ERTH/OCN 312: Advanced Mathematics for
Scientists and Engineers I
Instructor: Garrett
Apuzen-Ito (gito@hawaii.edu, POST 810), Office hrs 10:30-12:00 Wed.
& Thu. POST 819D
TA: Ally Morris (morr2088@hawaii.edu);
Office hrs Wed & Thu. 2-3:30 pm, MSB 113
Classes:
MWF, 9:30-10:20 POST 733
Textbook (recommended): Advanced Engineering Mathematics 2nd Edition, by Michael. D.
Greenberg
By taking ERTH/OCN
312 students will…
•Gain confidence and skills in solving problems in calculus, vector
calculus, differential equations, and linear algebra
•Develop familiarity with using computer programs (e.g., Matlab) for
solving simple problems, visualization, and applying basic numerical methods
•Gain the mathematical background needed to solve problems in more
advanced coursework leading to careers in Earth Sciences, Ocean Sciences,
Biology, and Engineering
•Improve abilities in learning independently, solving problems
creatively, and communicating math clearly and accurately
Class format. Course material will be
learned by a combination of reading assignments, video lectures, in-class
discussions, weekly problem sets, and studying for three exams. This is a “flipped” class so lectures are
to be viewed online via YouTube PRIOR to
class and homework will be started in class. Be prepared to take a quiz
on video material for each class, which will be done and turned in on paper.
ONLINE LECTURES: Links to the lecture videos
for each class are provided on the syllabus below. Again the lectures must be viewed prior to
class.
WEEKLY PROBLEM SETS: Problem sets are due on Fridays at 9:30 a.m. at the beginning of class. Everything
must be hand-written (why? click here
and here and here),
with the exception of Matlab codes/plots.
Hard-copies of homework are preferred (they are easier for your TA to
grade and a happy grader is a good thing for everyone!); however, neatly
organized e-files using sketching software may be turned in via Laulima. Photo
copies of work done on paper will not be accepted. Only under unusually
extenuating circumstance can a problem set be turned in late; and you must
obtain permission prior to the due date. Unexcused late work will be
charged 10% per late day late up to 50%.
Software: Computer
programming literacy is an important
part of applied math. Some of the class
exercises will provide practice in this.
For these I will teach using Matlab, so you
should download and install, following “How to get Matlab TAH Software”, this
asap. Alternatively, if you know R or
Python, you may use those; although I haven't used those much myself I should
be able to help you.
grading: 20% class participation & quizzes, 40%
problem sets, 40% exams (12% midterm 1, 12% midterm 2, 16% final).
|
Rubric for Grading
Individual Problems |
|||
|
Grade |
Score |
# points per problem |
Evidence of learning |
|
A+ |
100% |
10 |
All work & reasoning
easy to follow & answer is correct |
|
A- |
90% |
9 |
Work & reasoning clear
but 1 or 2 minor mistakes made |
|
B |
85% |
8.5 |
Work/reasoning mostly
correct but missed a minor step; the answer could be correct but not the
steps in getting there are not clear |
|
B- |
80% |
8 |
Work/reasoning mostly
correct but missed an important step |
|
C |
75% |
7.5 |
50%-60% of work/reasoning
is correct; e.g., an incorrect method is executed correctly. |
|
C- |
70% |
7 |
40%-50% of work/reasoning
is correct. Answer is correct but there is little work to show how the answer
was derived. |
|
D |
65% |
6.5 |
~30% of work/reasoning is
correct; or the correct method is identified but not followed |
|
F |
50% |
5 |
The problem or problem set
was attempted. |
|
F minus, minus |
0% |
0 |
Problem was left blank, or
problem set not turned in (DON’T DO THIS) |
Quiz scoring: 5pts for answering all questions+ 5 pts for assessment: 10 pts for getting everything correct, 9 pts
for getting 80% correct, 7.5 pts for answer the questions and getting ~50%
correct.
