Bionics Lab › Education > Classes > MAE 82 - Mathematics of Engineering

# Classes

Instructor

Jacob Rosen
Office: Engineering IV Building, Room 37-146
Voice Office: 831.459.5302
e-mail: jacobrosen@ucla.edu
Anonymous Email (For the Subject Line use: MAE 82A)
Office Hours: Wed 2:00-3:00

MAE 82 Mathematics of Engineering

Course Summary:
Methods of solving ordinary differential equations in engineering. Review of matrix algebra. Solutions of systems of first- and second-order ordinary differential equations. Introduction to Laplace transforms and their application to ordinary differential equations. Introduction to boundary value problems. Nonlinear differential equations and stability

Prerequisite: (Matlab)

Textbooks
TA Office Hours
Syllabus
Book Notes / Problems (11th Edition)
Class Notes
Supplement References

Plan A Load High Content Grading Textbook Pro. - Part 1 & 2 Project Matlab Required: Yes Problem Sets - 20% Projects - 9% Attendance - 5% Exam 1 Mid - 33% Exam 2 Final - 33% Textbook Pro. - Part 1 Project Matlab Required: Yes Problem Sets - 10% Projects - 9% Attendance - 5% Exam 1 Mid - 38% Exam 2 Final - 38% Textbook Pro. - Part 1 & 2 Matlab Required: No Problem Sets - 20% Attendance - 5% Exam 1 Mid - 37.5% Exam 2 Final - 37.5% Textbook Pro. - Part 1 Matlab Required: No Problem Sets - 10% Attendance - 5% Exam 1 Mid - 42.5% Exam 2 Final - 42.5%

Textbooks

Textbook (Required): Elementary Ordinary Differential Equations and Boundary Value Problems”. William E. Boyce & Richard C. DiPrima, 11th Edition,  Wiley 2017
ISBN: 978-1-119-32063-0

Textbook (supplement): Differential Equations with Boundary-Value Problems" Zill et al. 7th / 8th editions, Cengage Learning
ISBN-13: 978-1111827069 ISBN-10: 1111827060

Textbook (supplement): Differential Equations, A Primer for Scientists and Engineers, Christian Constanda

Textbook (supplement): Engineering Diffrential Equations, Theory & Applications, Bill Goodwine - Errata

Textbook (supplement): Differential Equations and Thier Applications, Martin Braun

TA Office Hours

Changyeob Shin (TA)
Office: Engineering IV
Office Hours: Mon 13:00 - 15:00; ENG IV 43-147
E-mail: shinhujune@ucla.edu

Yi-jui Chang (TA)
Office: Engineering IV
Office Hours: Wed 15:00 - 17:00; ENG IV 43-147
E-mail: michaelchang0928@gmail.com

Syllabus

1. First & Second order Linear Differential equations

1.1 Classifications of differential equations, linear/nonlinear, order

1.2 First order Linear Differential equations
1.2.1 Method of integrating factors
1.2.2 Variation of parameters

1.3. First Order non linear Differential Equations
1.3.1 Separable equations
1.3.2 Integrating factor
1.3.3 Change of variables and parametric solutions

1.4 Second order Linear Differential equations
1.4.1 Homogeneous equations with constant coefficients
1.4.2 Characteristic equation, distinct and repeated solutions
1.4.3 Nonhomogeneous equations, method of undetermined coefficients and variation of parameters
1.4.4 Applications to selected engineering problems

2. High order linear equations

2.1 Characteristic equation. Consider distinct and repeated solutions
2.2 Variation of Parameters (Wronskian)
2.3 Undetermined coefficients

[Mid Term Exam]

3. Series solution method

3.1 Power series solution for a linear equation (general n-th order) with constant coefficients
3.2 Introduction to the use of power series when coefficients are not constant
3.3 Series solution near an ordinary point
3.4 Series solution near a regular point
3.5 Error and accuracy of power series solution representation

4. Laplace Transform

4.1 Definition and convergence of Laplace Transform
4.2 Solution to initial value problems
4.3 Linear differential equations with discontinuous forcing term (Dirac delta, step fiunction)

5. Systems of linear equations

5.1 Review of matrices, eigenvalues, eigenfunctions
5.2 Homogeneous and no homogeneous linear systems with constant coefficients
5.3 Discussion on the function e^At
5.4 Systems of higher order Linear Equations and state space representation
5.5 Nonlinear Systems of Differential equations (Equilibrium points)
5.6 Concepts of stability and steady state Solutions
5.7 Special functions, Dirac Delta, Step function

[Final Exam]

6. Numerical Methods

Numerical Methods for first order equations
7.1 Introduce Euler Method
7.2 Runge-Kutta Method
7.3 Multistep Methods
7.4 Errors and stability

Book Notes / Problems (11th Edition)

Week

Assignment
& Pre-Class

Class / Homework
Submission

1a

Book Ch. 1

Class Notes
Class 00 : Course Info.
Class 01 : Introduction.

