Math 1C CALCULUS -- 3rd quarter
Prerequisite: Math 1B with a grade of C or better, or equivalent placement
Text: JAMES STEWART: Calculus Early Transcendentals SIXTH edition
(Note that we are NOT using 7th edition)
Graphing calculator required: TI- 83+, 84+ are the recommended models.
I will generally be demonstrating with a TI-83 or 84 in class.
TI-89 or any other calculator that can do symbolic mathematics, has a computer
algebra systems or can graph in 3D will NOT be allowed on any exams or quizzes in this class.
If you have a TI-89 or similar calculator, it will be wonderful for homework and learning but
out of fairness to all students, you can not use it for exams or quizzes.
TI-83, 84, 86 calculators are available on loan from the library for several hours or several
days at a time. There is a limited supply.
Includes tentative schedule on last page.
This course will use a website in CATALYST at
Catalyst is De Anza College's course management system.
Enrolled students will be able to log in to the course website as of the beginning of spring quarter:
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
Calculus Tutorials from Harvey Mudd College: http://www.math.hmc.edu/calculus/tutorials/
History of Calculus
Sections and Topics Covered
Sections 10.1 & 10.2 Derivatives (tangent lines and concavity)
and Areas for Parametric Curves
Sections 10.3 & 10.4 Calculus with Polar Coordinates
Chapter 11 Sequences and Series
Chapter 12 Vectors in 3 dimensional space and Quadric surfaces
Chapter 13 Vector Valued Functions
QuickLinks to Chapter Resources
Chapter 10 Resouces
: Parametric and Polar Curves
Chapter 11 Resouces :
Sequences and Series
Chapter 12 Resouces
: Vectors and Surfaces in 3 dimensions
Chapter 13 Resouces :
Vector Valued Functions
CHAPTER 10 RESOURCES,
Interactive Graphing Applets: be patient - it takes a minute for the Java code to load
Applet to trace out a cycloid: http://www.ies.co.jp/math/java/calc/cycloid/cycloid.html
Applet to graph parametric curves http://www.ies.co.jp/math/java/calc/sg_para/sg_para.html
Applet to graph polar curves http://www.ies.co.jp/math/java/calc/sg_kyok/sg_kyok.html
When using integrals with parametric curves, some of the area, arclength and surface area
problems have integals requiring numerical integration or have integrals for which you can find
the antiderivatives but with a good amount of careful work. You can use the definite integrals
to get/check your numerical answers or you can use the indefinite intregral calculator online
to check your antiderivatives. remember that on a test you will not have these resources
available, so use them as an aid to checking and understanding, not as a substitute for learning.
I have NOT tested these sites; they may be of varying levels of helpfulness, usefulness,
user-friendliness, or accuracy.
Definite Integral Calculator:
http://www.webmath.com/nintegrate.html by Discovery Education Webmath
http://www.solvemymath.com/online_math_calculator/calculus/definite_integral/index.p by Solve My Math
Indefinite Integral Calculator:
http://integrals.wolfram.com/index.jsp by Mathematica
http://www.numberempire.com/integralcalculator.php at number empire
Videos: Polar Graphing and Calculus in Polar Coordinates:
Video Lessons from Univ. of Houston Math Department created by
For section 10.3: http://www.mathvids.com/lesson/mathhelp/435-polar-coordinates-and-graphs
For section 10.4: http://www.mathvids.com/lesson/mathhelp/436-areas-and-lengths-using-polar-coordinates
You Tube Lessons on Polar Graphing and Calculus in Polar Coordinates
from the "Refigerator Math Professor" (Prof. Theresa Sutclffe of Los Angeles Valley College)
- choose from her playlist of mini-lessons:
Polar Graph Paper: Not required, but you may find it helpful for chapter 10.3 and 10.4 homework
involving polar graphs.
CHAPTER 11 RESOURCES : SEQUENCES AND SERIES
Tests for Convergence of Infinite Sequences and Series
Some You-Tube videos about convergence of SEQUENCES (11.1) , from
Dr. Tisdell, Mathematics Department Univ. of New South Wales, Australia
Dr. Sutcliffe at LA Community College, CA,
"BullCleo1" instructor at Pheonix College, AZ
Some You-Tube videos about convergence of SERIES
From community college math profs:
Send me more links if you find any on your own that you really like.
