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Online resources for calculus & graphing

Calculus   Books   Graphing

Calculus

Tutorials for the Calculus Phobe
Animated little flash movies about limits, continuity and derivative.
www.calculus-help.com/tutorials

Graphics for the Calculus Classroom
Animations illustrating basic calculus concepts.
www.ima.umn.edu/~arnold/graphics.html

Visual Calculus
A collection of modules from pre-calculus till sequences and series that uses lots of numerical and graphical illustrations, Flash tutorials, animations, etc.  Some of the discussion is on college level. 
archives.math.utk.edu/visual.calculus

IntegralCalc
A collection of clear and simple video tutorials for precalculus, limits & continuity, derivatives & their applications, integrals & their applications, sequences, series, polar & parametric functions, vectors, and differential equations.
integralcalc.pathwright.com

Calculus for Beginners and Artists
By Daniel Kleitman. Includes 20 chapters of text, Java applets, and some Flash dialogs all completely free and online.
www-math.mit.edu/~djk/calculus_beginners/

Online Calculus Course Video Tutorials
A collection of free videos for the calculus student.
www.straighterline.com/landing/online-calculus-video-tutorials

Calculus by Gilbert Strang
A free download of a regular calculus book for undergraduates. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.
ocw.mit.edu/resources/res-18-001-calculus-online-textbook-spring-2005/textbook/

Calculus video tutorials from Midnight Tutor
Videos of calculus problems and their solutions. You can also send in your problem and they will post a video of its solution.
www.midnighttutor.com/math_tutor_online.php

Calculus video course
Free videos from university of Houston, covering a complete college calculus course.
online.math.uh.edu/HoustonACT/videocalculus

MathTV.com
Over 6,000 free, online video lessons for basic math, algebra, trigonometry, and calculus. Videos also available in Spanish. Also includes online textbooks. I've written a review of MathTV lessons when they used to be offered on CDs.
www.mathtv.com

BrightStorm Math
Over 2,000 free videos covering all high school math topics from algebra to calculus. Registration required (free).
www.brightstorm.com/math

Notes on first-year Calculus
Free college level calculus text in PDF form.  Good for refreshment or for concise notes but not for first time learners.
www.math.umn.edu/~garrett/calculus

Calculus in Context
An introductory calculus textbook you can download for free (PDF). It is based on studying calculus as it is used in contemporary science, so that mathematical ideas and techniques grow out of scientific questions.
www.math.smith.edu/Local/cicintro/cicintro.html

Calculus Made Easy
A free download (PDF) of an old textbook, acclaimed to be a lively introduction to calculus, with clarity and simplicity.
djm.cc/library/Calculus_Made_Easy_Thompson.pdf

Derivative Calculator and Integral Calculator
Online symbolic calculators for derivatives and integrals. Both tools are designed for intuitive user interaction. While you type in your expression, it is transformed into a graphical formula in real-time and shown to you, which helps reducing input mistakes. The calculators do not show step-by-step differentiation or integration (not intended for cheating) but work great for checking your homework, or finding the derivative or integral for some other usage.
www.derivative-calculator.net
www.integral-calculator.com

Visualizing an Infinite Series
An on-line tutorial illustrating geometrically how an infinite series can have a finite sum.
math.rice.edu/~lanius/Lessons/Series/infinite.htm

Integral Definida
A tutorial with a series of Java applets about definite integral.  En Español.
www.xtec.es/~jlagares/integral.esp/integral.htm#E1

MathLogarithms.com
A math ebook by Dan Umbarger explaining logarithm how's, why's, and wherefore's in all detail for students.
www.MathLogarithms.com

An Easy Way to Remember How Logarithms Work
This is a visual mnemonic to help remember what goes where in the logarithmic equation.
www.zooktutoring.com/an-easy-way-to-remember-how-logarithms-work

Calculus7.com
Contains video animations on calculus topics that are most useful for college and high school math instructors to reinforce or clarify what is explained in the class/lecture.
calculus7.com

 

Books

Calculus by Ron Larson
Larson's Calculus is a basic textbook with long history on the market. It contains lots of illustrations and plenty of exercises. It has been praised by a students and professors for its effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments.
www.amazon.com



Mathematical Modeling and Computational Calculus
This is a DIFFERENT kind of calculus book: it doesn't go through theorems and such, but instead teaches you about mathematical modeling using differential equations that are computed with the aid of computers, without the need of any advanced mathematics. Systems studied include satellite orbits, the orbits of the earth and moon, rocket trajectories, the Apollo mission trajectory, the Juno space probe, electrical circuits, oscillators, filters, tennis serves, springs, friction, automobile suspension systems, lift and drag, and airplane dynamics.
www.amazon.com

Calculus Without Tears
Calculus Without Tears is a collection of worksheets (in 4 volumes) that teaches basic concepts of calculus very step-by-step, without need of much algebra. They are intended to be self-teaching workbooks that even students before high school can study. Calculus Without Tears starts with studying the simplest of motions, which is a runner running with constant speed (or sometimes standing still!). Volume 2 (Newton's Apple) concentrates on the motion of a falling apple. Volume 3 goes about finding the derivatives of polynomials, trigonometric functions, roots, exponential and logarithmic functions. See my review.