Post Week Homework - HW1
Part 1
P. 8, Pr. 2
P. 8-9, Pr. 11-16
P. 9, Pr. 20
P. 15, Pr. 3
P. 22, Pr. 1
P. 22, Pr. 7

Part 2
P. 8, Pr. 3
P. 9, Pr. 19
P. 15, Pr. 4
P. 22, Pr. 3
P. 22, Pr. 8

Project 1 (Pendulum)

HW Due Date -
Friday Week 2 (Midnight)
Project Due Date -
Monday Week 3
(Midnight)

(*) Note 1:
Directional Field Example (Matlab)
(*) Note 2:
Vectorfiled2D Matlab Help

HW 1 Solution
Project 1 Solution
Project 1 - Matlab (M-File)

Preclass
None

1b

Book Ch. 2
Sections
2.1-2.4

Pre - Class
Pg. 58 Pr. 26

Class Notes
Class 02 : First Order Diff Eq. - Linear

Preclass

S1

Section Notes

None

2a

Book Ch. 2
Sections
2.5

Pre - Class
Pg. 67 Pr. 2

Class Notes
Class 02 : First Order Diff Eq. - Linear

Post Week Homework - HW2

Part 1

P. 31, Pr. 3
P. 38, Pr. 3
P. 39, Pr. 25
P. 48, Pr. 11
P. 68, Pr. 20
P. 75, Pr. 8

Part 2
P. 31, Pr. 12
P. 38, Pr. 6
P. 39, Pr. 25
P. 48, Pr. 14
P. 75, Pr. 21

Project 2 (Alle Effect)
(*) Note: Problem 3 in the project refers to phase portrait which is similar to draw the direction field and integral curves of N vs t. You may refer section 2.5 Autonomous Equations and Population Dynamics on page 58 to 66 of the textbook. The figures 2.5.3, 2.5.6, and 2.5.8 are good examples.

HW Due Date -
Friday Week 3 (Midnight)
Project Due Date -
Monday Week 4
(Midnight)

HW 2 Solution
Project 2 Solution
Project 2 - Matlab (M-File)

Preclass

2b

Book Ch. 2
Sections
2.6, 2.8

Pre - Class
Pg. 75 Pr. 1

Class Notes
Class 03 : First Order Diff Eq. - Non-Linear.

Preclass

Fri - HW1

S1

Section Notes

3a

Book Ch. 3
Sections
3.1-3.4

Pre - Class
Pg. 131 Pr. 7

Class Notes
Class 04 : Second Order Diff Eq. - Homogeneous

MathLets - POLES AND VIBRATIONS

Post Week Homework - HW3

Part 1

P. 109, Pr. 9 (real roots)
P. 125, Pr. 6 (complex roots)
P. 132, Pr. 2 (identical roots)
P. 141, Pr. 17 (Non Homo)
P. 146, Pr. 11 (Non Homo)
P. 168, Pr. 9
(MKC)

Part 2
P. 109, Pr. 11
P. 125, Pr. 7
P. 132, Pr. 8
P. 141, Pr. 21
P. 168, Pr. 8

Project 3 (Bungee Jumping)

HW Due Date -
Friday Week 4 (Midnight)
Project Due Date -
Monday Week 5
(Midnight)

HW 3 Solution
Project 3 Solution
Project 3 - Matlab (M - File)

Mon - Project 1

Preclass

3b

Book Ch. 3
Sections
3.7

Pre - Class
Pg. 158 Pr. 17

Preclass

Fri - HW2

4a

Book Ch. 3
Sections
3.5-3.6

Pre - Class
Pg. 141 Pr. 1

Post Week Homework - HW4

Part 1

P. 180 Pr. 16
P. 180 Pr. 29 a, b, c
P. 184 Pr. 1
P. 188 Pr. 3

Part 2
P. 180 Pr. 9
P. 184 Pr. 2
P. 188 Pr. 9

Project 4 (Tacoma Nerrows)

