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Math 1C CALCULUS -- 3rd quarter
Syllabus: Differential equations, infinite series, lines and surfaces in three dimensions, and vectors.
Prerequisite: Math 1B.
Text:
Graphing calculator required: TI-86 , 83+, 84 are the recommended models.
I will generally be demonstrating with a TI-83 or 84 in class.
If you have a TI-89, it will be wonderful for learning purposes but out of fairness to all students,
the TI-89 will not be allowed on exams or quizzes.
TI-86 calculators are available on loan from the library for several hours or several days at a time.
Math 1C Update
Math 1C Assignments
Math 1C Solutions
Useful Resources
Calculus Help
Visual Calculus: http://archives.math.utk.edu/visual.calculus/
Calculus on the Web: http://www.math.temple.edu/~cow/
SOS Calculus: http://www.sosmath.com/calculus/calculus.html
Mathematics Help Central: http://www.mathematicshelpcentral.com/
History of Calculus
http://www-history.mcs.st-and.ac.uk/history/HistTopics/The_rise_of_calculus.html
Using Your Calculator: Graphing & Table Basics
http://nebula.deanza.fhda.edu/math/FT/bloom/introcalculator1a.htm
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
.
CHAPTER 8 SEQUENCES AND SERIES
Tests for Convergence of Infinite Series
Summary of Tests for Convergence of an Infinite Series
http://www.math2.org/math/expansion/tests.htm
Tutorial for Convergence Tests for Infinite Series from Harvey Mudd College
http://www.math.hmc.edu/calculus/tutorials/convergence/
Javascript demos for Taylor Series
showing graphically how successive partial sums of Taylor Series (Taylor Polynomials) approximate the function
http://www.math.jhu.edu/%7Ejrm/vander/stable/TPTest.html
Tutorials from SOS Math: Power Series
http://www.sosmath.com/calculus/powser/powser01.html
http://www.sosmath.com/calculus/radcon/radcon01/radcon01.html
http://www.sosmath.com/calculus/tayser/tayser01/tayser01.html
Graphing Sequences and Series on TI Calculators
Instructions by Dr. Jack Weiss, Rochester Institute of Technology
Sequences and Series Using the TI-83 Calculator:
http://www.rit.edu/~jmwsma/calculators/ti83/ti83sequence/ti83sequence.html
Sequences and Series Using the TI-86 Calculator:
http://www.rit.edu/~jmwsma/calculators/ti86/ti86sequence/ti86sequence.html
Sequences and Series Using the TI-89 Calculator:
http://www.rit.edu/~jmwsma/calculators/ti89/ti89sequence/ti89sequence.html
Graphing Sequences and Series on TI-86 Calculator as a list or using parametric plots, by R. Bloom
Graphing Sequences and Series on the TI86 Calculator using lists and scatterplots
Graphing Sequences and Series 2 on the TI86 Calculator using parametric graphing
For graphing on a TI-83 or TI-89
The TI-83 and TI-89 support a sequence graphing mode that is not available on the TI-86.
You can use the sequence graphing mode to graph a sequence or partial sums of a series.
You can also adapt the methods posted above for the TI-86; the TI-83 and TI-89 have all
the same functionalities of the TI-86 that is used in those two sets of instructions.
Your keystrokes will be different in order to find those settings or functions;
if you can't locate a function or setting, look in the Catalog.
Note that the TI-83 and TI-89 do not support custom menus that can be set up in the TI-86.
Optional:
Proof by contradiction that e is irrational
http://mathforum.org/isaac/problems/eproof.html
This is an indirect proof that relies on the series expansion of e.
If you have taken Math 22 (Discrete Math), you have proved that the square root of 2 is irrational, using a proof by contradiction.
You now have the tools to prove that e is irrational.
CHAPTER 9 RESOURCES
Summary of Vector Products
http://nebula.deanza.fhda.edu/math/FT/bloom/Math1C/VectorProducts.doc
Cross Products on your Calculator
Entering Vectors on a TI-86
http://www3.interscience.wiley.com:8100/legacy/college/halliday/
0471320005/calculator/86calculators.html#_Entering_and_Displaying_1
Finding a Cross Product on a TI-86
http://www3.interscience.wiley.com:8100/legacy/college/halliday/
0471320005/calculator/86calculators.html#_Cross_(or_Vector)
The above links need to be copied and pasted or typed directly into your browser window because they are too long to post as active links on this page. If the link does not take you to the proper place of the page, scroll down the page to find the references for entering vector in component notation and for finding cross products.
TI-83: Your instructor has a cross product program for the TI-83 that you can download from her calculator.
Cross Product Applet: http://www.phy.syr.edu/courses/java-suite/crosspro.html
Cylindrical and Spherical Coordinates
Applet for viewing spherical and cylindrical coordinates in 3 space
Excellent drawing of relationship between rectangular, spherical, & cylindrical coordinates.
Link to the page below then scroll down to the bottom of the page to find a box where you need to click to open the applet.
http://surendranath.tripod.com/Applets/Math/Coordinates/SphCoordApplet.html
Relations between Cartesian, Cylindrical, and Spherical Coordinates
http://www.geom.uiuc.edu/docs/reference/CRC-formulas/node42.html
Freeware & Demos for the Computer
MathGV Graphing Software (freeware) for the PC
http://www.MathGV.com
WinPlot Graphing Software (freeware) for the PC
http://math.exeter.edu/rparris/winplot.html
MuPad Lite: trial and educational versions
http://www.sciface.com/index.php?menu=6
Follow links for licenses for students and educators
MuPad Lite has had free personal licences for students and teachers; check to see if this is still available.
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