Calculus Made Easy
Calculus Made easy is a classic textbook, making the subject at hand still more comprehensible to readers of all levels. Martin Gardner, himself an American mathematical landmark, says, "This is the leanest and liveliest introduction to calculus ever written." The book concentrates on little bits of x, called dx, their differences and sums among all kinds of functions, their geometric meaning, and what they can do for you.
www.amazon.com

Calculus by Benjamin Crowell
A short introductory free text for self-study of calculus. Available in many formats for downloading or viewing.
www.lightandmatter.com/calc

 

Graphing

Desmos
A free, online graphing calculator that is incredibly easy and intuitive to use, yet very powerful. You can use parameters with sliders, define your own functions and constants, graph inequalities, derivatives, and more. You can save, email, print, and embed your graphs.
www.desmos.com

Meta-Calculator
An online graphing/scientific/matrix/statistics calculator. Includes graphing implicit equations, finding interesections for equations, an equation solver, LCM, GCF, standard deviation, regressions, T-tests, and more.
www.meta-calculator.com

WebGraphing.com
An online graphing calculators for functions, equations, and inequalities with automatic analysis of graphs' properties. Automatic optimal viewing window, displays asymptotes, discontinuities, piecewise graphing, etc. Also 'guess the graph', galleries, articles on graphing concepts and tricks.
www.webgraphing.com

Online Graphing Calculator by EMathHelp
An online 2-D graphing calculator that can plot explicit, implicit, polar, and parametric graphs. You have lots of options for styling the graph (the axes, the tick marks, the grid, and the labels) and can export hte image as .svg, .png, or .jpg file.
www.emathhelp.net/calculators/calculus-1/online-graphing-calculator

Function Flyer
Create graphs of functions but also allows the manipulation of constants and coefficients in any function so the user can explore the effects on the graph by changing those numbers.  Great tool!
www.shodor.org/interactivate/activities/FunctionFlyer/

Function, derivative, and integral
Modify the given graph by dragging points and the applet dynamically shows the derivative, the integral, the tangent, the shading.  Would be more useful with a lesson plan (provide yourself?) but still very illustrative.
www.cut-the-knot.com/Curriculum/Calculus/CubicSpline.shtml

AnalyzeMath.com: Interactive Java Applets
Interactive tutorials and problems on precalculus graphing topics where the student interacts with a Java applet.
www.analyzemath.com

The Function Institute from Zona Land
Comprehensive discussion on definition of a function with Java applets that illustrate very clearly one-to-one, one-to-many, many-to-one concepts. Also has pages on different types of functions (linear, polynomial, rational, exponential, trigonometric) and interactive graphs of those.
zonalandeducation.com/mmts/functionInstitute/functionInstitute.html

Mathinsite Products
A collection of very instructive Java applets with tutorial worksheets on graphing different functions (line, parabola, exponential function, circle, ellipse, trig functions, complex numbers and more).
mathinsite.bmth.ac.uk/html/applets.html

Maths Online Gallery: Functions 1
Collection of Java applets with exercises and some lesson plans: Function and graph, Recognize function graphs puzzles, Polynomial of third order, and a Function plotter.
www.univie.ac.at/future.media/moe/galerie/fun1/fun1.html#funktion

Maths Online Gallery: Functions 2
Collection of Java applets with exercises:  Recognize function graphs puzzles that concentrate on negative power functions and trigonometric functions, and graph collections of exponential & logarithmic functions, and trigonometric functions.
www.univie.ac.at/future.media/moe/galerie/fun2/fun2.html#graphenel

Explorelearning Algebra Gizmos for Grades 9-12
Gizmos are dynamic online simulations that let students visualize and experiment with the mathematical concepts. They come with an exploration guide that serves as a lesson plan. Find gizmos for linear, quadratic, exponential, logarithmic, rational, radical, trigonometric functions, polynomials, conics, sequences and series, and more. Excellent resource! Free 30-day trial.
www.explorelearning.com/index.cfm?method=cResource.dspChildrenForCourse&CourseID=126" target="_blank

Software

GraphCalc—Graphing Calculator
This is a powerful, easy-to-use, scientific graphing calculator on your computer.  Make 2D and 3D graphs, different number bases, statistical analysis, calculus, etc.
Price: Free
www.graphcalc.com