SUPPORTIVE class
culturE: Our class culture will be a positive learning
environment that is inclusive of age, gender
expression, ethnicity, cultural and socio-economic background, scholastic
abilities, sexual orientation, political viewpoints, spirituality, physical
abilities, or any other that makes people who they are. Classroom interactions will promote respect
for everyone, as well as support and encouragement for learning.
HONOR CODE: You are encouraged to work together on your problem
sets, but all work turned in for grading (including computer programs) must
be yours, and yours alone. There
will be no collaborations during exams.
Cheating or other acts of academic dishonesty will not be tolerated and
is prohibited by the UH
Policy 7.208 Student Conduct Code. Everyone
is responsible for upholding our honor code.
WORKING SYLLABUS
Links to videos are blue underlined & must be viewed prior to the day (M,W,F) noted next to
them
Reading assignments are red in square brackets
Week 1 [read p 1-6, Schaum’s Outlines]
•M8/26: Class Introduction
•W8/28: Elementary functions (39 min): logarithms, exponentials, trigonometric
Check out videos like this to
learn how to do the Matlab plots: Basic
plotting, Making
Matlab scripts (or program files)
***Bring Laptops to Class with Matlab installed and ready to go*** (see
link above for downloading and installing Matlab)
•F8/30: Calculus: Limits and derivatives I (25 min) Quiz
SOLUTIONS
Limits
and derivatives II (23 min) PS0 Due TodayàTurn in copies of video lecture notes for
“Element.
functions” and Limits & derivatives I, II.
Everything
written/sketched in the video should be in your notes
Some helpful
tables:
Trig. functions,
limits, derivatives, and integrals,
Common derivatives and integrals
Week 2
•M 9/2 **** Happy Labor Day
Holiday ******
•W9/4 Calculus: Integrals I (16 min)
Fundamental
theorem of calculus (5 min)
u-substitution: Introduction
(5min),
definition (4min)
Integration by parts: Intro
(4min), example
1 (4m), example
2 (7min)
Trig. Substitution: Part 1
(7 min), Part2 (9 min)
•F9/6 Taylor Series (20 min) Examples of TS (7 minutes)[Greenberg pp. 629-636]
(see example Matlab codes from the video
and class for tips on PS2)
Functions of
Multiple Variables & Partial derivatives (20 min) [pp. 620-624]
PS1 DUE Today
Week
3
•M9/9: Complex
numbers video I (31 min) and video II (first 13 min)
[pp.1108-1113, 1116-1121, 1125-1129] Also review polar coordinates via Google
search and/or Wikipedia.
•W9/11: Taking roots of complex numbers (see Complex
#s video II, last 12 minutes)
•F9/13: Introduction
to Differential Equations (33 min))
Introduction to modeling (9 min) [Ch1,
pp. 1-16]
PS2 Due Today
Ordinary
Differential Equations (ODEs)
Week
4
•M9/16 Linear 1st-order ODEs:
[Ch2.2 pp. 18-31 ]
The homogeneous case (16 min)
Non-homogeneous case: Variation of
parameters (22
min)
•W9/18 Solving homogeneous and
non-homogeneous ODE’s
•F9/20: Linear
first-order ODEs: Applications [Ch2.3
pp. 33-43 ]
Mass on an
inclined plane (i.e., biking down a hill, 20 minutes)
Chemical mixing (10 min)
Radioactive decay(11 min) PS3 Due Today
Week
5
•M9/23 Separable
Equations (29 min) [§ 2.4]
Solving ODE’s as Exact Differentials (28 min) [§ 2.5.1]
•W9/25 Using Integrating
Factors to make Exact Differentials (28 min) [§ 2.5.2]
•F9/27 Numerical Methods [§ 6.1 & 6.2]
Euler’s Method (20 min) PS4 Due Today
Week
6
•M9/30 Euler’s Method: Errors and error analysis
(27 min)
Mid-Point rule
(28 min) [§ 6.3.1]
•W10/2 Runge-Kutta
(26 min) [§ 6.3.2]
•F10/4 Review for Exam PS 5 Due Today
Week 7
•M10/7 Midterm
1 on material for Problem Sets 2-4
Here’s what to study, this page will be provided. Bring 1 piece of
paper with hand-written notes (front & back ok) and no electronic
devices. You’ll have 50 minutes to do
the exam. Here are some study problems.
