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: 8 Surprise Quizes: 5% each... Midterm Exam: 25%... Classwork: 5%... 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 surprise quizes consisting of a single problem on current material. 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:

Sept 3: Vectors, 2x2 Matrices and Determinants 10.1-10.2
HW: 10.1/1,5,13,33,43* 10.2/ 1,3,5,11,17*, 33*, 39*, 65*
Sept 5: Dot Products and Cross Products 10.3-10.4
HW:10.3/ 3,9,17*,23*, 47a*, 59 10.4/11*, 13*, 35*, 49*
Weekend Review: Differentiation Techniques 2.2-2.3

Sept 10: Parametric Equations and Polar Coordinates 9.2-9.3, p 671-2,
9.2/1abd, 3, 15*, 29*, 38 & 45*, 59 & 61 *, 69a, p678/1, 9, 13
Sept 12: Cross Product, Lines and Planes 10.4-10.5 (quiz I on 10.1-4)
HW: 10.5: 3, 9, 25, 29*
Weekend Review: Conics 9.1

Sept 17: no class monday schedule (I speak at Rutgers)
Sept 19: Hyperboloids, Paraboloids...10.6
10.6/1,3,5,11*,21*,25*,47*, p678/5, 38, 39*
Weekend Review: limits and continuity methods 1.2-1.4

Sept 24: Cylindrical and Spherical Coordinates 10.7 (quiz II on 10.4-6)
10.7/5, 11, 17*, 23, 27, 39*, 45, 53
Sept 26: Review of 2.1-2.4 and 10.1-10.5
HW: Review page 722/ex 2 p732/ex 2, p737-9/ex 1-4, Redo Quizes 1 and 2, p765/11, 17
Weekend Review: pp 134-6/Examples 1-5, Chain Rule 2.4/1,3,9,15 also

Oct 1: Vector valued functions, limits and continuity 11.1 (10 pt quiz)
HW: 11.1/9*, 11,13,23*,31,59*, 65*
Oct 3: Differentiation of Vector valued functions and Velocity 11.2-11.3
HW:Read pp 777-778, pp 785-7 (not acceleration), p790 Do p783-4/7*, 11*,17*, 19a, 33* ; p791-793/3, 39*, 41* (not acceleration) There will be a quiz on this next Thursday!!!
Weekend Review: techniques of integration: 4.1, 4.4, 4.5

Oct 8: Acceleration and Tangent Vectors 11.3-11.4
Review for quiz 11.2/1,3,5,7, know trig and exp derivatives
HW: 11.3/1,3,5*, 11.4/ read 794-795, 800, do 3*
Oct 10: Integration and Arclength 11.2,11.5, (Quiz on 11.1-11.3).
HW: Read p 781-2, do 11.2/39, 45, 51 Read p788-789 ex 4,5,6 Do 11.3/21*, 25*
Read p803-805, Do 11.5/1,5*,7*
Weekend Review: surfaces 10.6

Oct 15:Functions of several variables 12.1
Practice for 10 point quiz using this link.
Oct 17: Level sets, 12.1, (10 pt quiz)
Read pages 819--824, do 827/7,33*, 35*, 45*, 55* Read page 825 Do 828/ 61*, 65, 67*, 73*, 79, 80
Weekend Review: Dot products, Cross products and planes 10.3-10.5
Extra Credit: 12.1/43, 44, 76 using a computer

Oct 22: Partial derivatives 12.3,
HW Read 12.3, Do p846/ 1,3, 7, 21, 29*, 31*, 47*, 59*
Oct 24: Gradients 12.6
HW: Read p857-8 for chain rule, Do p846/53, 69, 77 Read 868-871 Do p875/ 25, 29, 33,34 35,
Weekend Review: Extrema in One Variable 3.1,
Maple done in class is here.