HW Due Date -
Friday Week 5 (Midnight)
Project Due Date -
Monday Week 6
(Midnight)

HW 4 Solution
Project 4 Solution
Project 4 - Matlab (M-File)

Mon - Project 2

Preclass

4b

Book Ch. 3
Sections
3.8

Pre - Class
Pg. 167 Pr. 4

Preclass

Fri - HW3

5a

Book Ch. 4
Sections
4.1-4.2

Pre - Class
Pg. 180 Pr. 2

HW 5
Prep for the midterm using practice exam - No Need to submit

P. 31 Pr. 1
P. 75 Pr. 1
P. 167 Pr. 4,5
P. 184 Pr. 12
P. 188 Pr. 3

Project 5 (Beam Buckling)
Problem 1 a-e p. 12
Problem 2 a,b p. 15
Problem 3 a p. 16

HW Due Date - No Need to submit
Project Due Date -
Monday Week 7
(Midnight)

Mon - Project 3

Preclass

5b

Book Ch. 4
Sections
4.3-4.4

Pre - Class
Pg. 184 Pr. 2

Preclass

Fri - HW4

6a

Mon - Project 4

Preclass

6b

Mid Term
Thursday

In Class (Open Book & Open Notes)

7a

Book Ch. 5
Sections
5.1

Series Solution (Zill)

Series Solution (Xie)

Pre - Class
Pg. 195 Pr. 7

Post Week Homework - HW6

Part 1

P. 218 Pr. 3
P. 218 Pr. 13
P. 223 Pr. 10
P. 229 Pr. 10
P. 230 Pr. 12

Part 2
P. 218 Pr. 20
P. 223 Pr. 12
P. 229 Pr. 13

Project 6 - None
HW Due Date -
Friday Week 8 (Midnight)

HW 6 Solution

Preclass

7b

Book Ch. 5
Sections
5.2-5.3

Series Solution (Zill)

Series Solution (Xie)

Pre - Class
Pg. 204 Pr. 2

Preclass

8a

Book Ch. 5
Sections
5.5-5.6

Series Solution (Zill)

Series Solution (Xie)

Pre - Class
Pg. 223 Pr. 1

Mon - Project 5

Preclass

8b

Book Ch. 6
Sections
6.1-6.2

Laplace Transform

Pre - Class
Pg. 255 Pr. 8

Post Week Homework - HW7

Part 1

P. 255 Pr. 6,15,18
P. 263 Pr. 22
P. 268 Pr. 2
P. 269 Pr. 11
P. 273 Pr. 7
P. 274 Pr. 13
P. 279 Pr. 6

Part 2
P. 255 Pr. 19
P. 268 Pr. 6
P. 269 Pr. 12
P. 279 Pr. 9

Project 7 (Bessel)

HW Due Date -
Friday Week 9 (Midnight)
Project Due Date -
Monday Week 10
(Midnight)

HW 7 Solution
Project 7 Solution
Project 7 - Matlab (M-File)

Fri-HW6

Preclass

9a

Book Ch. 6
Sections
6.3-6.4

Laplace Transform

Pre - Class
Pg. 268 Pr. 1

Mon -
Project 7

Preclass

9b

Book Ch. 6
Sections
6.5-6.6

Laplace Transform

Pre - Class
Pg. 273 Pr. 1

Revew at Home - Book Ch. 7.1-7.4

Post Week Homework - HW8

Linear Algebra Review

(Review Only No Need To Submit)
P. 293 Pr. 4 a b c
P. 293 Pr. 5 a b c 6 a b c
P. 294 Pr. 8 a b c d
P. 294 Pr. 14
P. 297 Pr. 17
P. 303 Pr. 4,7,12,19

Project 8 (Mayfair Diner)

HW 8 Solution
Project 8 Solution
Project 8 - Matlab (M-File)

Preclass

Fri- HW7

10a

Book Ch. 7
Sections
7.5-7.8

System of ODE

Pre - Class
Pg. 343 Pr. 1

Post Week Homework - HW9

Part 1 (*)

