• Math sites on line:

  • Through these links, you can access to several Math sites. Most useful.

• Preliminaries

• Linear Inequalities and Absolute Value
  Explains the concepts of inequalities and absolute value/gives sample problems.

• Graphing Parallel and Perpendicular Lines
  Discusses relationship between slopes/gives examples.
• Section 2-3: Graphing Polynomials
  Explains how to graph a polynomial then gives quiz.
• Exponents and Logarithms
  Explains Logarithms and Exponential Functions and includes an interactive example.
• Angles, Functions, and Applications in Trigonometry
  Show angles, sines, cosines, tangents, trigonometry real-life applications, etc.
• Help With 'Moving' the Graph: Translation Technique for Functions
  The absolute value and square root functions are graphed, reflected, and translated.
• Secant Line and Tangent Line
  Animation that allows user to drag a red dot that secant line passes through.
• Solving Quadratic Equations
  A quadratic equation is given and solved using four different methods.
• Solving Trig Equations - Solutions

 

• Limits and Continuity

• Numerical Exploration of Limits
  Explores right-hand and left-hand limits.

• Computing Limits
  Gives properties of limits and a graphical example.
• Limits of Functions Using the Squeeze Principle
  Gives detailed solutions to problems where the Squeeze Theorem is used.
• Limits and Continuity
  Studies the behavior of functions near a particular point/graphs included.
• Limits as x Approaches Infinity
  Gives properties and example problems.
• The Definition of a Limit
  Explains definition of a limit and includes flash examples.
• Error Analysis: 5. Loss of Significance
  Series of slides giving definition and examples of loss-of-significance.
• Limits of Functions as x Approaches Infinity
  Several examples of problems with limits approaching infinity.
• The Concept of a Limit
  Explains concept of limit in layman's terms/limit compared to feeding hungry tiger.
• Continuity
  Defines continuity, gives proof and examples.

 

• Differentiation

• The Chain Rule
  Explains chain rule and gives examples.

• Definition of Differentiation
  Explains a derivative, tangent line, and secant line.
• Proof of the Power Rule
  Explains power rule then gives proof.
• Logarithmic Differentiation
  Gives logarithmic properties and sample problems.
• Engineering Fundamentals
  Gives the formulas for derivatives of trig. and inverse trig. functions.
• Rolle's Theorem and the Mean Value Theorem
  Explains Mean Value Theorem and gives tutorial using Flash.
• Differentiation Using the Product Rule
  Explains the product rule and gives several examples with detailed, step-by-step solutions.
• Differentiation Using the Quotient Rule
  Explains the quotient rule and gives several examples with detailed, step-by-step solutions.
• Tangents and Normals
  Gives illustration of line tangent to a curve
• Related Rates
  Explains related rates and gives several example problems.

 

• Applications of Differentiation

• Linear Approximations
  Explores tangent line approximation.

• Newton's Method Tutorial
  Tutorial that includes a simulator
• L'Hôpital's Rule
  Gives rules and examples of how and when to use L'Hôpital's Rule.
• Min, Max, Critical Points
  List of several derivative-related terms.
• Max-Min Problems
  Word problems with applets that let you see the solutions.
• Background Maths
  Defines increasing and decreasing, then shows the correlation to the slope of the tangent line.
• The First Derivative: Maxima and Minima
  Uses the first derivative test to see where f(x) is increasing or decreasing.
• Concavity and Inflection Points
  Provides theorems and examples of concavity and points of inflection as they apply to curve sketching.
• Visual Calculus: Graphs and Derivatives
  Short tutorial and examples using second derivative test for concavity.
• Differential Exercises
  Get hints and solutions to various differential exercises.

 

• Integration

• Applications of the Indefinite Integral
  Voltage across capacitor/Displacement-velocity-acceleration.

• Sigma Notation
  Explains sigma notation and how it correlates with area under a curve.
• Numerical Integration
  Simpson vs. Hermite
• The Definite Integral
  Explains definite integral and how to program into Maple or calculator.
• Substitution in the Indefinite Integral
  Teaches then asks mult. choice questions.
• Integral Calculus
  Discusses integrals and their uses.
• Applications of Integration
  Explains concepts behind using integration.
• Integration by Parts
  Explains integration by parts in depth.
• Physics Applications of Calculus
  Integration of acceleration to get velocity; integration of velocity to get position.
• Numerical Integration
  Numerical integration and rates of change.

 

• Applications of the Definite Integral

• Area Between Two Curves
  Several examples given and illustrated using Flash.

• The Length of a Curve
  Formula is derived and examples are given.
• Volume of a Solid of Revolution
  Gives links to four different methods.
• The Probability Integral
  Explains the probability integral.
• Hooke's law
  Explains Hooke's Law/includes equations.
• Finding Displacement from Velocity
  Explains the process and works out example.
• Using Integrals to Find the Area Between Two Lines and Volumes of Rotations
  Gives fundamental rules of volume integration and formulas.
• Arc Length and Surface Area
  Arc length and surface area are explained using illustrations.
• Manual Slide Show: Area Between Two Curves
  Graph gradually draws rectangles between the two curves.
• Solids of Revolution
  Explains solids of revolution/gives illustrations and examples.

