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