Introduction Chapter 12 MATH 2433 - 12631 Aarti Jajoo ajajoo@math.uh.edu Office : PGH 606 Lecture : MoWeFre 10-11am in SR 116 Office hours : MW 11:30-12:30pm and BY APPOINTMENT A. Jajoo, UH MATH 2433 1 / 22 Introduction Chapter 12 Course website http://www.math.uh.edu/∼ajajoo/Math2433 A. Jajoo, UH MATH 2433 2 / 22 Introduction Chapter 12 Key Points 1 CASA Account 2 Textbook 3 Homework 4 Daily class quizzes(poppers) 5 Weekly online quizzes 6 Weekly lab quizzes 7 Exams http://www.math.uh.edu/∼ajajoo/Math2433 A. Jajoo, UH MATH 2433 3 / 22 Introduction Chapter 12 1) CASA Account http://www.casa.uh.edu/ Open your CASA account as soon as possible! You will find your textbook, the weekly online quizzes, and the exam scheduler here. In order to access all of the above, you need to purchase an Access Code from the Book Store in the University Center. http://www.math.uh.edu/∼ajajoo/Math2433 A. Jajoo, UH MATH 2433 4 / 22 Introduction Chapter 12 2) Textbook CALCULUS, 9th edition, by Salas/Hille/Etgen. Publisher: John Wiley & Sons, Inc. You do not need to purchase this textbook. With the Access Code you can access the text electronically by logging into CASA at http://www.casa.uh.edu. A. Jajoo, UH MATH 2433 5 / 22 Introduction Chapter 12 3) Homework Homework will be collected each Monday in lab starting the third week of class. The list of problems will be posted on the course website by the previous Monday. Late homework will NOT be accepted. Your homework will NOT be returned. A. Jajoo, UH MATH 2433 6 / 22 Introduction Chapter 12 4) Daily class quizzes(Poppers) Daily poppers will be given in lecture starting the third week of class. Purchase a course pack of custom bubbling forms from the Book Store in the University Center. Make sure you get the correct packet. They are sold by Section Number: Section 12631 - 10-11am MWF Do NOT punch holes in the page, do NOT use ink, do fill all the required bubbles or you will NOT receive credit. A. Jajoo, UH MATH 2433 7 / 22 Introduction Chapter 12 5) Weekly Online Quizzes Online quizzes will be available at http://www.casa.uh.edu, starting the first week of class. You can take them up to 20 times and only the best score is used for the grade. Check the weekly quizzes calendar at the course website to know when they close. http://www.math.uh.edu/∼ajajoo/Mah2433 A. Jajoo, UH MATH 2433 8 / 22 Introduction Chapter 12 6) Weekly Lab Quizzes Quizzes will be given every week in lab, starting the second week of class. Quizzes will be given either on Monday or on Wednesday and will be collected in lab the same day. There are NO make-up quizzes. If you miss a quiz, you will receive a zero, and the two lowest quiz grades will be dropped. http://www.math.uh.edu/∼ajajoo A. Jajoo, UH MATH 2433 9 / 22 Introduction Chapter 12 7) Exams Three tests during the semester and one final exam. Exams are given at CASA. You will schedule the time of your exam at http://www.casa.uh.edu. The scheduler will be available two weeks prior to the exams (I will inform you). Exam 1 Exam 2 Exam 3 Final exam Feb 13-14 Match 27-28 April 24-25 May 7-9 There are NO make-up exams! Plan on arriving early so if you are stuck in traffic etc. you don’t miss the exam. A. Jajoo, UH MATH 2433 10 / 22 Introduction Chapter 12 Grades Lab Quiz Online Quiz Homework and poppers Exam 1 Exam 2 Exam 3 