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- Recommended Sources

This guide is for most of Ohio State's calculus courses

Mathematical Sciences Librarian

Science Education Specialist

**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).
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*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:

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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.

- Vertical Line Test
- Domain and Range
- Khan Academy: What is a function?
- Khan Academy: Introduction to functions
- Khan Academy: Difference between equations and functions
- Khan Academy: What is the domain of a function?
- Khan Academy: Domain of a function
- Khan Academy: What is the range of a function?

- Precise Definition of the Limit
- Functions and limits
- One-sided Limits Calculus-Limits & Continuity: Definition of the Limit
- One-sided limits and limits involving infinity
- Khan Academy: Introduction to limits
- Khan Academy: Limits by factoring
- Khan Academy: Limits by direct substitution
- Khan Academy: Infinite limits intro
- Khan Academy: Limit examples (part 1
- Khan Academy: Limit examples (part 2)
- Khan Academy: Limit examples (part 3)

- Khan Academy: Limit properties

- Definition of the Derivative
- Khan Academy: Derivative as a concept

- Khan Academy: The graphical relationship between a function & its derivative (part 1)
- Khan Academy: The graphical relationship between a function & its derivative (part 2)
- Khan Academy: Graphs of functions and their derivatives example
- Khan Academy:Connecting f, f', and f'' graphically
- Khan Academy: Figuring out which function is the derivative
- Khan Academy: Identifying a function's derivative example

- Derivative rules and tangent lines
- Khan Academy: Basic derivative rules (Part 1)
- Khan Academy: Basic derivative rules (Part 2)
- Khan Academy: Basic derivative rules: table
- Khan Academy: Basic derivative rules: find the error

- Product Rule, Two Functions
- Khan Academy: Product rule
- Khan Academy: Quotient rule and common derivatives

- Chain Rule with Power Rule Calculus-Derivatives: Chain Rule
- Chain Rule for Multivariable Functions Calculus-Partial Derivatives: Chain Rule
- Chain Rule for Multivariable Functions and Tree Diagrams Calculus-Partial Derivatives: Chain Rule
- Higher derivatives and the chain rule
- Khan Academy: Power rule
- Khan Academy: Chain rule
- Khan Academy: Chain Rule Examples
- Khan Academy:Chain rule proof
- Khan Academy:Chain rule with the power rule
- Khan Academy: Common chain rule misunderstandings
- Khan Academy: Multivariable chain rule

- Higher derivatives and the chain rule
- Higher Order Partial Derivatives
- Khan Academy: Second derivatives
- Khan Academy:Second derivatives (implicit equations): find expressio
- Khan Academy: Connecting f, f', and f'' graphically
- Khan Acacemy: Second derivatives (implicit equations): evaluate derivative

- Implicit Differentiation
- Implicit Differentiation, Equation of the Tangent Line
- Khan Academy: Implicit differentiation
- Khan Academy: Implicit Differentiation
- Khan Academy: Implicit Differentiation (part 2)
- Khan Academy: Worked example: Implicit differentiation
- Khan Academy: Showing explicit and implicit differentiation give same result
- Khan Academy: More implicit differentiation
- Khan Academy:Worked example: Evaluating derivative with implicit differentiation

- Logarithmic Derivatives
- Logarithmic Derivatives Example 2
- Logarithmic Differentiation
- Logarithmic Differentiation Example 2
- Khan Academy Logarithmic functions differentiation
- Khan Academy: Differentiating logarithmic functions using log properties
- Khan Academy: Derivative of natural logarithm
- Khan Academy: Proof: d/dx(ln x) = 1/x
- Khan Academy: Derivative of log with arbitrary base

- Inverse Functions and Logarithms
- Khan Academy: Derivatives of inverse functions
- Khan Academy: Derivatives of inverse functions: from equation
- Khan Academy: Derivatives of inverse functions: from table

- Khan Academy: Applied rate of change: forgetfulness
- Khan Academy: Introduction to rate-of-change problems
- Khan Academy: Introduction to average rate of change

- Ladder Sliding Down the Wall
- Radius of the Balloon
- Price of the Product
- Water Level in the Rank
- Observer and the Airplane
- Khan Academy: Related rates intro
- Khan Academy: Related rates: Approaching cars
- Khan Acacemy: Analyzing related rates problems: expressions
- Khan Academy: Related rates: water pouring into a cone

- Khan Academy: Calculus: Maximum and minimum values on an interval
- Khan Academy: Critical points introduction
- Khan Academy: Introduction to minimum and maximum points
- Khan Academy:Absolute minima & maxima (entire domain)
- Khan Academy: Multivariable maxima and minima
- Extrema and max/min word problems

- Circles, Center and Radius Calculus-Precalculus: Graphing Functions
- Sketching Graphs Calculus-Applications of Derivatives: Optimization
- Vertical Line Test Calculus-Precalculus: Functions
- Crazy Graphs Calculus-Limits & Continuity: Solving Limits
- Removable Discontinuities Calculus-Limits & Continuity: Continuity
- Curve sketching