•W10/9 Higher Order ODEs [§ 3.3]
Summary and Linear Dependence vs Linear
Independence (27 min).
General
solution of the n-order linear ODE (28 min)
Quiz
SOLUTIONS (LI vs LD and Theorem 3.3.3)
•F 10/11 Harmonic
Oscillator, Free Oscillation;
Solution to
Homogeneous Equation: Constant
coefficients (36 min) [§ 3.4]
PS 6 Due Today
Week 8
•M10/14 Application
to Harmonic Oscillator (26 min.) [§ 3.5]
2-minute video of a harmonic
oscillator in the lab
Quiz SOLUTION (constant coeffs)
•W10/15 Higher Order
Homogeneous Equations with Non-Constant
Coeffs (31 min) [§ 3.6]
Quiz SOLUTION (Cauchy-Euler
equations)
•F10/18 Higher Order
Nonhomogeneous ODE’s preliminaries (11 min): [§ 3.7]
Solving the the
non-homogeneous case (22 min) PS7 Due Today
Matrices and Linear Algebra
Week 9
•M10/21 System of Linear Equations [Ch. 8]
Gauss Elimination (36 min)
Matrices & Gauss-Jordan Reduction (39
min)
•W10/23 Introduction to
Linear Algebra (13 min) [§
10.1-10.3]
Matrix
Multiplication (18 min)
Matrix Definitions (11 min)
•F10/25 Determinants
(30 min) [§ 10.4] PS8 Due Today
Week 10
•M10/28 Vector
Space of a Matrix (17 min) [§9.9.2, §10.5.1]
Rank of a Matrix (16
min) [§10.5.1]
Rank, Linear Dependence, and Solution to Ax=c (30 min) [§10.5.2]
Rank: Application to Stoichiometry (11 min) [§10.5.1] Quiz
SOLUTION
•W10/30 Inverse Matrix
(31 min) [§10.6.1] and
Cramer’s Rule (9
min) [§10.6.2]
•F11/1 Basis of a vector (15
min) [§9.9]
Vector
Transformations and Change of Basis (39 min) [§10.7] PS9 Due Today
Week 11:
•M11/4 Eigenvalue Problem [§11.1-11.2]
Geometric description of
eigenvalues and eigenvectors
Solving the Eigenvalue problem (34
min.)
•W11/6 Applications to solving systems of ODEs and
Marcov Processes (21 min)
Eigenvectors
of Symmetric Matrices (7 min.) [§11.3]
•F11/8 Midterm 2 Study Questions PS10 Due Today
Week 12
•M11/11 Veterans
Day Holiday
•W11/13 Midterm 2 on material for Problem
Sets 6-9 (see learning objectives & study problems).
•F11/15 Diagonalization
(35 min) [§11.4]
Week 13
•M11/18 Vectors in 3D space (36 min) [§ 14.1-14.5]
•W11/20 Scalar and Vector Fields (10 min) [§ 16.1-16.2]
Divergence (40
min) [§16.3]
Conceptual
description of divergence Quiz SOLUTIONS
•F11/22 Gradient
(27 min) [§16.4] PS11 Due Today
Week 14
•M11/25 Curl (exercises, 29 min) [§16.5]
Illustrative
video of curl
•W11/27 Combinations
of and with the “del” operator (31 min) [§16.6]
•F11/29 No Class: Happy Thanksgiving
Week 15
•M12/2 Work on PS 12
•W12/4 Final Exam Prep: Final Learning Objectives
•F12/6 Final Exam Prep: Final Learning Objectives
Study Questions
for PS10-12
PS12 Due Today
Week 16:
•Study for the final