P. 318 Pr. 11 (Homo - Regular)
P. 328 Pr. 7 (Homo - Complex)
P. 344 Pr. 17 (Homo - Repated)
P. 351 Pr. 2,3,4
(Non Homo)
Note:
Sketck phase portraits for all solutions (See Video)

Part 2 (*)
P. 318 Pr. 12 (Homo - Regular)
P. 328 Pr. 8 (Homo - Complex)
P. 344 Pr. 18 (Homo - Repated)
P. 351 Pr. 1,5,8 (Non Homo
)
(*) Note: Sketck phase portraits for all solutions (See Video)

Project 9 (Arms Races)
Notes (Typos)
1. Q3a - second eq. - dy/dt
2. Q3b - y*=e+fx

Due date - Friday Week 10
HW Due Date -
Friday Week 10 (Midnight)
Project Due Date -
Friday Week 10
(Midnight)

HW 9 Solution
Project 9 Solution
Project 9 - Matlab (M-File)

Mon -
HW8
Project 8

Preclass

10b

Book Ch. 7
Sections
7.9

System of ODE

Pre - Class
Pg. 351 Pr. 1

Preclass

Fri or Mon- HW9
Project 9

Exam 2 - Final

Prep for the Final using
practice Exam - No Need to submit

P. 218 Pr. 4
P. 218 Pr. 6
P. 223 Pr. 6
P. 229 Pr. 5
P. 268 Pr. 6
P. 273 Pr. 3
P. 273 Pr. 6
P. 351 Pr. 1
P. 351 Pr. 4
P. 352 Pr. 6
P. 352 Pr. 8

Class Notes

Post Class Slides (Annotated)

Class 00
: Course Info.
Class 01 : Introduction.
Class 02 : First Order Diff Eq. - Linear
Class 03 : First Order Diff Eq. - Non-Linear.
Class 04 : Second Order Diff Eq. - Homogeneous
Class 05 : Second Order Diff Eq. - Nonhomogeneous.
Class 06 : Second Order Diff Eq. - Nonhomogeneous - Force Vibration
Class 07 : High Order Diff. Eq. - Homogeneous.
Class 08 : High Order Diff. Eq. - Nonhomogeneous.
Class 09 : Series Soultion - Intro.
Class 10 : Series Soultion - Ordinary Point.
Class 11 : Series Soultion - Regular Singular Point.
Class 12 : Laplace - Intro & Diff Eq.
Class 13 : Laplace - Step Function.
Class 14 : Laplace - Impulse Function.
Class 15 : Laplace - Systems (S- Plane).
Class 15 Appendix : Linear Algebra - Review.
Class 16 : System of First Order Linear Diff. Eq. - Homogeneous.
Class 17 : System of First Order Linear Diff. Eq. - NonHomogeneous.
Class 18 : Numerical Approuch - First Order
Class 19 : Numerical Approuch - System

TA Sessions

TA1 Session 01 , TA2 Session 01
TA1 Session 02 , TA2 Session 02
TA1 Session 03 , TA2 Session 03
TA1 Session 04 , TA2 Session 04
TA1 Session 05 , TA2 Session 05
TA1 Session 06 , TA2 Session 06
TA1 Session 07 , TA2 Session 07
TA1 Session 08 , TA2 Session 08
TA1 Session 09 , TA2 Session 09
TA1 Session 10 , TA2 Session 10

Supplement References

First & Second Order Diff Eq.: ODE 1ODE 2
Laplace (Tables): Laplace Transform
Laplace Transform
Seriers Solution
System of First Order ODE
The Theory of the Rainbow - Ariy' Diff Eq.

Matlab Tutorilas [PDF]

MATLAB Tutorial

MATLAB Books
Free access books for UCLA stdents (on campus or via VPN)
MATLAB Mathematical Analysis, César Pérez López
MATLAB Matrix Algebra, César Pérez López
MATLAB Graphical Programming, César Pérez López
MATLAB Differential Equations, César Pérez López

The Complete MATLAB Course: Beginner to Advanced

1) Create SEASnet account
www.seasnet.ucla.edu > Accounts > Create Account

(After applying through website, you need to visit SEAS help desk for getting account)

2) Remote Connection
www.seasnet.ucla.edu > LABS > Seasnet Terminal Server > Terminal Server (Remote Desktop Connect) > Follow instructions

Intro to Matlab - Matlab Script