MATH 2605 C1-C5, Spring 2015

   1st midterm exam Feb 3

   2nd midterm exam Mar 3

   3rd midterm exam Apr 14

   Final exam Apr 29 (Wed) 8:00am - 10:50am

Project due on Mar 31 at 11:59pm.

Course schedule

Week 1. Jan 5-9 
[Thomas 12.1-12.5] and
Class notes for week 1.
Homework: in MyMathLab. Due: Jan 15.
12.1: 21,35,43,47,55,57, 63,65
12.2: 7,17,21, 31,25,41,45,47
12.3: 3,7,9,27,33,47
12.4: 1,9,15,19,29,47
12.5: 1,7,9,15,25,29,43

Week 2. Jan 12-16  
[Webnotes] Sec 4,5 and class notes for Week 2.
Complementary: [Strang] Chapter 2 (sections 1-4,6).
Complementary: [Lay] Chapter 1 (sections 5,7-9), Chapter 2 (sections 8,9), Chapter 4 (sections 2-5,7)
Review of linear algebra: linear combinations, linear independence and dependence, null and range space of a matrix, basis, coordinates, representation of a linear transformation as a matrix. Change of basis.
Homework for week 2 in T-square. The content of this homework will be the basis for Quiz 1.
Complementary problems:
[Strang] 2.3: 1,2,5,11
[Strang] 2.4: 3,4,19 (only null space and range)
[Strang] 2.6: 1,2,6,8.

Quiz 1 is on Thursday Jan 22 during the first 15 min of recitation. It will include material on linear algebra from Week 2.

Week 3. Jan 20-23 (Jan 19 Institute holiday) 
[Webnotes] Sec 6 and class notes for week 3 .
Complementary: [Strang] Chapter 3 (sections 1-4).
Complementary: [Lay] Chapter 6 (sections 1,2,4-6)
Orthogonality. Gram-Schmidth orthogonalization. Least squares. Orthogonal projection.
Homework: in T-square . Homework is not due, but the material from the homework will help you study for the next quiz.
Complementary problems:
[Strang] 3.1: 7, 9, 10,21,35.
[Strang] 3.2: 3, 17.
[Strang] 3.3: 7, 14.
[Strang] 3.4: 1, 12, 13.

Quiz 2 on Thursday Jan 29, in the first 15 min of recitation. It will include material from Week 3 and up to what's covered on Wed, Jan 28: Orthogonality, Gram-Schimdt, QR, least squares with QR, eigenvalues and eigenvectors.

Week 4. Jan 26-30  
[Webnotes] Sec 7 and class notes for Week 4.
Complementary: [Strang] Chapter 5 (sections 1-2,6), Chapter 6 (section 3).
Complementary: [Lay] Chapter 5 (sections 1-4), Chapter 7 (section 4)
Eigenvalues and eigenvectors. Spectral theorem.
Homework: in t-square.

First midterm exam: Tuesday Feb 3. The exam will cover all material seen from week 1 to week 4. SVD has not been covered; homework for week 4 was modified accordingly. On Monday Feb 2, there will be a review.

Week 5. Feb 2-6 
Monday: review. Tuesday: First midterm exam
After midterm exam: SVD. Norm of matrix.
[Webnotes] Sec 7, [Webnotes] Sec 1 Num , and class notes for week 5.
Complementary: [Strang] Chapter 7 (sections 1,2) . Chapter 1 (section 5).
Complementary: [Lay] Chapter 2 (section 5)
Homework in t-square.

Quiz 3 is on Thu Feb 12. It will include SVD, norm of a matrix, condition number, and up to what is covered on Wednesday Feb 11. It will take place in the first 15 minutes of recitation.

Week 6. Feb 9-13 
Computations with matrices. Relative error, norm of a matrix, condition number. LU decomposition. QR revisited: Householder reflections and Givens rotations.
[Webnotes] Sec 2 Num, [Webnotes] Sec 3 Num , and class notes for week 6, first part and second part .
Complementary: [Strang] Chapter 7, section 3. It is about computation of eigenvalues, but the ideas of how to use Householder reflections to get triangular matrices are there.
Quiz 4 on Thursday (Feb 19) will include LU decomposition, QR with HouseHolder and Givens, and up to what's covered on Feb 18. The quiz is for 15 minutes
Homework: in t-square.