Dr. Sutcliffe at LA Valley College, CA,
(11.2) Series Convergence http://www.youtube.com/watch?v=O-lwnWaZ1ug&feature=related
(11.2) Sequence of Partial Sums
(11.2) Geometric Series
(11.2)Convergence or Divergence of a Series
(11.2) Test for Divergence (The videos call it the nth term test; our books calls it the test for divergence)
Minilecture by "BullCleo1", at Pheonix College, AZ
(11.2) Telescoping Series
Dr. Sutcliffe at LA Valley College, CA,
(11.3) Integral Test http://www.youtube.com/watch?v=9NSXmNJjqz8&feature=related
(11.3)Integral Test http://www.youtube.com/watch?v=bubJWKokkCk&feature=related
(11.4)Comparison Test http://www.youtube.com/watch?v=EjPjsi8KruQ&feature=related
(11.4)Limit Comparison Test http://www.youtube.com/watch?v=voAgKKxNJ0Q&feature=related
(11.5)Alternating Series Test http://www.youtube.com/watch?v=o5fgCWGgOYg&feature=related
"BullCleo1", at Pheonix College, AZ
(11.3)Integral Test http://www.youtube.com/watch?v=qQlnPrpwKY8&feature=related
(11.4)Comparison Test http://www.youtube.com/watch?v=2J9vhLkA1Xo&feature=related
(11.4) Limit Comparison Test http://www.youtube.com/watch?v=LQ_ktobTEp0&feature=related
(11.6)Absolutely and Conditionally Convergent Series: http://www.youtube.com/watch?v=rEyeRKd3TWo&feature=related
(11.6)Ratio Test: http://www.youtube.com/watch?v=76BzmM9zDIA&feature=related
(11.6)Root Test: http://www.youtube.com/watch?v=ZE5Pj7s9PWg&feature=related
"PartickJMT",. at Austin Community College, TX,
(11.6)Absolute and Conditional Convergence
(11.6)Ratio Test examples
Summary of Tests for Convergence of an Infinite Series
Tutorial for Convergence Tests for Infinite Series from Harvey Mudd College
Some cool views of convergence of Taylor polynomials:
appropriate for Sections 11.9, 11.10, 11.11
(one at the top, couple more further down, little slow)
(scroll down a little, this one's interesting because the successive graphs morph
smoothly from one to the next, its fast so watch if a few times to really see it)
(scroll way down)
(animations for a whole slew of functions, slower, but also show the interval of convergence)
Tutorials from SOS Math: Power Series
Instructions for Sequences and Series on the Ti-83, 84 calculators
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.
Proof by contradiction that e is irrational
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 12 RESOURCES
Dot Products : These reference pages have interactive 3D illustrations for angle between
two vectors, projections, and direction angles and direction cosines, and parallelpipeds
You can rotate the illustrations to view from different angles
Interactive Geometric view of the Cross Product: http://www.phy.syr.edu/courses/java-suite/crosspro.html
Link to computer animations for quadric surfaces
Links to video mini-lectures for sketching Quadric Surfaces
Dr. Sutcliff at LA Valley College draws and explains Quadric Surfacesin R3:
Circular and Elliptic Cylinders
Spheres and Ellipsoids :
Double Napped Cones:
Hyperboloid of One Sheet in R3:
Hyperboloid of Two Sheets:
CHAPTER 13 RESOURCES
Online 3d parametric grapher that can graph vector valued functions and lets you rotate the graph to view from various angles. Enter parametic formulas for x, y, and z in terms of the parameter to get vector valued functions.
Online 3D parametric grapher that also illustrates the velocity and the acceleration vectors in 3D. Enter parametic formulas for x, y, and z in terms of the parameter t. The applet plots the corresponding curve, which can be traced while the velocity and the acceleration vectors are displayed together with their approximate values. The curve can be rotated in real time with the mouse."
Online 3D function grapher for z = f(x,y) in terms of x and y and the applet draws the surface in 3D. The graph can be rotated in real time by the user.
Online and downloadable 3D grapher -graphs surfaces in 3D
you can see surfaces or can see curves created by intersecting surfaces
(there is a free downloadable version or use it free online - these are lacking some features of the paid version - but the free versions are still cool and fun)
Finding Vector Valued Functions for intersections of surfaces
Determining the Tangential and Normal components of Acceleration
Relations between Cartesian, Cylindrical, and Spherical Coordinates
CHAPTER 15 RESOURCES
NOTE WE ARE NOT COVERING THIS MATERIAL IN MATH 1C ANY MORE.
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.
Freeware & Demos for the Computer
MathGV Graphing Software (freeware) for the PC
WinPlot Graphing Software (freeware) for the PC
Runiter grapher (2D and 3D - free version graphs nicely but can't print or save)