|
|
Math 1B
Calculus 1B: Fundmentals of Integral Calculus
Syllabus: not currently available
Students will use CATALYST https://catalyst.deanza.edu for this class.
Enrolled students will be able to log in and access the Catalyst site for this class at the above link during the appropriate quarter.
The textbook for this class will be Calculus Early Transendentals 6rd edition by James Stewart.
I will expect that you will have a graphing calculator for this course. The TI-83, 83+ or 84+ are recommended.
The TI-89 and TI-92 graphing calculators (or any other graphing calculator that have CAS systems or can do symbolic mathematics) will NOT be permitted on any quizzes or exams in this class.
The following is a partial list of calculators that have CAS systems and are therefore not permitted
Texas Instruments: TI-89 , TI-92 , TI-Nspire CAS
Hewlett-Packard: HP 48GII, model numbers that begin with HP 40G, HP 49G, HP 50G
Casio: Algebra fx 2.0, ClassPad 300 or 330, model numbers that begin with CFX-9970G
.
QuickLinks: Resources for Math 1B
Please let me know if you find that any of these links are not working. Some are old links and may need to be removed or updated.
Calculus Help
Riemann Sums
Definite Integral Calculator
The Integrator Indefinite Integral Calculator
Fundamental Theorem of Calculus
History of Calculus
Trigonometric Integrals
Trigonometric Substitution
Partial Fractions
Approximate Methods of Integration
Hyperbolic Functions
Volume of Solids
Area enclosed within Parametric Functions
Units for Work Problems
Software Links
Calculus Help
Visual Calculus: http://archives.math.utk.edu/visual.calculus/4/
Calculus on the Web: http://www.math.temple.edu/~cow/
SOS Calculus: http://www.sosmath.com/calculus/calculus.html
Riemann Sums
Format for Proof by Mathematical Induction (for Sum of a Sequence)
Use it if you need to when you practice for homework, but you must learn how to do it without this format sheet. For a quiz or exam you must know how to write it out without this.
http://nebula.deanza.edu/~bloom/Math1B/M1BProofByInductionFormat.pdf
Online Riemann Sum Calculators with graphs:
http://mathworld.wolfram.com/RiemannSum.html
http://www.math.ucla.edu/~ronmiech/Java_Applets/Riemann/
Graphical animation of right Riemann Sums:
http://www.ecs.fullerton.edu/~mathews/a2001/Animations/Quadrature/RightRiemann/RightRiemannaa.html
Graphical animation of left Riemann Sums:
http://www.ecs.fullerton.edu/~mathews/a2001/Animations/Quadrature/LeftRiemann/LeftRiemannaa.html
Two Interactive Graphical Applets for Riemann Sums
http://www.csulb.edu/~wziemer/Riemann/Riemann.html
http://www.calvin.edu/~rpruim/courses/m161/F01/java/RiemannSums.shtml
Riemann Sums and definition of the Definite Integral
http://www.math.hmc.edu/calculus/tutorials/riemann_sums/
The Integrator: online indefinite integral calculator
http://integrals.wolfram.com/index.jsp by Wolfram Mathematica
You input the function and the integrator will tell you the indefinite integral, which is a function, if it exists in closed form.
Sometimes the Integrator's answer might appear to be different from yours,
but will be equivalent after you do some algebra to re-express it.
Read the instructions - the Integrator is very particular about the syntax
and will not read your function correctly if you do not use its grammar correctly.
REMEMBER THAT YOU WILL NOT HAVE THIS AVAILABLE ON AN EXAM, so use it to check your work, not to circumvent learning the material.
Another online indefinite integral calculator:
http://www.webmath.com/integrate.html by Discovery Education Webmath
IMPORTANT NOTE: I just found this and have not used it extensively; if you find that it presents problems in use or is not accurate, please let me know by email or in class that I should remove this link.
Definite Integral Calculator:
http://www.webmath.com/nintegrate.html by Discovery Education Webmath
You input the function and the limits of integration and this will perform numerical integration to evaluate the integral and return a number as the answer.
IMPORTANT NOTE: I just found this and have not used it extensively; if you find that it presents problems in use or is not accurate, please let me know by email or in class that I should remove this link.
Remember! You need to learn how to do these integrals yourself
because you will be required to show your work on exams and quizzes
in order to receive credit. Use these tools to check your homework,
not to do the homework for you.
