Intermediate Calculus I

The aim of this course is to provide the students with a thorough knowledge of vector calculus. To succeed the students must attend class to learn new material and follow up by reading the corresponding sections of the textbook and completing the assigned homework. All work should be checked by the students using the back of the textbook and *ed problems will be reviewed in class. Each weekend there is additional Weekend Review with reading and problems from Single Variable Calculus (MAT 175-176) that will prepare the students for the following week's new material and quiz.

Grading Policy: 11 Quizes: 5% each... Midterm Exam: 15%... Final:30%...

The purpose of grading is to provide feedback on how well the students understand the material. For this reason there will be regular quizes consisting of a single problem on current material. THE QUIZES COUNT MORE TOWARDS THE GRADE THAN EITHER OF THE EXAMS! The best way to prepare for the quizes is to keep up to date on the homework and ask questions (in class and in office hours). Homework is not collected and students are encouraged to work together. Problems with a * will be put on the board by students and gone over at the beginning of class. The students who post their homework on the board will receive credit towards their classwork grade. The best way for students to prepare for the midterm and final exams is to review class notes and the corresponding chapters in the textbook and then practice old *ed and quiz problems without consulting the notes.  Always start studying at least 4 days before the exam and bring questions to the review class. The final exam will be similar to the midterm exam, emphasizing the material learned after the midterm but covering the rest of the semester as well.

Syllabus: (will be updated regularly)

Jan 31: Vectors and plotting 3D pictures 10.1-10.2
HW: 10.1/1,5,13,21, 33,43* 10.2/ 1,3,5,11,29*, 33*, 65*
Feb 2: Dot Products and Cross Products 10.3-10.4
HW:10.3/ 3,9,17,21, 47a, 61, 77 (draw) 10.4/1,3,5,11, 13, 35, 53
Weekend Review: Unit Circle Trigonometry (link)

Feb 7: Parametric Equations and Polar Coordinates 9.2, 9.4, p690
9.2/1,3,15, 39, 41, 42, 67, 69, 9.4/1,11,21,25,29,33,35,48
Feb 9: Lunar New Year (Review Chapter 10.1-10.3 and 2.1-2.2)
It is not mandatory to attend this class.
Weekend Review: Conics 9.1, Study for QUIZ 1, redo all HW!

Feb 14: Lines and Planes 10.5 up to page 756, conics 9.1 (QUIZ 1 on 10.1-3)
HW: 10.5: 1, 3, 5, 11, 25, 27, 33, 51 9.1/1,3,5,7
Feb 16: Distances (10.5) Hyperboloids, Paraboloids (10.6)
10.5/13, 19, 37, 45, 73, 77, 81 10.6/1,3,5, 19, 21, 23
Weekend Review: Review of Differentiation 2.1-2.4
HW: Do examples from 2.2 first trying them and then comparing your work with the text:ex 2, ex 3, ex 5, ex 6, ex 7, ex 8 ,ex 9

Feb 21: President's Day, no school
Feb 23: Click here for QUIZ 2 which is now due Monday.
Read Cylindrical and Spherical Coordinates 10.7 (QUIZ 2 on 2.2, 10.3-5)
10.7/5, 11, 17*, 23, 27, 39*, 45, 53
Weekend Review: Product Rule 2.3/ examples 1,2,3, Chain Rule 2.4/examples 3,4,5,9

Feb 28: Vector valued functions, limits and continuity 11.1
HW: 11.1/9,11,15,17,19,21,23,59,69
March 2: Differentiation of Vector valued functions and Velocity 11.2-11.3
HW:Read pp 794-797, Do 11.2/1,3,7, 41, Read 802-804 (not acceleration), Do 11.3/5, 13, 15, There will be a QUIZ on this next Wednesday!!!
Weekend Review: techniques of integration: 4.1, 4.4, 4.5

March 7: Acceleration and Tangent Vectors 11.3-11.4,
Review for QUIZ, know trig and exp derivatives
HW: 11.2/17,19, Read rest of 11.3 and all of 11.4, do 11.3/1,3,7,17,45, 11.4/5,7,13, 23
March 9: Projectiles, Integration and Arclength 11.2,11.5, (QUIZ 3 on 11.1-11.3).
HW: Read rest of 11.2, do 11.2/43, 55 Read 11.3 ex 5 Do 11.3/21, 27
Read p803-805, Read 11.5 up to curvature, Do 11.5/5, 7, 9, 15, 17,19
Click here for QUIZ 4 due Monday.
Weekend Review: Dot products, Cross products and planes 10.3-10.4, Surfaces 10.6

March 14: Functions of several variables 12.1 (QUIZ 4 DUE TODAY)
Read 838-840, look at images on page 845, review 765-766, do 12.1/ 11, 13, 17, 19, 21, 27, 29, 31, 33, 35, 37, 67, 79
March 16: Level sets, 12.1,
12.1/45, 47, 49, 51, 53, 69, 71, 73, 83, 85, 87
The Midterm will have a section on space curves (see practice from previous semester at this link. It will also have multiple choice problems to check for understanding of polar coordinates, vector addition and subtraction, cylindrical and spherical coordinates, projecting vectors, plotting vectors, and recognizing graphs of space curves. Redoing homework and the text's examples is good practice.

