MTH 362, Fall 2006

Topics and Assignments

Week Topics Assignments

Sept 6 - 8

Complex Numbers. Complex Plane: 13.1
Polar Form of Complex Numbers. Powers and Roots: 13.2

13.1 # 1,2,5,7--17
13.2 # 1,3,5,7,9,11,15--17,21,23,25

Sept 11 - 15

Exponential Function: 13.5
Matrices, Vectors: Addition and Scalar Multiplication: 7.1
Matrix Multiplication: 7.2

13.5 # 3,5,7,9,11,13--15
7.1 # 1,5,7,9,12,14
7.2 # 1,2,4,13,20,21

Sept 18 - 22

Linear Systems of Equations. Gauss Elimination: 7.3
Linear Independence. Rank of a Matrix. Vector Space: 7.4
Solutions of Linear Systems: Existence, Uniqueness: 7.5

7.3 # 1,3,5,9,11,15,17,19
7.4 # 1,3,5,7,13,17,19,27,29,31

Sept 25 - 29

Determinants. Cramer's Rule: 7.7
Inverse of a Matrix. Gauss-Jordan Elimination: 7.8
Review

7.7 # 5,7,9,11,15,19,21,23
7.8 # 1,3,5,7,13,17,19

Oct 2 - 6

Basic Concepts. Modeling: 1.1
Geometric Meaning of y'=f(x,y). Direction Fields: 1.2
Exam I

1.1 # 1,3,5,7,9,11,13,15,17,21
1.2 # 1,3,5,7,11,13
October 5

Oct 9 - 13

Separable ODEs. Modeling: 1.3
Exact ODEs. Integrating Factors: 1.4
Linear ODEs. Bernoulli Equation. Population Dynamics: 1.5

1.3 # 3,5,7,9,11,13,15,23,25,27
1.4 # 1,5,7,9,11,13,15,17,21
1.5 # 3,5,7,11,15,19,21,23,25,27

Oct 16 - 20

Homogeneous Linear ODEs of Second Order: 2.1
Homogeneous Linear ODEs with Constant Coefficients: 2.2
Modeling: Free Oscillations (Mass-Spring System): 2.4

2.1 # 1,3,5,7,9,11,13,17,19,21,23
2.2 # 1,3,5,7,9,11,13,15,17,19,21,23,25,31
2.4 # 1,3,5,7,9,11,13,17

Oct 23 - 27

Euler-Cauchy Equations: 2.5
Existence and Uniqueness of Solutions. Wronskian: 2.6
Nonhomogeneous ODEs: 2.7

2.5 # 1,3,5,11
2.6 # 1,3,5,7,9,13,15,17
2.7 # 1,3,5,7,11,13,15,17,19

Oct 30 - Nov 3

Modeling: Forced Oscillations. Resonance: 2.8
Modeling: Electric Circuits: 2.9
Solution by Variation of Parameters: 2.10

2.8 # 1,3,9,11,15,17
2.9 # 1,3,5,7,9,11,13,15,17
2.10 # 1,3,5,7

Nov 6 - 10

Review
Exam II

November 9

Nov 13 - 17

Homogeneous Linear ODEs: 3.1
Homogeneous Linear ODEs with Constant Coefficients: 3.2
Nonhomogeneous Linear ODEs: 3.3

3.1 # 1,3,5,7,9,11,13,15,17,19
3.2 # 1,3,5,7,9,11,13,15,17
3.3 # 1,3,5,9

Nov 20 - 24

Basics of Matrices and Vectors: 4.0
Systems of ODEs as Models: 4.1
Happy Thanksgiving !

4.1 # 5,7,11,13,15

Nov 27 - Dec 1

Basic Theory of Systems of ODEs: 4.2
Constant-Coefficient Systems. Phase Plane Method: 4.3
Criteria for Critical Points. Stability: 4.4

4.3 # 1,3,5,7,9,11,13,15
4.4 # 1,3,5,7,9,11,13,15,17

Dec 4 - 8

Qualitative Methods for Nonlinear Systems: 4.5
Nonhomogeneous Linear Systems of ODEs: 4.6
Review

4.5 # 1,3,5,7,9,11,13,15,17
4.6 # 3,5,7,9,11,13,15,17,19

Dec 19
Final!!

