M. Umut Isik

Math 240

Class times: MTWR 1:00pm-3:10pm
Room: DRL A7
Office hours: 3:10-4:00pm each class day in the classroom or my office 4N21, or by appointment
Contact info

The aim of this course is to understand, at a basic level, three important areas of mathematics:
- linear algebra
- ordinary differential equations
- vector calculus
These subjects are not only important within themselves, but also are the bread and butter of everyone that uses and applies mathematics in their subjects. You will learn to do many calculations that will be very useful to you in your daily life. You will also understand why the methods work and what they mean; which will also make applying the methods much easier. The philosophy of this course is to reach that sweet balance.

Schedule and homeworks

Extra credit homework : (total: 8%): This linear algebra assignment works up to a proof of the rank-nullity theorem that we stated and used in class. It is organized as a worksheet where I explain many things and then ask you to prove certain statements, labeled as exercises. I do not recommend that you attempt it if you think there are parts of the course you are not completely comfortable with. In either case, do take a look: Here it is

Day   Homework
Week 1
24 May Review of background, vectors,vector spaces, subspaces, pictures. (section 7.6 of the book) notes for lectures 1-2 (the notes are nice, but I recommend also looking at the book for review)

Read the section 7.6
Problems: 7.3: 15
7.6: 1,2,4,8,10,11-16,17,18,19,20
25 May Linear independence, Span, bases, dimension. matrices, solving linear equations. notes for lecture 2

7.6: 23,24,27
8.2: 5,7,9,11,13, 20
26 May Matrices, Rank of a matrix, rank-nullity theorem. notes for lecture 3 8.1: 3,12,15,18,23,33 8.3: 1,5,13,16,17
27 May Determinants, inverse of a matrix. notes for lecture 4
Homework session (some solutions)		 8.5: 15,16,22,38
8.6: 3,5,11,12,19,29, 32,35,36,37,39
Week 2
1 June Review of linear algebra concents. Eigenvalues, eigenvectors. notes for lecture 5
QUIZ! On everything we have done on week 1. Make sure you have done the homework problems. Solutions to Quiz 1		 8.8: 9,13,15,17,21,23
2 June More examples of eigenvalue problems. Diagonalization. notes for lecture 6 8.12: 1,5,7,11,13,15
3 June QUIZ! On linear algebra, including eigenvalues, eigenvector ans diagonalization. Solutions to Quiz 2
Ordinary differential equations, basics and examples. notes for lecture 7		 no homework
Week 3
7 June Linear equations with constant coefficients, solving non-homogeneous equations by guessing the answer (undetermined coefficients method) notes for lecture 8 3.3: 3,5,11,19,33,37,39, 43-48
3.4: 1,3,7,9,13,19,45 (two of the equations don't match any of these graphs)
8 June Cauchy Euler Equations, Spring mass systems, Solving multiple differential equations at the same time. notes for lecture 9 3.6: 3,7,13,15,25,27,29,39
9 June Spring mass systems. More than one spring. Systems of linear equations. Notes for lecture 10 3.11: 1,5,7
10.1: 1,3,11,14
10.2: 1,5,13,19
10 June Review. Past final problems. Here are the solutions  
Week 4 Extra office hours on 11 June: 6:30-7:30pm and on 13 June 2-4pm
14 June Midterm! Here are the solutions  
15 June Series solutions to differential equations; at ordinary and regular singular points. Notes for this lecture 5.1: 17,19,23
5.2: 13,15,17,21
16 June Example of series solution at a regular singular point. Review of Math114: Vector calculus. Review of partial derivatives, gradient. Motion on a curve. Curvature. Notes for this lecture 9.1: 1,11,13
9.2: 1,7,9
9.3: 17,19
9.4: 13,15,17
9.5: 1,3,5,9,23,25
9.6: 13,15,19,25
17 June Vector fields, curl and divergence. Line integrals, conservative vector fields, independence of path. Notes for this lecture

9.7: 7,9,13,29,30,32,33
9.8: 7,9,11,13,19,27,31,35
9.9: 14,17,21,23,25

Week 5
21 June Review of line integrals and conservative vector fields. Proof of the main theorem for conservative vector fields in 2d and 3d. Review of double integrals. Notes for this lecture. Quiz! Solutions. 9.10: 12,15,17
22 June Review of double integrals in polar coordinates. Green's theorem. Surface integrals. Computation of the flux of a vector field through a surface. Notes for this lecture 9.11: 25,27,31
9.12: 1,7,9,25
9.13: 1,11,15,17,25,31,34,35,37, 38
23 June More examples of calculation of flux. Stokes' theorem. Applications of Stokes' theorem in various problems. Notes for this lecture 9.14: 1,3,5,6,7,17
24 June Review of triple integrals, in regular coordinates, cylindrical coordinates and spherical coordinates. Divergence theorem. Notes for this lecture 9.15: 21,23,75,77
9.16: 3,5,9,17
Week 6
28 June Quiz 4! Solutions to Quiz 4. Then Review. Solutions to more practice problems  
29 June Review and problem session  
30 June Review and problem session  
1 July Final Exam!  







 



 

 

 

 




 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Course policies (homework, quizzes, exams, grading)
You do not need to turn in the homework. The only way to understand mathematics is to work out problems yourself; so you should make sure you do the homework from the previous class before the next class. This will also make sure that you are prepated for the quizzes and exams. You can turn in your homework to be reviewed by me if you are not sure you got all the exercises. In any case, you should ask me if there is a homework problem you cannot do or concept you do not understand.
There will be one mid-term exam, one final exam, and 4 quizzes. You are allowed to enter the exam with one letter size cheat sheet. The grading will be as follows:
- Quizzes 25%
- Midterm (14th ofJune) 30%
- Final 45% (1st of July)
Any questions about grading must be asked within a week after you get back your exams/quizzes. There is also an 8% extra credit assignment, for those of you who feel like they want to learn more linear algebra. See notes about it above.

Strategies for success in this course
- Do the homework. Do additional problems if you feel like you need more practice.
- Ask questions. In class, in office hours which are every class day, by email... You should not hesitate to ask about anything you do not fully understand.
- Harsha Reddy will be running the math help center Monday-Thursday 9:00 AM - 1:00 PM. This is a great resource.
- I encourage you to work in groups to prepare for quizzes and exams and to go over material. I would recommend that you attempt the homeworks yourselves before discussing with others.

Resources
Penn Math 240 Home page, includes past finals, resources etc.