Bozenna Pasik-DuncanProfessor, Department of Mathematics |
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MATH 243 VECTOR CALCULUS (HONORS) FALL 2009 243 Syllabus FALL 2009 243 Practice Exam II
Review the sections: 1.1, 1.2 and 1.3 with the focus on the section 1.3 "The Dot Product".
What we need to know:
Vector addition and its properties.
Scalar multiplication and its properties.
Standard Basis Vectors.
Geometric and algebraic definitions of the dot product.
Dot product and its properties.
What we still need to discuss is the following:
Parametric Equations of Lines.
Orthogonality of Vectors.
Vector Projections.
HW #1 due TOMORROW, August 26 1.1: 3, 6, 21
1.2: 13, 24, 34
1.3: 15, 20, 22, 25
Reading Assignment for tomorrow:
Sections 1.1 - 1.3 and 1.4 (The Cross Product)
LECTURE NOTES, MONDAY, AUGUST 26: (top)
Subject: The Cross Product, Section 1.4
1. Review of the methods for calculating determinants of matrices 3x3
2. Definition of the cross product, geometric and algebraic
3. Important distinction of the cross product from the dot product: the cross product of two vectors from R^3 is a vector whereas the dot product of two vectors is a scalar.
4. The Length and Properties of the cross product and the methods for proving those properties.
5. Using the dot and the cross products to determine whether vectors are parallel or perpendicular.
6. Applications of the cross product, in particular: * torque
* The length of the cross product of two vectors a and b (represented by directed line segments with the same initial point) is equal to the area of the parallelogram determined by a and b. Vectors a and b determine a parallelogram with base equal to the length of a and altitude equal to the length of b multiplied by sin (alfa) where alfa is the angle between a and b.
Therefore the area A = II a II ( II b II sin( alfa) ) = II a x b II .
Exercises Recommended for Practice:
Page 37-39: 8, 9, 11, 12, 13, 15, 20, 23, 25, 26
Next:
Review of Sections 1.5 - 1.7 * Equations for planes
* Some n-dimensional Geometry:
Cauchy- Schwarz Inequality and Triangle Inequality,
Matrices and Determinants,
Polar, Cylindrical and Spherical Coordinate Systems
25 minute Workshop # ! in class!
with problems similar to those listed above under Exercises Recommended for Practice.
See you in class tomorrow,
with my best,
Professor Pasik-Duncan
SUMMARY, LECTURE NOTES, AUGUST 28: (top)
Subject: Relations between the scalar product and the cross product.
Cauchy- Schwarz Inequality
Triangle Inequality
25 minute Workshop I for extra credit focused on using properties of the scalar and cross products.
We proved the Cauchy-Schwarz and Triangle Inequalities formulated on page 49.
Reading Assignment for Monday, August 31
Read Sections: 1. 4 - 1.7
Exercises Recommended for Practice ( with a potential to be selected as HW 2) by Jeremy:
Section 1.4: 12, 19, 24,
Section 1.5: 3, 6, 8, 24
Section 1.6: 31, 39, 41
Section 1.7: 23, 24, 25
Other recommendations are welcome! Submit yours!
Share your comments on Jeremy's selection. Thank You !
Next :
Reviewing Chapter 1 by going through True/False Exercises for Chapter 1 listed in Section 1.8 Have a Very Nice Weekend,
and see you in class on Monday,
Professor Pasik-Duncan
Good News:
All 11 students who participated in the Workshop today received 5 extra points!!! Congratulations on well done work! and
Thank you for your remarkable collaborative effort!
SUMMARY, LECTURE NOTES, AUGUST 31: (top) 1. We finished reviewing Chapter 1
2. Reminder: you are supposed to bring your proposal for HW 2 assignment of 10 problems based on the sections: 1.4- 1.8 ( write your name and 10 exercises (indicate the corresponding sections) on a piece of paper )
3. We will review the following sections this week:
2.1 Functions of several variables
2.2 Limits
2.3 Derivatives
2.4 Higher Order Partial Derivatives
2.5 The Chain Rule
2.6 Directional Derivatives and the Gradient
4. 3, 4.4 and 4.5 Extrema of Functions and their Applications
SUMMARY, LECTURE NOTES, SEPTEMBER 2: (top) Subject: Differentiation of Functions of Several Variables
Partial Derivatives and Continuity, Chapter 2
* Limits
Exercises focused on: find the limit if exists and show that the limit does not exist
* First and Higher Order Partial Derivatives
Gradient and Jacobian matrix ( more about them on Friday)
Next:
Extrema of Functions of Several Variables Remark:
The Homework #2 assignment was prepared by Shixiang Xia ( the winner of today's drawing!) . Homework:
HW 2, due Wednesday, September 9 Section 1.4 : 23
Section 1.5 : 8, 24
Section 1.6 : 9, 16, 19, 21
Section 1.7: 9, 12
Section 1.8: 22
Big thanks go to each of you for preparing the homework assignment! SUMMARY, LECTURE NOTES, SEPTEMBER 9: (top)
Subject: Review Sections 2.3: Derivative
Section 2.4: Properties of the Derivative and Higher Order Partial Derivatives
Section 2.5: The Chain Rule
Homework: Turn in HW 2, HW 3, Due Wednesday, September 16 SUMMARY, LECTURE NOTES, SEPTEMBER 11: (top) Subject: Sections 2.6 : Directional Derivative and the Gradient
Reading Assignment: Read Section 3.1 Parametrized Curves and Kepler's Laws SUMMARY, LECTURE NOTES, SEPTEMBER 14: (top) Subject: Arc length and Differential Geometry, Section 3.2
Discuss Section 3.1: Parametrized Curves and Kepler's Laws
Review in details:
Arc length and Differential Geometry Reading Assignment:
Read Section 3.3: Vector Fields SUMMARY, LECTURE NOTES, SEPTEMBER 16: (top) Subject: Vectors Fields, Section 3.3
Gradient, Divergence, Curl, and the Del Operator , Section 3.4
Homework: HW 4, Due Wednesday, September 23
Section 2.6: 6, 22
Section 3.2: 13, 31, 32
Section 3.3: 25
Section 3.4: 3, 7, 17, 28
Reading Assignment: Review Chapter 3 SUMMARY, LECTURE NOTES, SEPTEMBER 18: (top) Subject: Review Chapter 3, True/False Exercises, Section 3.5
10 minute Quiz for 10 pts or Question/Answer Session,
Professor Tyrone Duncan will decide.
Reading Assignment: Read Section 4.2 Extrema of Functions of Several Variables SUMMARY, LECTURE NOTES, SEPTEMBER 21: (top) Subject: Extrema of Functions of Several Variables, Section 4.2
Reading Assignment: Read Section 4.3: Lagrange Multipliers
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Updated 09/14/09 |
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