8:00-11:00 AM.

Week	Topics	Assignments
Sept 6 - 8	Complex Numbers. Complex Plane: 13.1 Polar Form of Complex Numbers. Powers and Roots: 13.2	13.1 # 1,2,5,7--17 13.2 # 1,3,5,7,9,11,15--17,21,23,25
Sept 11 - 15	Exponential Function: 13.5 Matrices, Vectors: Addition and Scalar Multiplication: 7.1 Matrix Multiplication: 7.2	13.5 # 3,5,7,9,11,13--15 7.1 # 1,5,7,9,12,14 7.2 # 1,2,4,13,20,21
Sept 18 - 22	Linear Systems of Equations. Gauss Elimination: 7.3 Linear Independence. Rank of a Matrix. Vector Space: 7.4 Solutions of Linear Systems: Existence, Uniqueness: 7.5	7.3 # 1,3,5,9,11,15,17,19 7.4 # 1,3,5,7,13,17,19,27,29,31
Sept 25 - 29	Determinants. Cramer's Rule: 7.7 Inverse of a Matrix. Gauss-Jordan Elimination: 7.8 Review	7.7 # 5,7,9,11,15,19,21,23 7.8 # 1,3,5,7,13,17,19
Oct 2 - 6	Basic Concepts. Modeling: 1.1 Geometric Meaning of y'=f(x,y). Direction Fields: 1.2 Exam I	1.1 # 1,3,5,7,9,11,13,15,17,21 1.2 # 1,3,5,7,11,13 October 5
Oct 9 - 13	Separable ODEs. Modeling: 1.3 Exact ODEs. Integrating Factors: 1.4 Linear ODEs. Bernoulli Equation. Population Dynamics: 1.5	1.3 # 3,5,7,9,11,13,15,23,25,27 1.4 # 1,5,7,9,11,13,15,17,21 1.5 # 3,5,7,11,15,19,21,23,25,27
Oct 16 - 20	Homogeneous Linear ODEs of Second Order: 2.1 Homogeneous Linear ODEs with Constant Coefficients: 2.2 Modeling: Free Oscillations (Mass-Spring System): 2.4	2.1 # 1,3,5,7,9,11,13,17,19,21,23 2.2 # 1,3,5,7,9,11,13,15,17,19,21,23,25,31 2.4 # 1,3,5,7,9,11,13,17
Oct 23 - 27	Euler-Cauchy Equations: 2.5 Existence and Uniqueness of Solutions. Wronskian: 2.6 Nonhomogeneous ODEs: 2.7	2.5 # 1,3,5,11 2.6 # 1,3,5,7,9,13,15,17 2.7 # 1,3,5,7,11,13,15,17,19
Oct 30 - Nov 3	Modeling: Forced Oscillations. Resonance: 2.8 Modeling: Electric Circuits: 2.9 Solution by Variation of Parameters: 2.10	2.8 # 1,3,9,11,15,17 2.9 # 1,3,5,7,9,11,13,15,17 2.10 # 1,3,5,7
Nov 6 - 10	Review Exam II	November 9
Nov 13 - 17	Homogeneous Linear ODEs: 3.1 Homogeneous Linear ODEs with Constant Coefficients: 3.2 Nonhomogeneous Linear ODEs: 3.3	3.1 # 1,3,5,7,9,11,13,15,17,19 3.2 # 1,3,5,7,9,11,13,15,17 3.3 # 1,3,5,9
Nov 20 - 24	Basics of Matrices and Vectors: 4.0 Systems of ODEs as Models: 4.1 Happy Thanksgiving !	4.1 # 5,7,11,13,15
Nov 27 - Dec 1	Basic Theory of Systems of ODEs: 4.2 Constant-Coefficient Systems. Phase Plane Method: 4.3 Criteria for Critical Points. Stability: 4.4	4.3 # 1,3,5,7,9,11,13,15 4.4 # 1,3,5,7,9,11,13,15,17
Dec 4 - 8	Qualitative Methods for Nonlinear Systems: 4.5 Nonhomogeneous Linear Systems of ODEs: 4.6 Review	4.5 # 1,3,5,7,9,11,13,15,17 4.6 # 3,5,7,9,11,13,15,17,19
Dec 19	Final!!	8:00-11:00 AM.