Math 147
PreCalculus
Section 008
William P. Clement
Center for Geophysical Investigation of the Shallow
Subsurface
Boise State University
Learning Community
You must be enrolled in
Math 147, section 008
and
Engineering 110
Engineering
"For Dr. Petroski, acceptance of uncertainty and
possible failure - he calls it "coping with the
imponderable" - is what separates the "given
world" of the scientist from the "built world" of
the engineer." (From the May 2, 2006 New York
Times article about Henry Petroski of Duke
University (page D3))
Fellow of the American Society of Civil Engineers
Member of the American Academy of Arts and Sciences
Member of the National Academy of Engineering.
From the Course Catalog
PreCalculus
Math 175
Section 008
5 Credits
Monday, Tuesday, Wednesday, Thursday, and Friday
3:40 to 4:30
ET 103
Professor
William P. Clement
Associate Research Professor
Center for Geophysical Investigation of the Shallow
Subsurface (CGISS)
Math/Geosciences 206B
http://cgiss.boisestate.edu/~billc
billc@cgiss.boisestate.edu
426-4307
Office hours: Friday’s Engineering 110
Available in my office, MG206B most of the time except
during exercise hour (11:30-2:00)
Who Am I?
I am a geophysicist – a geoscientist who uses physical
principles to understand the structure and processes of
the Earth.
I use FM frequency radio signals to produce images of
the upper 20 meters of the Earth.
I have been a research professor at Boise State University
since 1997.
Hopefully, my background as a scientist will provide
context to this course.
Geophysical Tomography
Borehole Tomography
Experiment
Borehole
Tomography
We know the physics of
the problem and the data
and we try to find the
model parameters.
Invaluable Help
Randi Walters
randiwalters@mail.boisestate.edu
Office hours: 4:40 to 5:30 (right after class)
- Monday and Wednesday
- Room MEC103
Course Aims and Objectives
Precalculus: foundation for calculus (Math 170
and 175)
Concepts and methods fundamental to:
Math
Engineering
Much of engineering math is taught here
Learn it now
- avoid later struggle
- enjoy engineering
Course Aims and Objectives
Determine how you learn best:
- Visually
- Listening
- Reading
- Combination
What is important is that you:
learn how to learn
learn how to enjoy learning
Course Aims and Objectives
Processing information is the key to learning.
I can transfer lots of information to you (tell you
the information), but until you process it, until
you work with it, you will not develop a deep
understanding the information.
Class Format and Procedure
Math 147
- lecture course
- self-learning through ALEKS
on your own (mostly)
in ENGR 110
Learning Community
You must be registered for both courses to participate
in this section (section 008) of Math 147.
Class Format and Procedure
Quizzes and exams
Fridays during Engineering 110
Homework
working through ALEKS
- on your own
- Friday’s Engineering 110 class
- after quiz or exam
My View on Mathematics
I view mathematics as a language.
Mathematics is often the best way to present engineering
and scientific theory.
Learning mathematics is not the end goal of this course.
The goal is to be sufficiently comfortable with
mathematics so that you can focus on new
engineering concepts without being confused by the
mathematics.
Your Challenge in Mathematics
But being comfortable with something means using it
frequently and understanding its nuances.
You must spend significant time practicing simple,
repetitive problems to fully understand the beauty of
mathematics.
What You Really Care About:
Grading
Homework and Quizzes – 30%
Exams (5 during semester) – 55%
Final exam – 15%
Grading
Quizzes and exams will be delivered through ALEKS
during Friday’s Engineering 110 class
For the exams only, you will write down your work
- for credit for the exam (i.e., you took it)
- for partial credit
Missed exams or quizzes: Do not miss them!
- Drop 1 (one) quiz (i.e., your missed one)
- Exams – let me know beforehand
better have incredible excuse
Class Website
http://cgiss.boisestate.edu/~billc/Math147
I also have a link to this page from my homepage.
Graphing Calculator Manual
To get the Graphing Calculator Manual
Go to: http://math.boisestate.edu/~bkenny
Follow the link:
Graphing Calculator Manual with Exercises
Behaviors and Grades
1. Attendance (commitment)
2. Preparation
3. Curiosity
4. Attitude (dedication)
5. Talent (ability)
6. Retention
7. Effort (time commitment)
8. Communication Skills
9. Results (performance)
Behaviors and Grades
• Observations
• What Happened
• Take-away Points
Behaviors and Grades
Come Prepared!! Stay on pace; work daily
Ask Questions!! Be interested
Understand Concepts!!