Final exam 10 10 10 15 15 15 25 90 % and above above 80% and below 90% above 70% and below 80% above 60% and below 70% above 60% % % % % % % % A B C D F http://www.math.uh.edu/∼ajajoo/Math2433 A. Jajoo, UH MATH 2433 11 / 22 Introduction Chapter 12 Classroom behavior Come to class on time. Attendance is NOT mandatory. If you have something to do more exciting than cal 3, do it outside the classroom and do not disturb other students. However, be aware that you will miss the points from the daily poppers. ASK QUESTIONS. If there is something you do not understand in what I am saying or working on, do not hesitate to raise your hand. ANSWER QUESTIONS. All the info about the course are available at the course website. Check info under Course Organization. http://www.math.uh.edu/∼ajajoo/Math2433 A. Jajoo, UH MATH 2433 12 / 22 Introduction Chapter 12 Sect. 12.1 Cartesian Space Coordinates Section 12.1 A. Jajoo, UH MATH 2433 13 / 22 Introduction Chapter 12 Sect. 12.1 Three dimensional space The z-axis is perpendicular to the xy -plane oriented to form a right-handed system Now we have 3 coordinate planes: xy -plane, xz-plane, yz-plane. A. Jajoo, UH MATH 2433 14 / 22 Introduction Chapter 12 Sect. 12.1 Plotting points The position of a point in 3D is given by its 3 coordinates (x, y , z). A. Jajoo, UH MATH 2433 15 / 22 Introduction Chapter 12 Sect. 12.1 Planes Example: write the equation of a plane that passes through (3, 1, -2) that is parallel to the xz-plane. A. Jajoo, UH MATH 2433 16 / 22 Introduction Chapter 12 Sect. 12.1 Take two points P1 (x1 , y1 , z1 ) and P2 (x2 , y2 , z2 ): Distance formula The distance between P1 and P2 is given by q d(P1 , P2 ) = (x2 − x1 )2 + (y2 − y1 )2 + (z2 − z1 )2 Midpoint formula The midpoint of the line segmente P1 P2 is given by x1 + x2 y1 + y2 z1 + z2 , , 2 2 2 A. Jajoo, UH MATH 2433 17 / 22 Introduction Chapter 12 Sect. 12.1 Example Given A(2, 0, −1) and B(2, 1, 3), find the distance between A and B and the midpoint of the line segment AB. A. Jajoo, UH MATH 2433 18 / 22 Introduction Chapter 12 Sect. 12.1 Sphere The sphere of radius r centered at P0 (a, b, c) is the set of all the points P(x, y , z) with d(P, P0 ) = r : (x − a)2 + (y − b)2 + (z − c)2 = r 2 . A. Jajoo, UH MATH 2433 19 / 22 Introduction Chapter 12 Sect. 12.1 Example Find the center and radius of x 2 + y 2 + z 2 + 4x − 8y − 2z + 5 = 0. A. Jajoo, UH MATH 2433 20 / 22 Introduction Chapter 12 Sect. 12.1 Vectors Section 12.3 A. Jajoo, UH MATH 2433 21 / 22 Introduction Chapter 12 Sect. 12.1 Vectors Definition A vector is an ORDERED triple of real numbers where addition and multiplication by scalars hold: (a1 , a2 , a3 ) + (b1 , b2 , b3 ) = (a1 + b1 , a2 + b2 , a3 + b3 ) α(a1 , a2 , a3 ) = (αa1 , αa2 , αa3 ). A. Jajoo, UH MATH 2433 22 / 22 Introduction Chapter 12 Sect. 12.1 Vectors We depict vectors with arrows. To depict the vector (a1 , a2 , a3 ), you can choose any initial point and use the arrow −→ −→ Notation: QR and OP or a = (a1 , a2 , a3 ). A. Jajoo, UH MATH 2433 23 / 22 Introduction Chapter 12 Sect. 12.1 Example −→ −→ Given P(1, −2, 5) and Q(5, −1, −3), find PQ and QP. A. Jajoo, UH MATH 2433 24 / 22 Introduction Chapter 12 Sect. 12.1 To Do Open your CASA account. Buy the Access Code. Syllabus is posted on the course website. Read Sections 12.1 and 12.3. A. Jajoo, UH MATH 2433 25 / 22