Department of Mathematics

MA 262

Course page with general information

Book: Differential Equations and Linear Algebra, Third Edition, by Stephen Goode & Scott Annin
Office hours: Monday 4:30-6:00; Thursday 10:30-12:00

Exams

Second Exam: Wednesday March 27 8p - 9p WTHR 104
Topics: Linear Algebra, up to eigenvalues and eigenvectors
Practice problems
Last semester exam and solutions


First Exam: Monday February 11, 8p - 9p, MATH 175
Practice problems
Last semester exam and solutions
The exam and its solutions

Homework list

(due Tuesday April 23 before Recitation): Lectures 39 and 40 Sections problems pages 7.1 1, 3, 7, 9 540 7.4 1, 3, 5, 9, 17, 20, 22 560 7.6 1, 3, 8, 10 576
(due Tuesday April 16 before Recitation): Lectures 37 and 38 Sections problems pages 6.5 3, 4, 5, 16, 17 495, 496 6.9 5, 6, 15, 16 528, 529 7.1 15, 17, 19 541 7.2 1, 3, 7, 8 545 7.3 1, 3, 4 551
(due Tuesday April 9 before Recitation): Lectures 33–35 Sections problems pages 6.3 1, 3, 4, 17, 19, 20, 21, 23, 26, 29, 31 480, 481 6.7 1, 5, 16, 19, 21, 22, 30 512, 513
(due Tuesday April 2nd before Recitation): Lectures 29 and 32 Sections problems pages 6.1 1, 3, 5, 6, 9, 13, 16, 20, 22, 31, 36 458, 459 6.2 5, 12, 14, 17, 19, 26, 28, 30, 32, 33, 35, 39 468, 469
(due Tuesday March 26 before Recitation): Lectures 26 and 28 Sections problems pages 5.3 1, 2, 3, 6, 14, 15, 17 368 5.7 1, 3, 5, 7, 17, 19 406
(due Tuesday March 19 before Recitation): Lectures 24 and 25 Sections problems pages 5.1 1, 4, 9, 10, 13, 16, 17, 23, 29, 30 351–353 5.6 5, 9, 13, 15, 20, 31, 32 398, 399
(due Tuesday March 5 before Recitation): Lectures 22 and 23 Sections problems pages 4.3 13, 14, 16, 17, 20, 21 257 4.4 17, 18, 25, 27, 28 265, 266 4.5 19, 21, 32, 34, 36, 41a 279, 280 4.6 7, 18, 23, 24 291, 292 4.8 3, 4, 8, 12 306, 307
(due Tuesday February 26 before Recitation): Lectures 18–20 Sections problems pages 4.3 18, 19 257 4.4 4, 9, 12, 13, 14, 20 265, 266 4.5 3, 9, 12, 13, 16, 17 279, 280 4.6 1, 4, 6, 11, 12, 17 291, 292
(due Tuesday February 19 before Recitation): Lectures 16 and 17 Sections problems pages 3.3 22, 27, 32, 36, 40, 42, 44 223, 224 3.5 15, 16, 22 232 4.2 16 249 4.3 2, 3, 5, 6, 8 257
(due Tuesday February 12 before Recitation): Lectures 12 and 13 Sections problems pages 3.2 1, 3, 9, 14, 15, 20, 21, 24, 42 209–211 3.3 7, 9, 15, 19, 21a 222, 223
(due Tuesday February 5 before Recitation): Lectures 9–11 Sections problems pages 2.3 2, 3, 9 138 2.4 3, 6, 7, 9, 11, 13, 20, 21 149 2.5 1, 7, 11, 17, 19, 22, 23, 33, 37, 47 159 2.6 1, 3, 9, 12 170
(due Tuesday January 29 before Recitation): Lectures 7 and 8 Sections problems pages 1.11 4, 11, 14, 18 103, 104 1.12 42 108 2.1 1, 3, 7, 13, 19 118 2.2 1, 2, 3, 5, 7 130, 131
(due Tuesday January 22 before recitation): Lectures 4–6 Sections problems pages 1.7 4, 7 65, 66 1.8 25, 26, 37, 38, 56, 57, 61 76–78 1.9 8, 9, 11, 13, 15 89
(due on the Second recitation): Lectures 1–3 Sections problems pages 1.1 6, 13 8, 9 1.2 8, 19, 21, 24 19 1.3 8, 11 30 1.4 3, 15, 23, 24 40, 41 1.5 2 47 1.6 2, 8, 17, 18, 21 55, 56

Extra practice problems

Differential equations Sections problems pages 1.4 22, 27, 28 40, 41 1.5 8, 9–11 48 1.6 27 56 1.7 8, 8 with r1=r2=r3 66

Lecture list / plan

Differential Systems: variation of parameters

Differential Systems: homogeneous systems

Differential Systems: definitions, vector form, general results

Higher-Order linear differential equations, finale: Oscillations


Handout and correction for exam 2


Higher-Order linear differential equations, non-homogeneous: Variation of parameters, undetermined coefficients

Higher-Order linear differential equations, non-homogeneous: Annihilators and variation of parameters

Higher-Order linear differential equations, non-homogeneous: Annihilators

Higher-Order linear differential equations: complex exponentials

Exam 2


Review for exam 2

Higher-Order linear differential equations: characteristic polynomials


Linear Transformations: kernel and range, geometry

Linear Transformations: uses in Differential Equations

Linear Transformations: multiple eigenvectors

Linear Transformations: eigenvectors

Linear Transformations: definitions


Vector Spaces: nullspace, rowspace, column space

Vector Spaces: function spaces, polynomial spaces, matrix spaces


Comments on exam 1


Vector Spaces: bases and dimension

Vector Spaces: span and linear dependency

Vector Spaces: constructing subspaces

Vector Spaces: definitions, subspaces


Determinants: Cramer's rule; Introduction to vector spaces


Exam 1


Review for exam 1


Determinants: Cofactor expansions

Determinants: Introduction and definitions


Matrices: Homogeneous systems; Matrix inversion

Matrices: Gauss-Jordan elimination, rank, (reduced) row-echelon form

Matrices: Systems of equations, elementary operations

Matrices: Introduction, multiplication by substitutions


Analytic techniques for differential equations: some second-order differentials

Analytic techniques for differential equations: exact differentials

Analytic techniques for differential equations: changes of variables

Model Monday: First-order Differential equations

Analytic techniques for differential equations: first-order linear

Analytic techniques for differential equations: separable equations

Introduction to differential equations, first-order differential equations