: Directional derivative, formal definition
- Khan Academy: Directional derivative
- Khan Academy: Directional derivatives and slope
- Khan Academy: Multivariable chain rule and directional derivatives
- Khan Academy: Gradient
- Khan Academy: Gradient 1
- Khan Academy: Why the gradient is the direction of steepest ascent
- Khan Academy: Gradient of a scalar field
- Khan Academy: Gradient and graphs

- 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.