What online resources are available for the Calculus portion of the Praxis 5161?
An outstanding site is Paul's Online Notes: http://tutorial.math.lamar.edu/
Here is a listing of all the material that is currently available in these notes:
http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,9,N
Calculus Notes
Review
Derivatives
Applications of Derivatives
Integrals
Applications of Integrals
Extras
An excellent site for Math video tutorials is http://patrickjmt.com/
CALCULUS videos
Here is a listing of all the material that is currently available in these notes:
http://tutorial.math.lamar.edu/downloadfile.aspx?file=B,9,N
Calculus Notes
Review
- Review : Functions
- Review : Inverse Functions
- Review : Trig Functions
- Review : Solving Trig Equations
- Review : Solving Trig Equations with Calculators, Part I
- Review : Solving Trig Equations with Calculators, Part II
- Review : Exponential Functions
- Review : Logarithm Functions
- Review : Exponential and Logarithm Equations
- Review : Common Graphs
- Tangent Lines and Rates of Change
- The Limit
- One-Sided Limits
- Limit Properties
- Computing Limits
- Infinite Limits
- Limits At Infinity, Part I
- Limits At Infinity, Part II
- Continuity
- The Definition of the Limit
Derivatives
- The Definition of the Derivative
- Interpretation of the Derivative
- Differentiation Formulas
- Product and Quotient Rule
- Derivatives of Trig Functions
- Derivatives of Exponential and Logarithm Functions
- Derivatives of Inverse Trig Functions
- Chain Rule
- Implicit Differentiation
- Related Rates
- Higher Order Derivatives
- Logarithmic Differentiation
Applications of Derivatives
- Rates of Change
- Critical Points
- Minimum and Maximum Values
- Finding Absolute Extrema
- The Shape of a Graph, Part I
- The Shape of a Graph, Part II
- The Mean Value Theorem
- Optimization Problems
- L’Hospital’s Rule and Indeterminate Forms
- Linear Approximations
- Differentials
- Newton’s Method
- Business Applications
Integrals
- Indefinite Integrals
- Computing Indefinite Integrals
- Substitution Rule for Indefinite Integrals
- More Substitution Rule
- Area Problem
- Definition of the Definite Integral
- Computing Definite Integrals
- Substitution Rule for Definite Integrals
Applications of Integrals
Extras
- Proof of Various Limit Properties
- Proof of Various Derivative Facts/Formulas/Properties
- Proof of Trig Limits
- Proofs of Derivative Applications Facts/Formulas
- Proof of Various Integral Facts/Formulas/Properties
- Area and Volume Formulas
- Types of Infinity
- Summation Notation
- Constant of Integration
An excellent site for Math video tutorials is http://patrickjmt.com/
CALCULUS videos
- What is a Limit? Basic Idea of Limits
- Calculating a Limit by Factoring and Cancelling
- Calculating a Limit by Getting a Common Denominator
- Calculating a Limit by Expanding and Simplifying
- Calculating a Limit by Multiplying by a Conjugate
- Calculating a Limit Involving Absolute Value
- sin(x)/x Limit as x Approaches Zero
- Squeeze Theorem for Limits
- Infinite Limits
- Infinite Limits – Basic Idea and Shortcuts for Rational Functions
- Infinite Limits with a Radical in the Expression
- Continuity – Part 1 of 2
- Continuity – Part 2 of 2
- Intermediate Value Theorem
- Partial Fraction Decomposition – Example 1
- What is a Derivative? Understanding the Definition
- Sketching the Derivative of a Function
- Derivatives – Basic Examples
- Derivatives: Product Rule
- Derivatives: Quotient Rule
- Derivatives: Chain Rule
- Tangent Line: Finding the Equation
- Chain Rule: Basic Problems
- Chain Rule + Product Rule + Factoring
- Chain Rule + Product Rule + Simplifying – Ex 1
- Chain Rule + Product Rule + Simplifying – Ex 2
- Chain Rule +Quotient Rule + Simplifying
- Chain Rule – Harder Ex 1
- Chain Rule – Harder Ex 2
- Chain Rule – Harder Ex 3
- Derivatives – More Complicated Examples
- Derivatives – More Complicated Examples
- Critical Numbers – Ex 1
- Critical Numbers – Ex 2
- Local Max/Min, Inc/Dec: From a Function
- Local Maximums/Minimums – Second Derivative Test
- Mean Value Theorem
- Proof By Contradiction – Calculus Based Example
- The Closed Interval Method to Find Absolute Maximums and Minimums
- Implicit Differentiation – Basic Idea and Examples
- Implicit Differentiation – Extra Examples
- Implicit Differentiation – More Examples
- Implicit Differentiation and Second Derivatives
- Concavity and Second Derivatives
- Related Rates – A Point on a Graph
- Related Rates Involving Baseball!
