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Math 49B
MATH 49B HOMEPAGE
Prerequisite Math 49A with a grade of C or better, or equivalent placement
Textbook: Larson & Hostetler PreCalculus with Limits, 2007
Graphing Calculator Required/ TI-83 or 84 recommended/TI-86 acceptable
If you already own an older model such as the
TI-82 or TI-85, they are also acceptable
The TI-89 and TI-92 graphing calculators (or any other brand or model of graphing calculator that can do symbolic mathematics) will not be permitted on quizzes or exams in this class.
Note: If you feel strongly about using your TI-89, please see the instructor to determine if a trial/experimental accomodation for doing part of your equizzes/exams without a calculator can be arranged; this accomodation, if arranged, can be discontinued at any time by the instructor if it is not working out to the instructor's expectations.
MATH 49B UPDATE
RESOURCES FOR STUDENTS ENROLLED IN MATH 49B PRE-CALCULUS
Link to PreCalculus 49B Assignments
Link to PreCalculus 49B Solutions
Practice Problems, Explanations, Calculator Instructions, Class Notes,and other useful resources:
Listed by Topic
This section will be expanded as the quarter progresses.
The following two items are review from Trigonometry class.
You are assumed to know it, and know it well, coming into Math 49B.
If you don't remember it, review those sections in the text and do odd numbered practice problems until you are proficient (meaning both capable and fast!)
Review for Converting between Degrees and Radians (Review of Section 4.1)
To find Radians: Multiply Degrees by (pi/180)
To find Degrees: Multiply Radians by (180/pi)
When using degrees, you must write the degree sign
If there is no degree sign, the convention is that radians are being used.
Recognize the standard angles in both degrees and radians and be able to locate them on the plane and on the unit circle.
Review of Definitions of Trigonometric Functions for right triangles, unit circle and angles on a plane. Review of sections 4.2, 4.3, 4.4
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/TrigFunctionDefReview.pdf
Copy of Section 5.4 & 5.5 Handout
(See solutions page for solutions to HW problems from this handout.)
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49BSect5pt4and5Handout.pdf
Copy of Section 4.6 Graphing Csc, Sec, Tan and Cot Handout (http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/GraphingTanCotSecCsc.pdf
Harmonic Motion handout can not be posted - it was handed out in class only.
Polar Conic Sections notes for section 10.9
Includes only typed side of page describing procedure for doing problems.
Does not include the photocopies
of the transparencies that were included on the second side of the handout distributed in class.
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/PolarConics.pdf
One Step Further: For Ellipse Example 3 on handout done in class
finding all the geometric relationships between the polar and rectangular forms of this ellipse.
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/PolarConicPlus1.gif
Two Steps Further: For Ellipse Example 3 on handout done in class
algebraically finding the rectangular form of the equation, from the polar form.
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/PolarConicPlus2.gif
Complex Numbers in Trigonometric Form
Examples from class for section 6.5 : converting complex numbers in rectangular form into trigonometric form.
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/PolarComplexExamples.GIF
Supplemental to Section 10.6: Fun with Parametric Curves
Links for animation of several famous parametric curves
Cycloid (the path of a fixed point on a rolling circle – such as a the path of a dot painted at the edge of your bicycle wheel rim)
http://en.wikipedia.org/wiki/Cycloid
Epicycloid (the path of a fixed point on a circle rolling on the outside of another circle)
http://en.wikipedia.org/wiki/Epicycloid
Hypocycloid (the path of a fixed point on a circle rolling on the inside of another circle)
http://en.wikipedia.org/wiki/Hypocycloid
Lissajous curves
http://en.wikipedia.org/wiki/Lissajous_curve
http://mathworld.wolfram.com/LissajousCurve.html
Witch (curve) of Agnesi Named after female mathematician Maria Agnesi - This curve appeared in her mathematical work written in 1748
http://mathworld.wolfram.com/WitchofAgnesi.html
Section 8.1: Solutions to Practice Problems Worksheet for solving systems of linear equations using row operations (Gauss Jordan Method)
http://nebula.deanza.fhda.edu/math/FT/Bloom/Math11/M11GJordPracticeAns.doc
Proof by Mathematical Induction
Format for writing a proof by mathematical induction to prove a formula for the sum of a finite series
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49BProofByInductionFormat.doc
Print this out and use this to get started on your homework
As you practice, you need to get to the point where you can write a proof by induction without this format in front of you. Do lots of practice problems until it becomes comfortable.
When you take the exam, you will need to do your proofs WITHOUT this to use as "training wheels"
Vector Applications
Forces in Equilibrium:
Each example is 2 pages due to diagrams, calculator instructions, and large size for easy reading.
Check out both links for each example.
Equilibrium Example done in class - lecture notes:
Example 1 Page 1 http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/VectorEquilibriumEx1Pg1.gif
Example 1 Page 2 http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/VectorEquilibriumEx1Pg1.gif
Another Equilibrium Example
Example 2 Page 1 http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/VectorEquilibriumEx1Pg1.gif
Example 2 Page 2 http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/VectorEquilibriumEx1Pg1.gif
Application of Vectors in 3D - another Airplane Problem and solution
For extra practice - similar to problem done in class and problem on applications handout
Problem on page 1 of document; solution on page 2 of document
http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/AirplaneVector3d.doc
Answers to Workheet for Vector Applications (blue handout)
If you find any errors in the answers, email the instructor so that corrections can be posted
#1&2: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns12.gif
#3: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns3.gif
#4: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns4.gif
#5: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns5.gif
#6: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns6.gif
#7: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns7.gif
#8,9,10: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns8910.gif
#11,12,13: http://nebula.deanza.fhda.edu/math/FT/Bloom/M49B/M49bVectorAppAns111213.gif
Graphing Freeware for PCs
Winplot Graphing Software (Free)for Windows PCs
Graphs 2 dimensional rectangular functions, parametric equations, polar equations
Graphs 2 dimensional implicit equations
Graphs direction (slope) fields for differential equations (Math 1B)
http://math.exeter.edu/rparris/winplot.html
MathGV Graphing Software (Free)for Windows PCs
Graphs 2 dimensional rectangular functions, parametric equations, polar equations
Graphs 3 dimensional rectangular functions
http://math.exeter.edu/rparris/winplot.html
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