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Contents

Applied Math for Engineers

These are notes on MATH 305 at UD by Toby Driscoll. All rights reserved.

Schedule for Spring 2021

Linear Algebra

Date	Section	Kapitula	Suggested practice
Feb. 23	Overview	–
Feb. 23	Vectors and matrices	–
Feb. 23	Linear algebraic systems	1.1.1, 1.1.2	1.1.1
Feb. 23	Row elimination	1.1.3
Feb. 23	RREF	1.1.3	1.1.2, 1.1.3, 1.1.5
Mar. 2	Vector algebra	1.2.1
Mar. 2	Matrix-vector algebra	1.2.2	1.2.1, 1.2.2
Mar. 2	Matrix multiplication	1.3	1.3.1
Mar. 2	Identity and inverse	1.4	1.4.1(a,b), 1.4.3
Mar. 9	Singularity	1.10	1.10.1, 1.10.2
Mar. 9	General solutions	1.5	1.5.1, 1.5.3
Mar. 9	Complex numbers	1.11	1.11.1, 1.11.3, 1.11.6
Mar. 9	Eigenvalues	1.12.1, 1.12.2	1.12.2 (a-d), 1.12.3, 1.12.8(a)
Mar. 9	Multiplicity	–

1st-order linear ODE

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
Mar. 16	Overview	–
Mar. 16	Quick tour	–
Mar. 16	Initial-value problems	–
Mar. 16	Operators	2.3		K2.3: 1,2
Mar. 16	Homogeneous solutions	2.4		K2.4: 1,2
Mar. 23	Variation of parameters	2.5.1, 2.5.2		K2.5.1, BD2.1: 39,41
Mar. 23	IVP formula	–		K2.5.2, BD2.1: 15,30
Mar. 23	(optional) Integrating factor	–	2.1
Mar. 23	Undetermined coefficients	2.5.3		K2.5.3
Mar. 30	Modeling	2.6.1	2.3	K2.6.3 (a-c), K2.6.4, BD2.3: 3,16

Steps and impulses

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
Mar. 30	Overview	–
Mar. 30	Unit step	5.1	6.3	K5.1.1, BD6.3: 11,13,15,20,22,33(hard)
Mar. 30	Impulse	5.1	6.5 (skip 2nd order)
Apr. 6	Laplace transform	5.2	6.1	K5.2: 2,3
Apr. 6	Solutions by transform	–

2nd-order linear ODE

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
Apr. 6	Overview	–	–
Apr. 6	Solution structure	–
Apr. 6	Homogeneous solutions	–	3.1,3.4	BD 3.1: 1-6, 9-12; 3.4: 1-2, 11-12, 18
Apr. 13	Complex exponentials	1.11	3.3	BD 3.3: 1-4, 7-9, 17-19
Apr. 13	Pure oscillation	–		BD 3.7: 1-3, 16
Apr. 13	Free oscillations	4.3.2	3.7	BD 3.7: 6, 7, 13, 17
Apr. 13	Undetermined coefficients	4.2.2		K4.2: 1(a-c), 2(a-c); BD 3.5: 1-3, 15-16
Apr. 13	Forced oscillations	4.3.3	3.8	BD 3.8: 5, 9, 10, 12

Laplace transforms

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
Apr. 20	Overview	–
Apr. 20	2nd order ODEs	5.3	6.2	K 5.3: 1(a),2(a), 3(a); 6.2: 1-4, 11-12
Apr. 20	Steps and impulses	5.3	6.3, 6.5	K 5.3: 1(b-c),2(b-c); BD 6.3: 7,11,15,20-21; 6.5: 3(a)-6(a)
Apr. 20	Convolution	5.5	6.6	K 5.5: 1(a-c), 2(a-c), 3(a-b) ; BD 6.6: 13-15

Linear ODE systems

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
Apr. 27	Overview	–	–
Apr. 27	Order & dimension	3.2		K 3.2: 1
Apr. 27	Solution structure	3.4 (part)
Apr. 27	Homogeneous solutions	3.4 (part), 3.5 (part)		K 3.4: 1
Apr. 27	Constant coefficients	3.5 (part), 3.5.4 (part)		K 3.5: 7, 8(a,c), 12, 20
May 4	Phase plane	3.5.1–3.5.5		K 3.5: 1, 2, 6, 14, 15
May 4	Matrix exponential	–
N/A	~~Variation of parameters~~	3.6.1

Nonlinear ODEs

Date	Section	Kapitula	Boyce & DiPrima	Suggested practice
May 4	Overview	–
May 4	Autonomous equations	–
May 11	Separable equations	–
May 11	The logistic equation	–
May 11	Direction fields	–
May 11	Linearization	–

1. Overview