## 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