PreCalculus with Math and Engineering Foundations

1. Math 147PreCalculusSection 008 William P. Clement Center for Geophysical Investigation of the Shallow Subsurface Boise State University

2. Learning CommunityYou must be enrolled inMath 147, section 008andEngineering 110

3. 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.

4. From the Course Catalog PreCalculus Math 175 Section 008 5 Credits Monday, Tuesday, Wednesday, Thursday, and Friday 3:40 to 4:30 ET 103

5. 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)

6. 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.

7. Geophysical Tomography

8. Borehole Tomography Experiment

9. Borehole Tomography We know the physics of the problem and the data and we try to find the model parameters.

10. Invaluable Help Randi Walters randiwalters@mail.boisestate.edu Office hours: 4:40 to 5:30 (right after class) - Monday and Wednesday - Room MEC103

11. 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

12. 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

13. 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.

14. 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.

15. 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

16. 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.

17. 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.

18. What You Really Care About:Grading Homework and Quizzes – 30% Exams (5 during semester) – 55% Final exam – 15%

19. 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

20. Class Website http://cgiss.boisestate.edu/~billc/Math147 I also have a link to this page from my homepage.

21. Graphing Calculator Manual To get the Graphing Calculator Manual Go to: http://math.boisestate.edu/~bkenny Follow the link: Graphing Calculator Manual with Exercises

22. Behaviors and Grades • Attendance (commitment) • Preparation • Curiosity • Attitude (dedication) • Talent (ability) • Retention • Effort (time commitment) • Communication Skills • Results (performance)

23. Behaviors and Grades • Observations • What Happened • Take-away Points

24. Behaviors and Grades Come Prepared!! Stay on pace; work daily Ask Questions!! Be interested Understand Concepts!! Be an active learner!!

25. Any Questions??

26. 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.

27. 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.

28. Any Questions??

29. 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.

30. 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.

31. 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.

32. 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.

33. 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.

34. 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.

35. s2 s1 s3 s4 Simple experiment 1 km t1=s1*d11+s2*d12+s3*0+s4*0 1 km t2=s1*0+s2*0+s3*d23+s4*d24 t3=s1*d31+s2*0+s3*0+s4*d34 d31=sqrt(1*1+1*1) Pythagorean theorem 1 km 1 km

36. 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

37. 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