18.02 Calculus
Spring 2015
Lecturer: Pavel I Etingof
Recitation Instructors: Spencer Thomas Becker-Kahn, Eva Belmont, Efrat Engel Shaposhnik, Teng Fei, Emmy Murphy
Lecture: TR11, F2 (54-100)
Information:
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Announcements
reminder - office hours/review tonight
Hi all,
I remind about the office hour/review I will hold tonight at 7-9pm in E17-133.
Please prepare your questions.
See you there!
Best, Pavel
I remind about the office hour/review I will hold tonight at 7-9pm in E17-133.
Please prepare your questions.
See you there!
Best, Pavel
Announced on 20 May 2015 3:15 p.m. by Pavel I Etingof
Practice final solutions and review
Hi all,
1. Solutions for the practice final have just been posted.
2. I will do a review Wednesday May 20, 7-9pm, in Rm. E17-133. If you need help earlier, please see one of the TA at the office hours.
3. Please bring your questions to the review. I will spend the review time answering your questions.
Good luck with the final!
Best, Pavel.
1. Solutions for the practice final have just been posted.
2. I will do a review Wednesday May 20, 7-9pm, in Rm. E17-133. If you need help earlier, please see one of the TA at the office hours.
3. Please bring your questions to the review. I will spend the review time answering your questions.
Good luck with the final!
Best, Pavel.
Announced on 18 May 2015 9:33 p.m. by Pavel I Etingof
Office Hours for the Final Week
Office Hours for the next few days are as follows:
Monday:
4-5: Eva Belmont (E18-401B)
Tuesday:
10-11: Emmy Murphy (E18-306)
2-3: Emmy Murphy (E18-306)
5-7: Spencer Hughes (E18-376)
Wednesday
10.30-11.30: Efrat Engel Shaposhnik (E17-406)
5-6: Eva Belmont (E18-401B)
7-9 Pavel Etingof (Room TBC)
Monday:
4-5: Eva Belmont (E18-401B)
Tuesday:
10-11: Emmy Murphy (E18-306)
2-3: Emmy Murphy (E18-306)
5-7: Spencer Hughes (E18-376)
Wednesday
10.30-11.30: Efrat Engel Shaposhnik (E17-406)
5-6: Eva Belmont (E18-401B)
7-9 Pavel Etingof (Room TBC)
Announced on 17 May 2015 11:11 p.m. by Spencer Thomas Becker-Kahn
Practice final, review and other things
Hi all,
1. A practice final has just been posted. Solutions will be available Monday May 18 at 10pm.
2. I will be out of the office Monday, Tuesday, Wednesday (but will answer e-mail) and will not have office hours Tuesday, but will run a review session Wednesday May 20, 7-9pm, Room to be announced.
3. Please fill out course evaluations.
4. If you were excused from any homeworks or exams or came from 18.02A, please make sure to remind your TA and
attach the corresponding e-mails/documents, to be certain that it's recorded adequately.
Best, Pavel.
1. A practice final has just been posted. Solutions will be available Monday May 18 at 10pm.
2. I will be out of the office Monday, Tuesday, Wednesday (but will answer e-mail) and will not have office hours Tuesday, but will run a review session Wednesday May 20, 7-9pm, Room to be announced.
3. Please fill out course evaluations.
4. If you were excused from any homeworks or exams or came from 18.02A, please make sure to remind your TA and
attach the corresponding e-mails/documents, to be certain that it's recorded adequately.
Best, Pavel.
Announced on 17 May 2015 8:55 a.m. by Pavel I Etingof
18.02: List of topics for the final
Hi all,
Here is a list of problem types that you may see on the final.
So for preparation, you should just make sure that you know how to do the things
listed below. Please ask your TA or me if you are not sure how to do any of these.
I will review the most difficult ones tomorrow.
1. Operations with vectors in 2D and 3D (linear combination,
dot and cross products).
2. Finding angles using dot product.
3. Finding areas using cross product.
4. Parametric equations of lines and curves. Write equations for:
*Line through two given points.
*Line through a point parallel to a given line.
*Line through a point perpendicular to two given lines or to a plane.
*Line through a given point parallel to two planes.
5. Equations of plane:
*Through three points.
*Through a point and a line.
*Containing two intersecting lines.
*Through a point perpendicular to a line.
*Through a point parallel to two lines.
*Through two points perpendicular to a plane.
*Through two points parallel to a line.
6. Computation of determinants. Solving linear systems by
matrix inversion (2 by 2 and 3 by 3).
7. Computation of partial derivatives.
8. Writing linear approximation. Equation of the tangent plane to a
graph of a function or a curve (surface) given by an equation, at a given point.
