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Office Hours: T.B.A You are also welcome to stop by UTR 8:00 - 9:00 & 3:00 - 3:30 since I am usually there, but check with me especially for 3:00 - 3:30 as sometimes I cannot be present. Feel free to send me email or contact me through WebCT, where you will also find the most important handouts such as homework assignments, etc. The TA is Nasr Ziyada and you are welcome to ask him questions on the homework, etc. For help with Maple, just send me an email asking for the right commands to type, or ask the Maple TA, Tasnim Kamal. Calculus on the Net: I am compiling a list of useful websites that might be useful to students in this course as well others. They are arranged according to the section numbers in our textbook: General Calculus resources MathServ Toolkit, Vanderbilt University - Graph equations (including multiple equations), solve definite/indefinite integrals, compute derivatives, find limits graphically, etc. Maple Application Center - Dozens of Maple tutorials dealing specifically with Calculus II that you can download and run on your own version of Maple. (Let me know if you have trouble running the animations, sometimes it's not clear how to start them.) The Integrator - Calculates indefinite integrals, powered by Mathematica.
Chapter 4 - Integration 4.1 Antiderivatives Seminole College - Powerpoint presentation on antiderivatives. 4.2 Substitution Visual Calculus - Flash discussion and lots of practice problems with solutions. Harvey Mudd College - Tutorial with several examples, including definite integrals. 4.3 Inscribed/Circumscribed Rectangles Visual Calculus - Series of animations in Flash describing how these methods work. 4.4 Riemann Sums Visual Calculus - Interactive tutorial showing the various types of Riemann sums for a specific example. Cal State Fullerton - Series of animations showing the various types of Riemanss for a different example. Seminole College - QuickTime movie showing how Riemann sums approximate the area under sin x. Harvey Mudd College - Explanation of the link between the graphs of Riemann sums and the algebraic formula. Don't miss the Exploration link near the bottom of the page! 4.5 Average Value of a Function Visual Calculus - Derives the average value formula, includes graphical illustrations and examples (solved both algebraically and graphically). University of British Columbia - Explanation of what the formula means, as well as interactive graphical illustrations. 4.6 Fundamental Theorem of Calculus Visual Calculus - Nice animation for a specific example. Maple Worksheet - Animated example to try on your own computer (if you don't have Maple on your own computer, then run this animation in the MathLab, SCI 608). 4.7 Numerical Integration Visual Calculus - Flash explanation of the Trapezoidal and Simpson's formulas, including animations and examples. University of British Columbia - Tutorial on the Trapezoidal and Simpson's rules.
Chapter 5 5.1 Area between curves Metro State College of Denver #1 - QuickTime movie of an example requiring only one integral (no equations). Metro State College of Denver #2 - QuickTime movie of an example requiring two integrals (no equations). Visual Calculus - Several examples showing graphs, setting up the integrals and final answers (examples #3 - 6 are especially helpful because they show how multiple integrals can be set up). Also several practice (drill) problems with solutions, although sometimes they use integration techniques not yet covered. 5.2 Disk/Washer method Visual Calculus - Examples and explanation of the disk/washer method. Don't overlook the examples near the bottom of the page showing rotation about the lines y = -1 and y = 2! There is also a cool animation here. Lake Tahoe Community College - Examples and pictures showing the disk and washer method. Georgia College - Examples demonstrating the washer method. There is also a great gallery of animations to accompany the examples; very well done. 5.3 Cylinder method Visual Calculus - Example and Flash animation of the cylinder method. ThinkQuest - Discussion and comparison of the disk, washer and cylinder methods (note that we don't do the cross-section method). Includes animations and worked examples - written by students for students! University of British Columbia - Explanations and examples of the disk and cylinder method and arc length, including how to calculate the volume of a crocodile's jaw! 5.5 Arc length and surface area Visual Calculus - Animated derivation of the formula and several examples. Harvey Mudd College - Tutorial and several examples. National Curve Bank - animated examples of the surface area of an object (that little section at the end of 5.5 that is so easy to overlook!). See an example of an object with finite volume enclosed by infinite surface area! Lamar University - explanation of where the formula for surface area comes from and several examples. Chapter 6 6.1 The slope of the inverse function Visual Calculus - Explanation of how the main theorem in this section comes about, and also several examples how to solve problems of this type. MIT - Java applet that lets you plot any function of your choice and its inverse. (This doesn't say much about the slope of the inverse, but it can help you visualize the inverse better.) 