System DEs , Modelling , Differential Equations>, First Order Differential Equations , Fourier Series , Modelling with Differential equations , Modelling with First Order DEs

I. Homework set:

Section 1.2. Problems 36,42

Section 1.3. Problems 12,15,19,29,33.

Section 1.4. Problems 20,30,32.

II. Homework set: (due February 15)

Section 1.5. Problems 20,25,31,32

Section 1.6. Problems 15,30,33,57,58,59.

III. Homework set: (due February 22)

Section 2.2. Problems 10,11,21,23,24

IV. Homework set: (due March 1)

Section 3.2 Problems (page 162) 9,10,17,21,27,28

Section 3.2 Problem 20. Solve this problem by using Maple.

You print the output and attach it to the homework.

V. Homework set: (due March 8)

Section 3.4 Problems (page 182) 10,21,23,27,29,42

Page 172 Problem 5. Solve this problem by using Maple

You print the output and attach it to the homework.

VI. Homework set: (due March 15)

1. Section 3.5. Page 195 Problems 28,32,33

2. Section 3.6. Page 212 Problems 32,51,52,53

3. Page 196. Solve the linear system

3 x1+2 x2-x3+4 x4=-1

2 x1+3 x2-2 x3+5 x4=0

x1-2 x2+x3+ x4=-4

-x1+x2+x3-3 x4=0

by the use of Maple

first midterm with solutions

VII. Homework set: (due March 22)

1. Section 4.1 (page 233) Problems: 28,32,35,41

2. Section 4.2 (page 241) Problems: 22,27,31

VIII. Homework set: (due April 5)

1. Section 4.3 (page 248) Problems: 16,19,27,28,29

2. Section 4.4 (page 255) Problems: 13,18,25,29,31.

IX. Homework set: (due April 12)

1. Section 4.5 (page 263) Problems: 17,21,23,24,30

2. Section 4.6 (page 271) Problems: 20,28,30.

X. Homework set: (due April 26 )

1. Section 5.1 (page 294) Problems: 30,32,51,52

2. Section 4.6 (page 306) Problems: 17,18,37,38.

second midterm with solutions

Sections 5.4 and 5.6 are exluded

XI. Homework set: (due May 10)

1. Section 5.5 (page 346) Problems: 36,37,38,41

2. Section 5.5 (page 347) Problems: 47,51,58,59

(Section 7.4 is excluded)

In the Final Exam You will be responsible from

Chaper 1, Section 1 to Chapter 7, Section 5.

Final exam with solutions

Final exam with solutions

1. Introduction, First order Differential equations

2. First Order ODes, Integrating Factot

3. Homogeneous Differential Equations. Mathematical Models.

4. Systems of Linear equations. Matrix Form

5. Echelon matrices. Matrix Operations

6. Inverse Matrices. Determinant.

7. Vector Space R^3.

8. Multidimensional spaces, subspaces, linear combinations.

9. Linear independence, basis and dimension

10. General vector spaces.

11. Second order linear differential equations, its space of solutions.

12. Method of undetermined coefficients. Variation of parameters.

13. Higher order linear differential equations.

14. Eigenvales and eigenvectors.

15. Diagonalization of matrices and systems of linear ODEs