- Khan Academy: Graphing with Calculus

- Mean Value Theorem for Derivatives
- Khan Academy: Mean value theorem
- Khan Academy: Mean value theorem example: polynomial
- Khan Academy: Mean value theorem | Derivative applications
- Khan Academy: Mean value theorem application
- Khan Academy: Mean value theorem example: square root function
- Khan Academy: Justification with the mean value theorem: table
- Khan Academy: Conditions for MVT: graph

- Vertical asymptotes
- Horizontal Asymptotes
- Slant Asymptotes
- Sketching Graphs
- Global Extrema of Multivariable Functions
- Critical Points
- Increasing and Decreasing
- Concavity
- First Derivative Test
- Second Derivative Test
- Extrema on a Closed Interval
- Khan Academy: Optimization with Calculus 1
- Khan Academy: Optimization with Calculus 2
- Khan Academy: Optimization with Calculus 3

- Dimensions that Minimize Page Size with a Given Printed Area
- Dimensions of a Rectangle that Minimize its Perimeter
- Two Real Numbers with Minimum Product
- Two Real Numbers with Minimum Sum of Squares
- Point on the Line Closest to Another Point
- Time when Velocity is Minimum
- Dimensions that Maximize the Volume of a Box
- Dimensions that Minimize the Surface Area of an Open Top box
- Width that Minimizes the Surface Area of an Open Top Box
- Dimensions that Maximize the Volume of a Cylinder
- Production Level and Sale Price that Maximize Profit
- Sales Level that Maximizes Revenue
- Khan Academy: Optimization: profit
- Khan Academy: Optimization: cost of materials
- Khan Academy: Optimization: box volume (Part 1)
- Khan Academy: Optimization: box volume (Part 2
- Khan Academy: Optimization: sum of squares

- L'Hospital's Rule
- Khan Academy: Introduction to l'Hôpital's rule
- Khan Academy: L'Hôpital's rule example 1
- Khan Academy: L'Hôpital's rule example 2
- Khan Academy: L'Hôpital's rule example 3
- Khan Academy: Proof of special case of l'Hôpital's rule
- Khan Academy: L'Hopital's Rule to solve for variable
- Khan Academy: Tricky L'Hopital's Rule problem

- Area Under or Enclosed by the Curve
- Trapezoidal Rule
- Khan Academy: Introduction to definite integrals
- Khan Academy: Definite integrals (part II)
- Khan Academy: Definite Integrals (area under a curve) (part III)
- Khan Academy: Definite Integrals (part 4)

- Area Under or Enclosed by the Curve Calculus-Integrals: Definite Integrals
- U-Substitution in Definite Integrals Calculus-Integrals: U-Substitution
- Definite integrals and Riemann sums
- Khan Academy:ntroduction to definite integrals
- Khan Academy: Definite integral as the limit of a Riemann sum
- Khan Academy: Finding definite integrals using area formulas
- Khan Academy: Definite integral of rational function
- Khan Academy: Definite integral properties (no graph): breaking interval
- Khan Academy: Worked examples: Definite integral properties 1
- Khan Academy: Worked examples: Definite integral properties 2

- Khan Academy: Area between a curve and the x-axis

- Part 1 of the FTC
- Khan Academy: Fundamental theorem of calculus (Part 1

- Part 2 of the FTC
- Khan Academy: Fundamental theorem of calculus (Part 2)

- Disks, Vertical Axis
- Washers, Horizontal Axis
- Work Done to Empty a Tank
- Work Done by a Variable Force
- Hydrostatic Pressure
- Vertical Motion
- Rectilinear Motion
- Centroids of Plane Regions
- Single deposit, Compounded Continuously
- Income Stream, Compounded Continuously
- Income Stream, Compounded Continuously, Present Value
- Consumer and Producer Surplus
- Area Between Upper and Lower Curves
- Arc Length of y=f(x)
- Surface Area of Revolution
- Surface of Revolution Equation
- Cylindrical Shells, Vertical Axis
- Cylindrical Shells, Vertical Axis
- Work Done on Elastic Springs
- Single Deposit, Compounded n Times, Future Value

- Integration techniques
- U-Substitution
- Khan Academy: U-substitution intro
- Khan Academy: U-substitution with definite integral
- Khan Academy: U-substitution: definite integrals
- Khan Academy: U-substitution and back substitution

- Integration techniques
- Khan Academy: Introduction to integral calculus

- 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 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

- Alternating Series Test
- Khan Academy: Alternating series test
- Khan Academy: Alternating series remainder
- Khan Academy: Worked example: alternating serie
- Khan Academy: Worked example: alternating series remainder

- 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

- Khan Academy: What is a differential equation
- Khan Academy:Differential equation introduction
- Khan Academy: Writing a differential equation
- Khan Academy:Differential equations (playlist)

