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Math 281 WINTER 2005, List of lectures
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On this page I will post content of all lectures with reference to the
book. All handouts also will be posted here.
Monday, January 3: Coordinates in three-dimensional space; formula for
the distance between points in three-dimensional space. M Section 13.1;
ETM Section 12.1. We had quiz0 (pdf file) today;
here are the answers. Here is
homework!
Tuesday, January 4: Equations and surfaces in three-dimensional space;
equation of a sphere; vectors: definition, addition, multiplication by a
number, components. Sections 13.1/12.1-13.2/12.2.
Wednesday, January 5: Additions and multiplication by scalar in
coordinates; vectors i,j,k; unit vectors; equilibrium of forces; definition
of dot product. Sections 13.2/12.2-13.3/12.3.
Friday, January 7: Dot product and its properties; calculation of angles:
Section 13.3/12.3.
Monday, January 10: Physical interpretation of dot product as work;
cross-product. Sections 13.3/12.3-13.4/12.4.
Tuesday, January 11: Basic properties and applications of cross-product;
scalar triple product. Section 13.4/12.4. We will have a QUIZ on Friday!
Wednesday, January 12: Equations of lines. Section 13.5/12.5.
New homework!
Friday, January 14: Equations of planes. Section 13.5/12.5. We had
quiz1 today; here are the
solutions.
Tuesday, January 18: More on plane equations. Section 13.5/12.5.
Wednesday, January 19: Cylinders and quadratic surfaces. Section 13.6/12.6.
New homework!
Friday, January 21: More of quadratic surfaces; cylindrical coordinates;
spherical coordinates. Sections 13.6/12.6-13.7/12.7. We will have QUIZ on
Monday!
Monday, January 24: More on spherical coordinates; vector functions.
Sections 13.7/12.7 and 14.1/13.1. We had
quiz2 today; here are the
solutions.
Tuesday, January 25: Derivatives of vector functions and tangent vectors;
differentiation rules for vector functions. Section 14.2/13.2. We will have
MIDTERM on Friday!
Wednesday, January 26: Review before midterm.
New homework!
Friday, January 28: We had
midterm1 today; here are the
solutions.
Monday, January 31: Derivatives and integrals of vector functions;
formula for arc length. Sections 14.2/13.2-14.3/12.3.
Tuesday, February 1: Curvature. Section 14.3/13.3.
Wednesday, February 2: Normal and binormal vectors; velocity and
acceleration. Sections 14.3/13.3-14.4/13.4.
New homework!
Friday, February 4: Projectiles and planets. Section 14.4/13.4.
We will have QUIZ on Monday!
Monday, February 7: Functions of two and more variables. Section 15.1/14.1.
We had quiz3 today; and here are the
solutions.
Tuesday, February 8: Limits and continuity for the functions of two and
more variables. Section 15.2/14.2.
Wednesday, February 9: Partial derivatives. Section 15.3/14.3.
New homework!
Friday, February 11: Tangent planes and linear approximations.
Section 15.4/14.4.
Monday, February 14: Differentials and Chain rule. Sections
15.4/14.4-15.5/14.5.
Tuesday, February 15: More on Chain rule. Section 15.5/14.5.
We will have QUIZ on Friday and MIDTERM on next Wednesday!
Wednesday, February 16: Implicit differentiation and directional
derivatives. Sections 15.5/14.5-15.6/14.6.
New homework!
Friday, February 18: The gradient vector for two and three variables;
maximal value of directional derivative. Section 15.6/14.6.
We had quiz4 today; and here are the
solutions.
Monday, February 21: Tangent planes to the surfaces F(x,y,z)=k;
interpretations of the gradient vector. Section 15.6/14.6.
Tuesday, February 22: Review before midterm. Chapters 14/13-15/14 (up
to 15.6/14.6).
Wednesday, February 23: We had
midterm2 today; here are the
solutions.
New homework!
Friday, February 25: Local and absolute maximuma/minima; critical
points; second derivative test. Section 15.7/14.7. There will be no
Office hours on Monday!
Monday, February 28: Examples of finding maximum/minimum; absolute
maximum and minimum on a bounded closed set. Section 15.7/14.7.
Tuesday, March 1: Example of finding maximum and minimum on a closed
bounded set; some details on the second derivative test; Lagrange multiplier(s).
Sections 15.7/14.7-15.8/14.8.
Wednesday, March 2: Examples for Lagrange multipliers.
Section 15.8/14.8. New homework!
Friday, March 4: Lagrange multipliers for two constraints. Section
15.8/14.8. We will have QUIZ on Monday!
Monday, March 7: Lagrange multipliers in rocket science. Applied
project after Section 15.8/14.8. We had quiz5 today;
and here are the solutions.
Practice exam is now available!
Tuesday, March 8: Review, part 1. Chapters 13/12-14/13. We will have
EVALUATIONS on Wednesday!
Wednesday, March 9: Review, part 2. Chapter 15/14.