6.2 The natural log function Analyze Math - Java applet that shows how ln(x) is defined (via a definite integral). Lamar University - Short tutorial on the derivative of natural log and exponential functions. Visual Calculus - Drill problems for log differentiation - great practice! 6.3 The exponential function Visual Calculus - Java applet that allows the user to explore the graphical effects of changing various constants (you can leave c and d to their default values, but investigate changes of a and b!) International Education Software - Java applet that illustrate the special number e. 6.4 Integration using log and exponential functions Howard Community College - Examples of integrals from this section. John Taylor - Further examples of integrals of this type (also examples of derivatives). 6.5 General exponential and log functions Pheng Ving - Very good summary of the relevant material. Penn State University - Another good summary of the material in this section. International Education Software - Java applet that illustrate the special limit on p. 565. 6.6 Exponential growth and decay University of Guelph - Explanation and solved problems. Dartmouth College - Java applet that illustrates the effect of changing the two unknowns in the growth/decay equation. Also some worked examples. 6.7 Inverse trig functions University of British Columbia - Java applets that show the inverse functions for tan, sin, cos. Visual Calculus - Derives a formula for the derivative of the inverse of all 6 trig functions. University of Georgia - PowerPoint presentation on the inverse functions of sin, cos, tan. 6.8 Hyperbolic functions Analyze Math - Java applet showing graphs of all 6 hyperbolic functions, and their definitions S.O.S. Math - Introduction the hyperbolic functions including graphs and basic properties; derivation and graphs of the inverse of sinh and cosh can be found here. Pheng Ving - Nice summary of hyperbolic functions, including definitions, derivatives and graphs. Pheng Ving - As above, nice summary but this time of the inverse hyperbolic functions, including derivatives and graphs. 6.9 L'Hospital's rule Lamar University - Several examples with solutions, including one involving logs. Texas A & M University - Guidelines when to use L'Hospital's rule, when not to use it, frequently confused similarities, and why 0^0 can't be 1. Visual Calculus - Problems to practice on with solutions (finite limits only). Visual Calculus - More practice problems with solutions (involving infinity). Chapter 7 7.1 Integration by parts Harvey Mudd College - Short tutorial with examples to illustrate the main points. Visual Calculus - Explanation/derivation of the integration by parts formula, and lots of practice problems with solutions. Southwest Texas State University - Guidelines on choosing u and dv (with examples). University of California Davis - 23 practice problems with detailed solutions (in increasing order of difficulty!) 7.2 Reduction formulas for integrating powers of cos and sin Pheng Ving - A short summary of this section. Rutgers University - Another short summary. Calc101.com - Examples of how to use reduction formulas. 7.3 Trig substitutions Lamar University - One long & thorough example for each of the 3 substitutions covered in this section. Visual Calculus - Lots of practice problems, with hints and solutions. Pheng Ving - A nice summary of this section, with practice problems and solutions. 7.4 Integrals of rational functions (partial fractions) University of California Davis - Good summary of partial fractions, with 20 practice problems and detailed solutions. Visual Calculus - Tutorial on partial fractions, with lots of practice problems and solutions. Lamar University - Summary of partial fractions plus several examples. Pheng Ving - Another summary of the partial fraction method with several examples. University College of London - Tutorial on partial fractions, with 3 examples. 7.5 Quadratic expressions Lamar University - Tutorial with several examples. 7.7 Improper integrals Visual Calculus - Explanation including graphs, also practice problems with solutions. Lamar University - Tutorial with several examples and guidelines for improper integrals. Pheng Ving - Explanation of improper integrals with graphs and examples. In summary: Integration strategies (pick one and stick with it!) More websites on the way soon!! Let me know if you would like to add more websites, or if the above have become outdated. Before leaving, be sure to read some Math jokes to brighten your day! |
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this page was last updated on May 3, 2005 |
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