 

• Exponential, Logarithms and Other Transcendental Functions

• Integrals Involving Inverse Hyperbolic Functions
  The formulas for finding the integrals of inverse hyperbolic functions.

• Euler's Method
  A demo that generates a graphical approximate solution to an initial value problem.
• Integrals Involving Inverse Trigonometric Functions
  Gives the integrals of three trig functions/the others are negatives of these.
• Inverse Trig. Function and their Graphs
  Inverse trig. functions and their graphs.
• Exponential and Natural Logarithm
  Gives formula for finding the integral of the natural logarithm.
• Drill - Finding Inverse Functions
  Asks user to find the inverses of several functions then gives step-by-step solutions.
• The Integration of Exponential Functions
  Several problems are given along with detailed solutions.
• Other Differential Equations
  Discusses Newton's Law of Cooling and other equations.
• Separable Differential Equations
  Gives a form of a differential equation and a general solution of a differential equation.
• Hyperbolic Functions
  Gives graphs of all hyperbolic functions as well as their definitions.

 

• Integration Techniques

• Techniques of Integration: Substitution
  Formulas and examples for substitution integration.

• Integration by Parts
  The formulas and examples of integration by parts.
• Integration by Parts
  Practice problems using integration by parts with hints.
• Integrating Powers and Products of Sines and Cosines
  The formulas and examples for integrating powers of trigonometric functions.
• Methods of Integration: Trigonometric Substitutions
  The formulas for and an example of integration by trigonometric substitution.
• Integration by Partial Fractions
  An explanation and examples of integration by partial fractions.
• Reduction Formulas
  Reduction formulas and their derivations.
• Indeterminate Quotient Forms
  Using L'Hopital's Rule for indeterminate forms.
• Improper Integrals
  Definitions and examples of improper integrals with discontinuous integrands.
• Improper Integrals
  Definitions and examples of improper integrals with infinite limits of integration.

 

• Infinite Series

• Limit of a Sequence
  Gives definition and several graphical examples.

• Infinite Series--Types and Tests
  Gives definitions of different types of series and tests for convergence
• Improper Integrals and Series: The Integral Test
  Explains integral test and gives examples.
• The Number PI
  Uses infinite series to calculate pi.
• Definition of Alternating Series and the Alternating Series Test
  Gives the definition and examples.
• Absolute Convergence of Improper Integrals
  Gives definition and explains several examples.
• Power Series
  Definition, theorem, and examples with solutions using Flash and Java.
• Taylor Series
  Defines Taylor series and gives examples.
• Fourier Series
  Definitions, theorems, and examples.
• Fourier Series
  Gives definition, mean value convergence theorem, and Fourier series of selected functions.

 

• Parametric Equation and Polar Coordinates

• Graphing Parametric Equations and Polar Coordinates
  Interactive Java Applets for Parametric Equations and Polar Coordinates.

• Parametric Equations
  Definition and Illustration of Parametric Equations.
• Tangent Lines and Parametric Curves
  Finding the first and second derivatives of parametric equations.
• Polar Coordinates
  Definition of and conversion into polar coordinates.
• Parametric Surfaces: Area
  Examples of finding the surface area of parametric curves.
• Polar Coordinates
  Explanation and examples of using polar coordinates.
• Polar Equations
  Investigation of the rose drawn by a polar equation.
• Limaçon
  A history and description of the properties of a limaçon.
• Conic Sections
  A description of conic sections and relevant equations.
• Polar Equations of Conics
  Uses polar coordinates to describe conic sections.

 

• Vectors and the Geometry of Space

• Vectors in a Plane
  Gives definitions and examples on all aspects of vectors.

• Unit Vectors
  Gives definition and several examples of unit vectors.
• Vector Dot Product
  Gives definition of dot product.
• Dot Product in the Plane
  Gives definition of dot product.
• The Vector Cross Product - A JAVA Interactive Tutorial
  Allows user to change the length and position of vectors and the normal vector changes accordingly.
• Development of the Idea of the Vector Cross Product
  Gives definition and graph.
• Vector Equation of a Line
  Gives a step-by-step approach to solving a Vector Equation of a Line.
• The Vector Equation of a Plane
  Derives formula, gives examples and equivalent cartesian, vector, and unit vector equations/links to other types of vector problems.
• Ellipsoid
  Gives the equation and a graph.
• Plane Vectors I -- Introduction:
  Concepts on one side, definitions on the other/allows user to change parameters.

 

• Vector-Valued Functions

• The Velocity Vector and its Components
  Discusses vectors in two and three dimensions/includes nice graphic.