History of Calculus
http://www-history.mcs.st-and.ac.uk/history/HistTopics/The_rise_of_calculus.html
Fundamental Theorem of Calculus
JAVA Applet for FTC Part 1:
http://archives.math.utk.edu/visual.calculus/4/ftc.2/index
Fundamental Theorem of Calculus Parts 1 and 2. Contains more interesting links:
http://archives.math.utk.edu/visual.calculus/4/ftc.9/index.html
Animated Graphic for FTC Part 1:
http://archives.math.utk.edu/visual.calculus/4/ftc.3/index.html
Interactive Website and Discussion of FTC:
http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/integration/ftc.html
ANY RESOURCES LISTED BELOW THIS POINT ARE FROM PRIOR QUARTERS
FOR SPRING 2009 SOME OF THESE RESOURCES MAY BE UPDATED OR REVISED (or removed if no longer working).
Trigonometric Substitution
http://www.math.hmc.edu/calculus/tutorials/trig_substitution/
http://www.sosmath.com/calculus/integration/trigsub/trigsub.html
Partial Fractions
link currently not available
Approximate Methods of Integration
Animated Graphics for various Approximate Methods of Integration
http://www.ecs.fullerton.edu/~mathews/a2001/Animations/Quadrature/Quadrature.html
Volumes of Solids
Interactive Model of the Volume a Solid of Revolution
as a sum of volumes of discs using the slicing method
http://www.math.dartmouth.edu/~klbooksite/4.08/408.html
In the top left corner of the applet window that contains the picture,
there is a small gray arrow.
Click on the arrow to get a pull down menu to use to change n,
the number of disks.
Solids of Revolution from Visual Calculus:
http://archives.math.utk.edu/visual.calculus/5/volumes.4/
3 more applets for volumes of solids and solids of revolution: Link through
http://www.runet.edu/~wyang/MAPLE/java/java/calcjava.html
Hyperbolic Functions
Hyperbolic Functions are not adequately covered in our textbook.
There will be a supplement either posted on Catalyst or handed out in class.
Here are some additional online resources for hyperbolic functions;
http://www.ucl.ac.uk/Mathematics/geomath/level2/hyper/MHhy.html
http://www.math.utah.edu/~renzo/1220fall2003/Hyperbolic.pdf
http://www.zaimoni.com/HyperbolicTrig.htm
Interactive graphs of hyperbolic functions :
http://www.rfbarrow.btinternet.co.uk/htmasa2/Hyper1.htm
Interactive Catenary Curve Applet:
http://www-groups.dcs.st-and.ac.uk/~history/Java/Catenary.html
Inverse hyperbolic functions:
http://www.sosmath.com/trig/hyper/hyper03/hyper03.html
http://www.sosmath.com/trig/hyper/hyper04/hyper04.html
Area Enclosed Within a Parametric Function
link currently not available
Units for Work, Force, Mass, Distance, Acceleration
link currently not available
CHAPTER 7 DIFFERENTIAL EQUATIONS
Section 7.2 - Calculations done in class illustrating Euler's method. http://nebula.deanza.fhda.edu/math/FT/bloom/Math1C/M1C7pt2Euler.doc
Direction Fields are also commonly referred to as Slope Fields. Both names refer to the same concept.
Graphing Direction Fields on your TI86 or TI83
IMPORTANT: The program name for the TI-83 & 84 as downloaded from your instructor is SLOPFLD
(not SLPFLD as indicated in the instructions on this link.)
Graphing Slope Fields on your TI-89:
http://staff.imsa.edu/math/sharing/BCworksheets/TI89EulerSlope.pdf
On-Line Slope Field Calculator and Grapher
http://alamos.math.arizona.edu/ODEApplet/JOdeApplet.html
Visual Calculus on slope fields, including calculator instructions and another on-line slope field grapher.
http://archives.math.utk.edu/visual.calculus/4/slope_fields.3/
The TI-83 does not have the capabilitiy to graph slope fields built into it.
A program is available for the TI-83 that will draw the direction fields;
this program may be downloaded from your instructor's TI-83 calculator.
Other TI-83 programs may be found on the web.
Alternatively, for homework you can use the On Line Slope Field Calculator at the links above
or WinPlot Graphing Software (freeware) for the PC http://math.exeter.edu/rparris/winplot.html
.
SOFTWARE LINKS:
Two Easy and Free Graphing Software programs for the PC:
MathGV: http://www.MathGV.com (function and parametric, rectangular and polar, 2D and 3D)
Winplot: http://math.exeter.edu/rparris/winplot.html (function, implicit, parametric, rectangular and polar, slope/direction fields, 2D and 3D)
30 Day Trial version of Scientific Notebook
http://www.mackichan.com/licensing.net/dnloadreq.aspx
(No free version available for permanent copy of Scientific Notebook software.
After 30 days it expires unless you pay)
|
|
|
