## Homework

All sections refer to Polking text (2nd edition) unless otherwise specified. Problems in **bold** do not appear in the 1st edition.

Maple tutorial from the Connected Curriculum Project at Duke University.

*Basic ODE Theory*

Section 2.1# 9,11,13,21,25 (the Maple commands **dfieldplot** and **DEplot** are useful here)

Section 9.8# 15,17 (just rewrite as a system) (NOTE: Section 9.7 in 1st edition)

Section 2.7# 25-31 odd

Section 2.9# 7,9,13,15,17,21

Section 2.2# 3,5,7,15,17,19

Section 2.4# 3,7,15,19,21,22,23,27,31,33,39

Section 2.3# 11,14

Section 3.1# 7,10,11,20 (#7,9,10,19 in first edition)

Strogatz Section 2.1# 1-3, Section 2.2# 3,7,8-10, Section 2.3# 2

Strogatz Section 3.1# 1, Section 3.2# 1 (transcritical bifurcation),5, Section 3.4# 5,6,12,14,16 (Maple or Matlab is useful for the last problem; note the location of the minima for the potential function.)

Section 6.1# 1 *Optional*: Helpful module on numerical ODEs from the Connected Curriculum Project.

*Basic Linear Algebra*

Section 7.3# 1,3,5 (you may Gaussian eliminate with or without using the matrix formulation) Note: these three problems are not found in the first edition.

Section 7.5# 1,3,5,9,11,13,17,19,21,23

Handout: (second sheet) 1,2,4,10-15 (third sheet) 1-6,9-12

Section 7.5# 25,27,29,33,35,37,39 (corresponds to finding basis of nullspace for #1,3,5 and basis for span of #9,11,13 in 1st edition)

Handout: (second sheet) 16-25,27 (third sheet) 13-17, 23

Section 7.1# 14-22, 27,33, 47-53(odd)

Section 7.6# 13,15,17,21,23,25 (Section 7.4# 8,12,18,20,22 in 1st edition)

Section 7.7# 17,19,23,27,35,37,41,43,51-54 (Section 7.6 in 1st edition)

Handout "Problems in Linear Algebra" #1-5

Section 9.1# 1,3,9,11(for the preceding questions, find eigenvectors also), 14,53,55,56

*Basic Theory of Systems of ODEs*

Section 8.1# 1-9 odd, 21,22,27,28 (#1-9 odd, 25,26,29,30 in first edition)

Section 8.2# 7-11 odd, 18,20,21-25,29 (#7-11 odd, 13-17, 23,25,29 in first edition)

Section 8.3# 3,7

Section 8.4# 11-15 odd (1-5 odd in first edition)

Section 8.5# 1,3,7,9,13,15,17,19,21 (8,10,14,16,20,22,24,26,28 in first edition)

Handout #3-12 (M_n(\R) refers to square nxn matrices with real numbers, and in #10,11 k=\R)

Strogatz 5.1# 4,6,9,13

Section 9.2# 1,3,7,9,**13**,17,19,23,25,28,29,35,57,**58** (#1,3,7,9,17,19,24,26,30,32,36,37,43,65 in 1st edition)

Strogatz 5.2# 1-3,5,7,9

Section 9.4# 1,3,5,13-16,20,21 (Section 9.3#24,26,28,36-39,43,44 in 1st edition)

Section 9.6# 1,2,5-10,11,**13**,14,18,27,29,36 (Section 9.5# 1,2,5-10,11,13,17,26,28,35)

Section 9.7# 2,4,10,13 (Section 9.6 in 1st edition)

Handout "Exercise: Linear Ordinary Differential Equations with Constant Coefficients"

Section 9.8# 14,22,29 (Section 9.7 in 1st edition)

Handout "Method of Undetermined Coefficients"

Section 10.1# 1,3,9,11,17,19,20,21-25(odd)

Section 10.2# 9-15(odd)

Section 10.3# 1-11(odd),13,17,18

Section 10.4# 1,3,5,6,7,9,10,11,12,23,27

Strogatz 6.1# 1-5(odd), 8-14

Strogatz 6.2# 1-2

Strogatz 6.3# 9-13,15-16