MIT: 18.02, Spring 2008

18.02, Spring 2008: Multivariable calculus

Final Examination

Final Examination	1:30pm, Monday 19 May	Johnson Track
Review Session, I	2:00pm, Saturday 17 May	4-163
Review Session, II	2:00pm, Sunday 18 May	4-163

Practice Tests: A, B | Practice Test Solutions: A, B

Announcements

13 May

Prof. Staffilani's review problems can be found here.

Course Information

Course information
Schedule and syllabus
Grade management system (to review grades and change recitation sections)

Class	Time	Location	Instructor	E-mail (@math)	Office	Office hours
Lec	TR 1, F 2	54-100	Gigliola Staffilani	gigliola	2-246	TR 230-330
Rec 1	MW 9	2-131	Pedro Reis	preis	2-335	M 11-1
Rec 2	MW 10	2-131	Pedro Reis	preis	2-335	M 11-1
Rec 3	MW 11	2-139	Tong Hoon Suk	tonghoon	2-091	W 2-4
Rec 4	MW 11	2-142	Chris Evans	lcevans	2-088	W 12-2
Rec 5	MW 12	2-131	Liat Kessler	kessler	2-180	W 2-3, R 2-3
Rec 6	MW 12	2-142	Ilya Tyomkin	tyomkin	2-147	M 3-5
Rec 7	MW 1	2-131	Liat Kessler	kessler	2-180	W 2-3, R 2-3
Rec 8	MW 1	2-135	Anna Teytelman	teytanna	2-130	T 8-10
Rec 9	MW 2	2-151	Josephine Yu	jyu	2-348	M 1-2, W 1-2
Rec 10	MW 2	2-135	Wenchuan Hu	wenchuan	2-101	M 4-5, W 1-2
Rec 12	MW 2	4-261	Michael Manapat	mlm	4-144	W 4-6
Rec 12	MW 3	2-151	Josephine Yu	jyu	2-348	M 1-2, W 1-2
Rec 13	MW 3	2-135	Wenchuan Hu	wenchuan	2-101	M 4-5, W 1-2

Prof. Staffilani's Lecture Notes

Course Summary

Lecture 1, Tuesday 5 February	Introduction, vectors, dot product
Lecture 2, Thursday 7 February	Determinants, cross product
Lecture 3, Friday 8 February	Matrices, inverse matrices
Lecture 4, Tuesday 12 February	Square systems, equations of planes
Lecture 5, Thursday 14 February	Planes, parametric equations for lines and curves
Lecture 6, Friday 15 February	Velocity and acceleration, Kepler's second law
Lecture 8, Friday 22 February	Partial derivatives, tangent plane approximation
Lecture 9, Tuesday 26 February	Max-min problems, least squares approximation
Lecture 10, Thursday 28 February	Second derivative test, global max-min, boundaries and infinity, level curves and level surfaces
Lecture 11, Friday 29 February	Summary of global max-min, boundaries and infinity, chain rule, differentials
Lecture 12, Tuesday 4 March	Vector fields, gradient, directional derivatives, tangent plane (to level) surfaces
Lecture 13, Thursday 6 March	Lagrange multipliers
Lecture 14, Friday 7 March	Non-independent variables, partial differential equations
Lecture 15, Tuesday 11 March	Double and iterated integrals in the plane
Lecture 17, Friday 14 March	Changing order of integration, double integrals, applications
Lecture 18, Tuesday 18 March	Polar coordinates, applications
Lecture 19, Thursday 20 March	General change of variables
Lecture 20, Friday 21 March	Vector fields and line integrals in the plane
Lecture 21, Tuesday 1 April	Conservative fields and path independence, gradient fields and potential functions
Lecture 22, Thursday 3 April	Fundamental theorem for line integrals, grad test, potential functions
Lecture 23, Friday 4 April	Green's theorem
Lecture 24, Tuesday 8 April	Green's theorem: why it works, examples
Lecture 26, Friday 11 April	Simply connected regions
Lecture 27, Tuesday 15 April	Triple integrals, cylindrical coordinates
Lecture 28, Thursday 17 April	Cylindrical and spherical coordinates
Lecture 29, Friday 18 April	Surface area, vector fields in 3D, surface integrals and flux
Lecture 30, Thursday 24 April	Surface area and flux across cylinders and spheres, divergence theorem
Lecture 31, Friday 25 April	Divergence theorem: applications
Lecture 32, Tuesday 29 April	Line integrals, conservative vector fields, curl and potential functions in 3D
Lecture 33, Thursday 1 May	Stokes' theorem
Lecture 34, Friday 2 May	Stokes' theorem continued, applications
Lecture 35, Tuesday 6 May	Review
Lecture 37, Friday 9 May	Applications of Stokes' and the divergence theorem