- Related Rates Problem Using Implicit Differentiation
- Related Rates Involving Trigonometry
- Related Rates Using Cones
- Linearization at a Point
- Sketching the Curve Using Calculus – Part 1 of 2
- Sketching the Curve Using Calculus – Part 2 of 2
- Sketching the Curve Summary – Graphing Ex 2 – Part 1 of 4
- Sketching the Curve Summary – Graphing Ex 2 – Part 2 of 4
- Sketching the Curve Summary – Graphing Ex 2 – Part 3 of 4
- Sketching the Curve Summary – Graphing Ex 2 – Part 4 of 4
- Optimization Problem #1
- Optimization Problem #3 – Making a Rain Gutter!
- Optimization Problem #2
- Newton’s Method
- Definite Integral – Understanding the Definition
- Approximating a Definite Integral Using Rectangles
- Riemann Sums: Calculating a Definite Integral – Part 1
- Riemann Sums: Calculating a Definite Integral – Part 2
- Integration by U-Substitution: Antiderivatives
- Integration by U-Substitution, Definite Integral
- Integration by U-Substitution – Indefinite Integral, Another 2 Examples
- Integration by U-substitution, More Complicated Examples
- Areas Between Curves
- Fundamental Theorem of Calculus Part 1
- Area Between Curves – Integrating with Respect to y
- Area Between Curves – Integrating with Respect to y – Part 2
- Volumes of Revolution: Disk/Washers about Vertical Lines
- Volumes of Revolution: Disk/Washers – Ex 1
- Volumes of Revolution: Disk/Washers – Ex 2
- Volumes of Revolution: Cylindrical Shells
- Volumes of Revolution: Cylindrical Shells – Longer Version
- Volumes of Revolution: Disk/Washers – Ex 3
- Work and Hooke’s Law – Ex 1
- Work and Hooke’s Law – Ex 2
- Work Required to Drain a Tank
- Work: The Cable/Rope Problem Part 1
- Work: The Cable/Rope Problem – Part 2
- Derivatives of Exponential Functions
- Exponents: Negative Exponents
- Integrals: Exponential Functions – Ex 1 and 2
- Integrals: Exponential Functions – Ex 3 and 4
- Derivatives of Logarithmic Functions
- Derivatives of Logarithmic Functions – More Examples
- Logarithmic Differentiation – Ex 1
- Logarithmic Differentiation – Ex 2
- Logarithmic Differentiation – Ex 3
- Inverse Trigonometric Functions: Derivatives – Ex 2
- Inverse Trigonometric Functions: Derivatives – Ex 3
- Integrals: Inverse Trigonometric Functions – Ex 1
- Integrals: Inverse Trigonometric Functions – Ex 2
- Hyperbolic Functions – The Basics
- Derivatives of Hyperbolic Functions
- Derivatives of Inverse Hyperbolic Functions
- Integrals: Hyberbolic Functions
- L’Hospital’s Rule – Indeterminate Quotients
- L’Hospital’s Rule – Indeterminate Products
- L’Hospital’s Rule – Indeterminate Differences
- L’Hospital’s Rule – Indeterminate Powers
- Integration by Parts – Ex 1
- Integration by Parts – Definite Integral