9. Computing directional derivatives, gradient, direction of fastest
increase/decrease of a function, rate of decrease/increase of a function
in a given direction.
10. Finding critical points and solving unconstrained max/min problems.
11. Determining types of critical points (two variables).
12. Constrained min/max problems. Lagrange multipliers.
13. Computing partial derivatives of an implicit function at a point.
Computing partial derivative of a function of non-independent
variables (i.e., linked by constraints).
14. Reducing double integrals to iterated integrals and computing them.
Volume under a graph.
15. Changing order of integration in iterated integrals.
16. Reducing double integrals to iterated integrals in polar coordinates and
computing them.
17. Computing area, mass, center of mass, moment of inertia in 2D.
18. Using change of variables in computing double integrals.
19. Computing line integrals in 2D and 3D by using parametrizations.
Computing length of a curve.
20. Finding for which values of parameters a vector field is conservative,
in 2D and 3D. Computing the potential.
21. Computing flux of a vector field through a curve and its work along a curve
in the plane directly.
22. Using Green's theorem to compute work and flux integrals over closed
curves in the plane. Divergence and curl of a vector field in 2D,
computing them.
23. Reducing triple integrals to iterated integrals in rectangular coordinates
and computing them.
24. Reducing triple integrals to cylindrical and spherical coordinates,
and computing them.
25. Computing volume, mass, center of mass, moment of inertia in 3D.
26. Area element for a parametrized surface. Surface area (integral of
area element).
27. Flux through a surface, direct computation using parametrization
(in particular, for a graph of a function).
28. Computing divergence of a vector field. Computing flux integrals
using divergence theorem.
29. Computing curl of a vector field. Using Stokes' theorem to compute line
integrals.
Here is a list of problem types that you may see on the final.
So for preparation, you should just make sure that you know how to do the things
listed below. Please ask your TA or me if you are not sure how to do any of these.
I will review the most difficult ones tomorrow.
1. Operations with vectors in 2D and 3D (linear combination,
dot and cross products).
2. Finding angles using dot product.
3. Finding areas using cross product.
4. Parametric equations of lines and curves. Write equations for:
*Line through two given points.
*Line through a point parallel to a given line.
*Line through a point perpendicular to two given lines or to a plane.
*Line through a given point parallel to two planes.
5. Equations of plane:
*Through three points.
*Through a point and a line.
*Containing two intersecting lines.
*Through a point perpendicular to a line.
*Through a point parallel to two lines.
*Through two points perpendicular to a plane.
*Through two points parallel to a line.
6. Computation of determinants. Solving linear systems by
matrix inversion (2 by 2 and 3 by 3).
7. Computation of partial derivatives.
8. Writing linear approximation. Equation of the tangent plane to a
graph of a function or a curve (surface) given by an equation, at a given point.
9. Computing directional derivatives, gradient, direction of fastest
increase/decrease of a function, rate of decrease/increase of a function
in a given direction.
10. Finding critical points and solving unconstrained max/min problems.
11. Determining types of critical points (two variables).
12. Constrained min/max problems. Lagrange multipliers.
13. Computing partial derivatives of an implicit function at a point.
Computing partial derivative of a function of non-independent
variables (i.e., linked by constraints).
14. Reducing double integrals to iterated integrals and computing them.
Volume under a graph.
15. Changing order of integration in iterated integrals.
16. Reducing double integrals to iterated integrals in polar coordinates and
computing them.
17. Computing area, mass, center of mass, moment of inertia in 2D.
18. Using change of variables in computing double integrals.
19. Computing line integrals in 2D and 3D by using parametrizations.
Computing length of a curve.
20. Finding for which values of parameters a vector field is conservative,
in 2D and 3D. Computing the potential.
21. Computing flux of a vector field through a curve and its work along a curve
in the plane directly.
22. Using Green's theorem to compute work and flux integrals over closed
curves in the plane. Divergence and curl of a vector field in 2D,
computing them.
23. Reducing triple integrals to iterated integrals in rectangular coordinates
and computing them.
24. Reducing triple integrals to cylindrical and spherical coordinates,
and computing them.
25. Computing volume, mass, center of mass, moment of inertia in 3D.
26. Area element for a parametrized surface. Surface area (integral of
area element).
27. Flux through a surface, direct computation using parametrization
(in particular, for a graph of a function).
28. Computing divergence of a vector field. Computing flux integrals
using divergence theorem.
29. Computing curl of a vector field. Using Stokes' theorem to compute line
integrals.
Announced on 13 May 2015 7:06 p.m. by Pavel I Etingof