Problem Sets

Problem sets are due on Thursdays by 1:00pm in 2-106.

	Out	Due
Problem Set 1	Thursday, 7 February	Thursday, 14 February	Part B Solutions
Problem Set 2	Thursday, 21 February	Thursday, 28 February	Part B Solutions
Problem Set 3	Thursday, 28 February	Thursday, 6 March	Part B Solutions
Problem Set 4	Thursday, 13 March	Thursday, 20 March	Part B Solutions
Problem Set 5	Thursday, 20 March	Thursday, 3 April	Part B Solutions
Problem Set 6	Thursday, 10 April	Thursday, 17 April	Part B Solutions
Problem Set 7	Thursday, 17 April	Thursday, 24 April	Part B Solutions
Problem Set 8	Thursday, 24 April	Thursday, 1 May	Part B Solutions

Tests

Final Examination	1:30pm, Monday 19 May	Johnson Track
Review Session, I	2:00pm, Saturday 17 May	4-163
Review Session, II	2:00pm, Sunday 18 May	4-163

Practice Tests: A, B | Practice Test Solutions: A, B

Test 4	1:00pm, Thursday 8 May	Walker Memorial (Building 50)
Review Session	8:00pm, Tuesday 6 May	4-163
Make-up 1	7:45pm, Monday 12 May	2-139
Make-up 2	7:45pm, Tuesday 13 May	2-139
Make-up 3	4:10pm, Wednesday 14 May	2-190
Make-up 4	4:10pm, Thursday 15 May	2-190

Practice Tests: A, B, C | Practice Test Solutions: A, B, C | Test | Test Solutions

Test 3	1:00pm, Thursday 10 April	Walker Memorial (Building 50)
Make-up 1	7:45pm, Monday 14 April	2-135
Make-up 2	7:45pm, Tuesday 15 April	2-135
Make-up 3	4:10pm, Wednesday 16 April	4-370
Make-up 4	4:10pm, Thursday 17 April	4-370

Practice Test | Practice Test Solutions | Test | Test Solutions

Test 2	1:00pm, Thursday 13 March	Walker Memorial (Building 50)
Review Session	7:30pm, Wednesday 12 March	32-141
Make-up 1	7:45pm, Monday 17 March	2-135
Make-up 2	7:45pm, Tuesday 18 March	2-135
Make-up 3	4:10pm, Wednesday 19 March	2-190
Make-up 4	4:10pm, Thursday 20 March	2-190

Practice Test | Practice Test Solutions | Test | Test Solutions

Test 1	1:00pm, Thursday 21 February	Walker Memorial (Building 50)
Review Session	7:30pm, Wednesday 20 February	4-163
Make-up 1	7:45pm, Monday 25 February	2-135
Make-up 2	7:45pm, Tuesday 26 February	2-135
Make-up 3	4:10pm, Wednesday 27 February	4-370
Make-up 4	4:10pm, Thursday 28 February	4-370

Practice Test | Practice Test Solutions | Test | Test Solutions

Applets

Lagrange multipliers
Functions of two variables