• Curvature
  Gives the three formulas for curvature and discusses a helix and a circle.
• Normal Vector and Curvature
  Formula for normal vectors/includes pictures.
• Tangent Vector and Curvature
  Gives the properties of curves and an example of a tangent line.
• Determining the Normal Vector
  Illustration of someone operating a camera with derivation of formula.
• Acceleration as a 2D Vector
  Formulas for magnitude and direction of acceleration vectors.
• Parametric Equation of a Plane
  Gives example and solution and includes great illustrations.
• Arc Length in 3d
  Derivation of arc length formula.
• Vector-Valued Functions
  Several graphs of different vector-valued functions/includes problem set.
• Mathematical Structure Differentiating Vector-Valued Functions
  Definition, proof, theorem, and sample problems.

 

• Functions of Several Variables and Partial Differentiation

• Graphing functions of Several Variables
  Graphs and explains three different examples.

• Tangent Planes
  Graphical examples of tangent planes.
• A Non-differentiable Function with all Directional Derivatives
  Example problem with graph.
• A Function without a Limit, although Limits Exist Along All Lines
  Sample problem with a graph.
• Partial Derivatives
  Gives explanation and examples of Partial Derviatives and includes a graph.
• The Chain Rule
  Discusses the chain rule and Leibniz's formula.
• Lagrange Multipliers
  Gives theorem and two examples-one minimization and one maximization.
• Maxima and Minima of Functions
  Lab designed to help students, includes definition, theorem, and exercises.
• Chain Rules for Functions of Several Variables
  Gives the formulas then examples.
• Gradient of f(x,y) and F(x,y,z) = f(x,y) - z, a Tangent Plane and More
  Gradient and tangent plane are computed, graph is shown.

 

• Multiple Integrals

• Multiple Integrals
  Discusses multiple integrals, including Fubini's Theorem.

• Double Integrals
  Gives a general strategy and examples.
• Uses of Double Integrals
  Using double integrals to find volume and surface area.
• Double Integrals and Polar Coordinates
  Shows how to use double integrals and find polar coordinates.
• Triple Integrals
  Gives a general strategy and examples.
• Uses of Triple Integrals
  Using triple integrals to find volume and surface area.
• Moments and Center of Mass
  How to calculate moments and center of mass.
• Cylindrical Coordinates
  Finding cylindrical coordinates.
• Cylindrical, Spherical, and Cartesian Coordinates
  The relationship between cylindrical, spherical, and Cartesian coordinates.
• Transformation on Random Vectors
  The transformations on random vectors.

 

• Vector Calculus

• Vector Valued Functions
  Description of and equations for vector fields.

• The Flow Lines of a Vector Field
  Example of a vector field problem.
• Line Integrals
  Definition and interpretations of line integrals.
• Conservative Vector Fields
  Description, properties, and examples of conservative vector fields.
• Special Case: Green's Theorem in the Plane
  Description of Green's Theorem.
• Examples of Green's Theorem
  Solves examples using Green's Theorem.
• Line Integrals and Work
  Defines line integrals and the fundamental theorem of line integrals.
• The Divergence of a Vector Field
  Definition, interpretation, and examples of the divergence of a vector field.
• The Curl of a Vector Field
  Definition, interpretation, and examples of the curl of a vector field.
• Stokes' Theorem
  Definition and interpretation of Stokes' Theorem.

 

Online materials Free online ebooks and material.

Online books Free online ebooks from the American Mathematical Society.

Math FEUP Online course on Mathematics. Da FEUP.

Math IST Online course on Mathematics.

The Math Page Online courses on Algebra, Calculus, etc.

Exambot Physics, Math and Economics. With solved exercises, etc.!

Math Study guides.

Mathworld (+) Online resources about all math subjects. From Wolfram (+ resources; INTEGRATOR).

MERLOT (Multimedia Education Resource for Learning and Online Teaching) Online resources about several Math and StatisticsTopis

Matemática Essencial Online resources about innumerous Subjects (Portuguese)

NIST Virtual Library: Electronic Journals/Publications * | Databases | Books | Labs at Nist | Associations/Institutions/Societies | Universities | Software/Language/Data | Conferences and Meetings | People | Other Web Resources |

Mathematics and its Application in Engineering and Science Online resources on Mathematics. Very useful

Physics With Math links

Mathematics Yahoo Math site

Mathematics Google Math site

Math dictionary Online dictionary

Mathematics and Statistics Articles online. From Wiley.

Mathematicians History from Turnbull.

Math Puzzles from Schlumberger.

Vectors Online resources on vectors. Good! (+ links)

 279 Math Applets Collection:

Manipula Math Applets Collection:

Applets for Statistical Concepts

Misc

• A list of statistical functions available in Excel
• StatSoft - Electronic Textbook
• SPSS online course
• Statistics success stories (sample Chapter) (.pdf)
• Introductory Statistics Concepts, Models, and Applications by David Stockburger
• Journal of Statistics Education (JSE) Home Page
• Web-oriented Teaching Resources in Probability and Statistics
• STATLETS™ 100% Pure Java Applets for Statistical Analysis and Graphics
• Portraits of Statisticians

See: http://biblioteca.fe.up.pt

See: http://pessoal.sercomtel.com.br/matematica/superior/superior.htm

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