Oct 29: Tangent Planes 12.7
HW Read 825, Do 827/ 67* c=0,-4,4
Read 843-845, do 847/ 59, 67, Read 877-880, do 883/11*, 13, 23*
Oct 31: Extrema and Saddle Points 12.8 and Example Handout (Quiz on partial derivatives, graphing f(x,y), computing gradients and drawing contour maps, level sets)
HW Read 12.8 and Example Handout/ Do 12.8/13*, 18*,35*, 37*, 41* The example handout is on my office door.
Weekend Review: The Midterm will have problems similar to the quizes including arclength and will definitely have a find the tangent plane to a surface and an absolute maximum problem. It will also have multiple choice problems to check for understanding of polar coordinates, vector addition and subtraction, cylindrical and spherical coordinates, recognizing graphs of space curves and functions of two variables and matching contour maps to graphs of functions of two variables, finding saddle points and other critical points by examining graphs, and identifying where the various partial derivatives are positive and negative. Redoing homework and the text's examples is good practice.

Nov 5: Maximizing Profit 12.9 and review
Nov 7: Midterm Exam (includes gradients/level sets)
Weekend Review: Definition of Integration 4.2-4.3

Nov 12: Lagrange Multipliers 12.10 (Nov 13 is withdrawal deadline)
HW: 12.6/Example 4, Example 7, do problem 5,9,47 12.7/ 1,3
Nov 14: More Lagrange Multipliers
Extra Credit quiz on normals to curves and surfaces, gradients, level sets, and maximization. Score out of 10 will be multiplied by (110-midterm grade)/50 and added to the midterm grade. So students with a 50 on the midterm can get up to 12 points added to their grades while students with a 70 can get up to 8 points added, and students with an 80 get up to 6 points added.
Weekend Review: Techniques of Integration 4.4-4.5 particularly 4.4/examples 1, 6, 8, 4.5/examples 1, 2, 5, 6, 7, 10
Read all of 12.10 except Example 5, Do 12.10/5*, 11*, 13*, 23*, 31*

Nov 19: Iterated Integrals and Area 13.1 (Practice Quiz on 4.5 and 12.10)
Review 4.5/examples 1-9, read 13.1 example 1,2 do 13.1/1*,5*,13*,17* HW will be collected!
Nov 21: Double Integrals 13.2 (Quiz on Lagrange Multipliers)
Review 4.7/ex 1, ex 3, ex 10, also trig substitution handout
Read 13.2 (926-9), Do 13.1/3*, 15*, 19*, 23, 13.2/7*, 13*, 21*, 19 Weekend Review: Cross Products 10.4, see also Thanksgiving Weekend's review

Nov 26: More integration 13.2
13.2/5,9,11,15,17,45,53*,56* (hand in)
Nov 28 Thanksgiving
Weekend Review: Polar Coordinates 9.3/
Extra Credit: Jacobians 13.8 requires determinants!

Dec 3: Integration and polar coordinates 13.3 (Quiz on Double Integrals)
13.3/1*, 13*, 15*, 17*, 23* (hand in)
Dec 5: Triple Integration 13.6 (study this on your own if you are snowed in)
HW: 13.6/ Example 1,2, 3,4, Do 13.6/3,5, 13, 17 (dxdydz and dydxdz)
Weekend Review: for final all *ed problems on gradients and parametric equations 9.2-9.3, 11.2-11.3

Dec 10: Vector Fields and Line Integrals 14.1-14.3 key topics
HW: Read 14.1 pages 986-988, do 994/1,3,5,9*,23* Read 14.2 pages 1001-1003, do 1007/29*,33*,39* Read 14.3 pages 1009-1011, do 1016/3*,11*
Dec 12: Last class: Review for final, (5pt in class assignment: Line integrals)
Students who miss this class can get a copy of the assignment on my door for studying purposes.

Weekend Review: all *ed problems and quizes of the semester for the Final. Partial differentiation, gradients, identify vector fields, maximizing problems with and without Lagrange multipliers, applying Fubini's theorem, poloar coordinates (unit circle) and integration, Graphing z=f(x,y), finding tangent planes, graphing planes, space curves, velocity, speed acceleration, arclength, line integrals, conservative vector fields and potential functions, parametric equations for lines.

Tuesday Dec 17: Practice Final Exam including line integrals 8:30-9:30 pm
Thursday Dec 19: Final Exam 8:00-10:00 pm Gillet Hall Auditorium