Calc98
Engineering, scientific and financial freeware calculator for Windows. Functions for statistics, use of different number bases, metric units conversions and physical properties and constants. Also has financial and time functions including investment, loan and mortgage calculations, a stopwatch.
Price: Free
www.calculator.orgdownload.html

SpeQ Mathematics
Small but extensive math program for calculations and graphing. Can also define variables and save your calculations.
Price: Free
www.speqmath.com

SVGCalc
An open-source scientific graphing calculator for web browsers. It can be stored on a hard drive, accessed over a local or wide area network, or made available via an internet webpage. Provides calculation and graphing tools commonly needed by high school math and science students.
Price: Free
svgcalc.software.informer.com

Microsoft Mathematics 4.0
Software that includes a full graphing calculator, equation solver, triangle solver, unit conversion tool, linear algebra solver, and more. Price: free.
www.microsoft.com/en-us/download/details.aspx?id=15702

A & G Grapher
A basic 2D/3D graphing program. Add tangent lines by clicking on the graph, trace the graph, calculate area.  Also draws implicitly defined functions/graphs. Easy to learn.
Price: $19.
www.runiter.org/grapher.htm

MathGV Function Plotting Freeware for Windows
Plot 2 dimensional, parametric, polar, and 3 dimensional functions. You can add lines, rectangles, circles, round rectangles, flood fills, and text for labels or for artistic effects.  Because the plots are shown with a big screen, and are extremely easy to zoom in/out or move around, MathGV is excellent for visualizing graphs and functions in middle/high school. It does NOT have calculus or tracing tools.
Price: Free
www.mathgv.com

Mathscribe Lite 2.5.1
Mathscribe is a simple dynamic graphing and mathematical modeling program for algebra, trigonometry and precalculus classes. The free download includes 13 ready-to-print-n-use assignments, which I consider a real benefit of this program.  They cover linear equations, systems of linear equations, and quadratic equations. Also, the program comes with lots of pre-made examples of different kinds of functions for the high school algebra/pre-calculus student. You can also use Mathscribe to mathematically model scientific data, either by typing in the data from scratch, or simply pasting it from a spreadsheet or other program. Mathscribe lacks the zooming in/out and centering functions present in many plotting programs. Its strength is in the ready-made examples and lab sheets, helping the student to connect both symbolic and visual thinking through guided discovery.
Price: Free
www.mathscribe.com

InquiSoft
A software that includes eight different graphing modes, including implicit mode for conic sections. Other modes support polar, parametric, and piecewise-defined functions, as well as slope fields. You can save your graphs or copy and paste them into other programs, and you can customize colors, line styles, captions, and legends. Includes over 100 built-in functions from calculus, statistics, vectors, complex numbers, and more.
Price: $29
www.inquisoft.com

MathProf
A comprehensive program, like a math professor on your desktop. Not only for algebra, but for analysis, geometry, 3D figures, stochastics, vector algebra, and linear algebra.
Download is free. Price: $45.
www.edu-soft.de/en

Graphmatica
Very easy to use, fast, compact graphing program.  Plots 2D graphs, implicitly defined functions, in polar coordinates, piecewise, parametric graphing.  Finds derivative and area under curve.  Use a parameter/free variable. Data plotting, curve fitting, differential equations.  Recommended for middle school/high school algebra and calculus.
Price: It's up to you what you pay; if you find Graphmatica easy, helpful, and convenient to use, you are asked to support the release of future versions by sending your contribution to the developer.
www.graphmatica.com

Advanced Grapher
Intuitively easy to use 2D graphing program.  Many calculus and function analysis features including derivative, tangent/normal, zeros, intersection, integral/area, regression.  Choose between 8 languages.
Price: $29, has 30-day free trial
www.alentum.com/agrapher

Handy Graph
HandyGraph produces cartesian graphs and number lines - including empty ones - and graph paper. Especially designed for teachers.
Price: $59 download, a free trial available.
www.handygraph.com

Autograph
Autograph is a dynamic and very powerful PC graphing program spanning many levels, including Pre-Algebra, Algebra I, Geometry, Algebra II, Trigonometry, Pre-Calc, Discrete Math, Calculus, Differential Equations, Probability, and Statistics.
The numerous features include

  • Cartesian plots, implicit functions, gradient/derivative, integral function, reflection in y=x, inequalities, piecewise, parametric, polar equations, differential equations, use of constants, animations. 
  • Impressive zoom facilities and coordinate point manipulations, locus, shapes, transformations; regression lines
  • Solves zeros,  intersections; mid-points, centers
  • Finds tangent, normal; parallel, perpendicular; angle bisector.
  • Vector operations
  • several numerical methods/area calculations
  • geometrical transformations.
  • statistical diagrams and data analysis 

You can download a nice collection of examples, materials and worksheets. Recommended for those who are serious about mathematics in high school or college. Single user price $99. Click here for 30-day preview free download
www.mathmitt.com/products/autograph