Be an active learner!!
Any Questions??
Bloom’s Learning Taxonomy
Knowledge: arrange, define, duplicate, label, list,
memorize, name, order, recognize, relate, recall,
repeat, reproduce state.
Comprehension: classify, describe, discuss, explain,
express, identify, indicate, locate, recognize, report,
restate, review, select, translate.
Application: apply, choose, demonstrate, dramatize,
employ, illustrate, interpret, operate, practice,
schedule, sketch, solve, use, write.
Bloom’s Learning Taxonomy
Analysis: analyze, appraise, calculate, categorize,
compare, contrast, criticize, differentiate, discriminate,
distinguish, examine, experiment, question, test.
Synthesis: arrange, assemble, collect, compose,
construct, create, design, develop, formulate, manage,
organize, plan, prepare, propose, set up, write.
Evaluation: appraise, argue, assess, attach, choose
compare, defend estimate, judge, predict, rate, core,
select, support, value, evaluate.
Any Questions??
Course Aims and Objectives
Precalculus lays the foundation for successful
completion of Math 170 and 175. The
concepts and methods learned in this course
will form the fundamental basis for further
studies in math and, most importantly for you,
in engineering. Much of the math you will do
in engineering is taught in this course. Learn it
now so you can avoid struggle in upper level
classes later.
Course Aims and Objectives
You need to determine how you learn best, for
example, by seeing the information, hearing
the information, or reading the information.
You might do best with a combination of
different methods. What is important is that
you learn how to learn and you learn how to
enjoy learning.
Course Aims and Objectives
Processing information is the key to learning. I
can transfer lots of information to you (tell you
the information), but until you process it, until
you work with it, you will not develop a deep
understanding the information.
Formats and Procedures
I expect you to attend class and to participate by being
actively involved in class. The simplest way to be
involved is to think about why a topic or method is
being presented. What is the purpose of posing or
solving the problem this way.
Ask questions if you do not understand something. Do
not be afraid to ask a question. If you do not know
the answer, many other students will not know the
answer too! If someone is brave enough to ask a
question, I expect you to honor their bravery by
showing respect to your classmate.
Formats and Procedures
I view mathematics as a language that more concisely
and accurately conveys and describes engineering and
scientific concepts. Mathematics is often the best way
to present engineering and scientific theory. Thus,
learning mathematics is not the end goal of this
course. The goal is to be sufficiently comfortable with
mathematics so that you can focus on new engineering
concepts without being confused by the mathematics.
But being comfortable with something means using it
frequently and understanding its nuances. You must
spend significant time practicing simple, repetitive
problems to fully understand the beauty of
mathematics.
Formats and Procedures
Math 147 is primarily a lecture course combined with
self-learning through ALEKS. This course is part of a
Learning Community which includes Engineering 110.
You must be registered for both courses to participate
in this section (section 008) of Math 147. Attendance
in both courses is beneficial to successfully passing
Math 147.
Quizzes or exams will be delivered most Fridays during
Engineering 110. Homework for Math 147 consists of
working through ALEKS on your own and during
Friday’s Engineering 110 class after the quiz or exam.
Simple experiment
s2
s1
1 km
t1=s1*d11+s2*d12+s3*0+s4*0
1 km
t2=s1*0+s2*0+s3*d23+s4*d24
s3
s4
t3=s1*d31+s2*0+s3*0+s4*d34
1 km
1 km
d31=sqrt(1*1+1*1)
Pythagorean theorem
System of Equations
t1 = s1*d11 + s2*d12 +s3*d13 + s4*d14
t2 = s1*d21 + s2*d22 +s3*d23 + s4*d24
t3 = s1*d31 + s2*d32 +s3*d33 + s4*d34
t4 = s1*d41 + s2*d42 +s3*d44 + s4*d44
t5 = s1*d51 + s2*d52 +s3*d55 + s4*d54
3x + 5y = 6
2x + 3y = 2
Simple Algebra problem
Gaussian elimination
Matrix Form
t1
l11 l12 l13 l14
s1
t2
l21 l22 l23 l24
s2
t3 = l31 l32 l33 l34
s3
t4
l41 l42 l43 l44
s4
t5
l51 l52 l53 l54
T=Ls