- Khan Academy: Creating a slope field
- Khan Academy: Differential equation from slope field
- Khan Academy: Slope field to visualize solutions
- Khan Academy: Euler's method
- Khan Academy: Worked example: Euler's method

- Khan Academy: Separable differential equations introduction
- Khan Academy: Worked example: separable differential equation
- 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

- Eliminating the Parameter
- Volume of Revolution of a Parametric Curve
- 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
- Surface Area of Revolution of 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

- Khan Academy: Representing points in 3d
- Khan Academy: 3d vector fields, introduction
- Khan Academy: 3d vector field example
- Khan Academy: Defining a plane in R3 with a point and normal vector

- Khan Academy: Proving vector dot product properties
- Khan Academy: Projection is closest vector in subspace
- Khan Academy: Visualizing a projection onto a plane

- Cross Product of Two Vectors
- Khan Academy: Cross product introduction
- Khan Academy: Dot vs. cross product

- Khan Academy: Differential of a vector valued function
- Khan Academy: Second derivatives (vector-valued functions)
- Khan Academy: Vector valued function derivative example
- Khan Academy: Partial derivatives of vector-valued functions
- Khan Academy: Computing the partial derivative of a vector-valued function
- Khan Academy: Derivative of a position vector valued function

- 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

- Linear Approximation in Two Variables
- Khan Academy: What is a tangent plane
- Khan Academy: Computing a tangent plane
- Khan Academy: Local linearizati

- Lagrange Multipliers
- Lagrange Multipliers Example 2
- Khan Academy: Meaning of Lagrange multiplier
- Khan Academy: Proof for the meaning of Lagrange multipliers
- Khan Academy: Lagrange multiplier example, part 1
- Khan Academy: Lagrange multiplier example, part 2
- Khan Academy: Finishing the intro lagrange multiplier example

- Khan Academy: Vector fields, introduction

- Line Integrals
- Khan academy: Introduction to the line integral
- Khan academy: Line integral example 1
- Khan academy: Line integral example 2 (part 1)
- Khan academy: Line integral example 2 (part 2)
- Khan academy: Evaluating line integral directly - part 1
- Khan academy: Evaluating line integral directly - part 2
- Khan academy: Line integrals and vector fields
- Khan Academy: Using a line integral to find the work done by a vector field example
- Khan Academy:Vector field line integrals dependent on path direction
- Khan Academy: Line integrals and Green's theorem
- Khan Academy:Path independence for line integrals

- Khan Academy: Curl 1
- Khan Academy: Curl 2
- Khan Academy: Curl 3
- Khan Academy: 2d curl intuition
- Khan Academy: 3d curl intuition, part 1
- Khan Academy: 3d curl intuition, part 2
- Khan Academy: 3d curl formula, part 1
- Khan Academy: 3d curl formula, part 2
- Khan Academy: 2d curl example
- Khan Academy: 3d curl computation example

- Khan Academy: Introduction to the surface integral
- Khan Academy: Vector representation of a surface integra
- Khan Academy: Example of calculating a surface integral part 1
- Khan Academy: Example of calculating a surface integral part 2
- Khan Academy: Example of calculating a surface integral part 3
- Khan Academy: Surface integral example part 1
- Khan Academy: Surface integral example part 2
- Khan Academy: Surface integral example part 3

- Khan Academy: Stokes' theorem intuition
- Khan Academy: Stokes' theorem intuition
- Khan Academy: Stokes' theorem proof part 1
- Khan Academy: Stokes' theorem proof part 2
- Khan Academy: Stokes' theorem proof part 3
- Khan Academy: Stokes' theorem proof part 4
- Khan Academy: Stokes' theorem proof part 5
- Khan Academy: Stokes' theorem proof part 6
- Khan Academy: Stokes' theorem proof part 7
- Khan Academy: Conditions for stokes theorem
- Khan Academy: Stokes example part 1
- Khan Academy: Stokes example part 2
- Khan Academy: Stokes example part 3
- Khan Academy: Stokes example part 4

- Khan Academy: Divergence 1
- Khan Academy: Divergence 2
- Khan Academy: Divergence 3
- Khan Academy: Divergence notation
- Khan Academy: Divergence theorem proof (part 1)
- Khan Academy: Divergence theorem proof (part 2)
- Khan Academy: Divergence theorem proof (part 3)
- Khan Academy: Divergence theorem proof (part 4)
- Khan Academy: Divergence theorem proof (part 5)
- Khan Academy: 2D divergence theorem
- Khan Academy: Conceptual clarification for 2D divergence theorem
- Khan Academy: Divergence intuition, part 1
- Khan Academy: Divergence intuition, part 2
- Khan Academy: Why we got zero flux in divergence theorem example 1
- Khan Academy: 3D divergence theorem intuition

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- 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.

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