MATH 2605 C1-C5, Spring 2015
|Dr. Luz V. Vela-Arevalo|
|Office: Skiles 133A.
Office Hours: Mon-Tue 3-4pm or by appointment.
|Section C1: Skiles 154||Section C2: Skiles 255||Section C3: Skiles 168||Section C4: Skiles 254||Section C5: Skiles 171|
|TA: Ranjini Vaidyanathan
Office: Skiles 142
Office hours: Tue 9-10, Thu 2-3. Math Lab: Wed 3-4
|TA: Bill Dorn
Office: Skiles 230
Office hours: Mon 12-1, Wed 1-2
|TA: Jamie Conway
Office: Skiles 165
Office hours: Tue 12-2
|TA: Xin Xing
Office: Skiles 140
Office hours: Tue 2-3
|TA: Shane Scott
Office: Skiles 252
Office hours: Tue 4:30-5:30, Wed 4-5
1st midterm exam Feb 3
2nd midterm exam Mar 3
3rd midterm exam Apr 14
Final exam Apr 29 (Wed) 8:00am - 10:50amProject due on Mar 31 at 11:59pm.
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
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.
[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.
[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).
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.
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.
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.
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
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