March 21: Midterm Exam

March 23: Partial derivatives 12.3,
HW Read 12.3, 12.3/1,3,5,7,19,25,29,33,35,49,75
Weekend Review: Planes 10.5,

March 28: Lehman Closed
March 30: Gradients 12.5-12.6 (Quiz 5 is HW from 12.1 and 12.3 due today)
HW: Read 12.6/3, 15, 29, 37, 51, 55 (sketch and check), 59 (sketch and check), 63, 71 Read in 12.5: ex 1, ex 3, Thm 12.7, ex 4 Do 12.5/ 1, 5, (7, 9)
Maple done in class is here. Extra credit, try a few more functions and print them out.

April 4: Tangent Planes 12.7
study for quiz 6 on partial derivatives, graphing f(x,y), computing gradients and drawing contour maps, level sets)
12.7/5,7,11,13,15,17,55
April 6: Extrema and Saddle Points 12.8 (QUIZ 6)
Tangent Planes quiz on Monday!!!
HW Do 12.8/1,9,13,27, 31, 37, 41, 44a 44e,

April 11: Maximizing 12.8-12.9 (QUIZ 7 on tangent planes)
Read example 5 of 12.8, do 12.8/53, 55, 59
Read examples 1 and 2 of 12.9 and do 12.9/1, 3, 19, 21
extra credit read example 3 of 12.9 and do 27 and 29.
April 13: Lagrange Multipliers 12.10
HW: Quiz 8: 12.10/5,13,15,17,25
Weekend Review: Definition of Integration 4.2-4.3

April 18: More Lagrange Multipliers (QUIZ 8=in class multipliers project)
No homework: just review integration from Calc II.
April 20: Iterated Integrals, Area and Double Integrals 13.1-2
Review 4.4/examples 1, 6, 8, 4.5/examples 5, 6, 7, 9
Read the first three pages of 13.2 for motivation
Read 13.1 which teaches how to integrate and set bounds
Do 13.1/ 1,3,5,7,9 checking as you go along
Do 13.1/11, 15, 21, 27, 29, 31,
Do 13.1/39, 41, 43, 45, 47, 49, 53, 59
Quiz 9 prep: 13.1/ 28, 32, 42, 56, 60

May 2: Double Integrals 13.2 Quiz 9 is due today.
Review 4.7/ex 1, ex 3, ex 10,
13.2/9,11,13,21
May 4: More integration 13.2, review of 9.4

review for quiz 10 is: 13.2/7, 15, 17, 19, 23, 25, 49, 51, 53, 55, 61, (63, 65) 9.4/ redo assignment from earlier this semester
Weekend Review: Cross Products 10.4, Polar Coordinates 9.3 and 10.7
Extra Credit: Jacobians 13.8 requires determinants!

May 9: Integration and polar coordinates 13.3 (QUIZ 10 on Double Integrals)
13.3/ 9, 13, 15, 17, 33, 55, 57
May 11: Triple Integration 13.6
HW: 13.6/ Example 1,2, 3,4, Do 13.6/3,5, 13, 17 (dxdydz and dydxdz)
Review space curves, dot products and integration for Quiz 11:
11.2-3 Do 11.2/7, 11.3/ex 2, ex 3, 1,3,5,7, 17
Those who've taken linear algebra: 13.8/ 1,3,7,11,27,29,30

May 16: Vector Fields and Potentials 14.1, 14.3 key topics (quiz 11 starts)
HW: Read 14.1 through ex 4, then ex 6, ex 8, handout
14.1/1,3,5,7,9,21,23,
Read 14.3 pp 1032-1034, ex 5a, do 11a, 13,
then imitate handout to do: 14.1/35, 51,
May 18: Divergence, Curl and Review for final,
Quiz 11 is to do handout and 14.1/39, 41, 53 using the handout's methods
It is due in my mailbox in the math dept office by 5pm May 25. (keep a copy and bring it to the final)
Weekend Review: There will be significant integration on the final. Be sure to practice the integration as suggested in the reviews (u substitution and product rules from Calc II). You will need to find multivariable integrals, arclengths and line integrals. You will need to be able to change the order of integration, draw regions and figure out bounds from drawn regions in polar and rectangular coordinates. You will need to find extrema both by maximizing functions in regions using grad f=0 and using method of Lagrange multipliers. You will need to be able to find gradients both to find tangent planes and to do maximization which means you need to know partial differentiation even with product and chain rules. You need to be able to identify gradient fields, level curves and graphs of z=f(x,y) with each other and with the functions. You need to be able to find formalas for lines and planes and graph them even in 3D, you need to know projections both drawn and how to compute, also tail to tip addition, know dot products and cross products, and parametric equations for curves, identify graphs, find velocity, speed, acceleration and tangential acceleration.

The exam will be similar to the midterm in style and not have as long problems as the quizes. The room will be available next week, so I recommend students come to class at the usual time and study together. I may stop by. Remember, ask for help from students who know the material. Do not go to the tutoring centers!!!!

Final Exam is Wed May 25 from 11am-1pm. Students with a conflict may take the final Monday May 23 8:30 am - 10:30 am.