Week 7. Feb 16-20  
Continuing with Householder reflections and Givens rotations.
Iterative methods to solve Ax=b: Jacobi and Gauss-Seidel. Computation of eigenvalues
[Webnotes] Sec 4 Num, and class notes for week 7.
Complementary: [Strang] Chapter 7, section 4.
Quiz 5 on Thursday Feb 26 is on iterative methods for Ax=b, and computation of eigenvalues. Cancelled due to snow

Week 8. Feb 23-27 (Drop day extended Mar 3) 
Continuing with computation of eigenvalues: Power method, inverse power method, shifted power method.
[Lay 7.2, Thomas Ch 12.6] Quadratic forms, cylinders and quadric surfaces.
Class notes for week 8.
Homework in MyMathLab. Due on Tuesday Mar 3 at 9am.
Lay 7.2: 2,4,5,7,10,11,19.
Thomas 12.6: 1,3,7,9,11,13,14,17,19,21,23,25,29.

Second Midterm Exam on Tue Mar 3 during recitation. It will include material from week 5 to week 8: SVD, norm of a matrix, condition number, relative error and error amplification, LU, QR with Householder, QR with Givens, Jacobi and Gauss-Seidel iterations, power method, quadratic forms and cylinders and quadric surfaces.

Week 9. Mar 2-6  
Monday: Review for second midterm
After Second Midterm Exam:
[Thomas Ch 13] Vector functions and curves, limits, continuity, tangent vector and motion, integrals, projectiles. Arc Length.
Class notes for week 9.
Homework in MyMathLab. Due on Tuesday Mar 10 at 11:59pm (end of Tuesday).
13.1: 1,3,5,7,8,9,11,13,15,19,20,21,23,26.
13.2: 1,3,7,11,13,17,19,21,22,25,27
13.3: 1,3,6,7,8,9,11,13

Project description is here. The project is due at the end of the day of March 31st.

Week 10. Mar 9-13
Cont. [Thomas Ch 13] Curvature and normal vectors.
[Thomas Ch 14] Functions of several variables, domain, graphs, level sets; limits and continuity. partial derivatives; chain rule.
Class notes for week 10.
Homework in MyMathLab. Due at the end of Mar 24 (11:59pm)
13.4: 1,2,4,5, 7,9,11,19,23,25.
14.1: 1,3,5,6,8,11,17,19,23,31,33,34,37,43,39,53,55,61,64
14.2: 1,3,5,13,16,19,31,39,41,51,60

Week 11. Mar 16-20. Spring Break  

Week 12. Mar 23-27  
Continuing [Thomas Ch 14] Partial Derivatives; chain rule. Gradients and directional derivatives, tangent planes and differentials.
Classnotes for week 12 and 13.
Homework in MyMathLab. Due on Thursday Apr 2 at 11:59pm.
14.3: 1,5,7,9,13,15,25,27,31,35,37,45,50,53
14.4: 1,3,5,7,9,11,33,46.
14.5: 5,7,9,11,17,19,25,29,33.
14.6: 1,7,9,13,15,41.

Week 13. Mar 30-Apr 3  
Continuing [Thomas Ch 14] Extreme values and saddle points. Lagrange multipliers. Taylor's theorem and proof of the second order partial test for local maxima, local minima and saddle points.

14.7: 3,15,21,31,33,35,49,53,55,61
14.8: 1,3,13,18,25,29,39,46
14.9: 1,3,7.

Week 14. Apr 6-10  
[Thomas Ch 15] Class notes for Week 14.
Multiple integrals: volume under the surface z=f(x,y) over a rectangular region.
Homework in MyMathLab. Not due.
15.1: 1,2,3,5,9,10,15,17,19,23,24, 27,28.

   3rd midterm exam Apr 14

Week 15. Apr 13-17  
Monday: Review for third midterm exam.
Continuing [Thomas Ch 15] Class Notes for Week 15.
Double integrals over regions of type I and II. Area by double integration.
Double integrals in polar coordinates. Triple integrals. Moments and centers of mass.
Homework in MyMathLab. Not due
15.2: 1,2,4,7,9,11,13,15,19,21,29,33,37,45,55,63,67,71.
15.3: 3,5,13,19,24.
15.4: 1,7,9,10,13,17,19,23,27,33,37,41.
15.5: 1,5,11,15,19,23,27,33,37,41.
15.6: 1,3,7,15,21,31.

Week 16. Apr 20-24. Last week of classes
Continuing [Thomas Ch 15]. Finished with 15.6, Moments and centers of mass. Review on Friday
Final exam will not include 15.7 and 15.8 (cylindrical and spherical coordinates, substitutions in multiple integrals).

   Final exam Apr 29 (Wed) 8:00am - 10:50am at Physics L2