GG/OCN 312: Advanced Mathematics for
Scientists and Engineers I

__Instructor:__ Garrett Apuzen-Ito (gito@hawaii.edu, POST 810), Office hours: Thu 1-3:30pm __POST 810__

__TA__: Eric Tong (etong@hawaii.edu), Office hrs: Mon. 10:30am-1:00 pm, Wed. noon-3pm,__
MSB 305__

__SOEST Math Tutor__*: Alma Trujillo-Costello (*acast@hawaii.edu), Office hrs: Wed 3-4 pm, Thu 2-3 pm. __MSB 306__

__Classes:__ MWF, 9:30-10:20 POST 723

__Required Textbook:__ *Advanced
Engineering Mathematics *by Michael. D. Greenberg

**By taking GG/OCN 312
students will…**

**•**Become comfortable in
applying mathematical operations commonly used to solve problems in calculus,
vector calculus, and differential equations

**•**Develop familiarity in using
computer programs (e.g., Matlab, FreeMat)
for solving simple problems, visualization, and applying basic numerical
methods

**•**Gain foundational knowledge
needed to solve problems in future coursework leading to careers in Earth
Sciences, Ocean Sciences, Biology, and Engineering

**•**Be able to learn
independently, solve problems creatively, and communicate math clearly and
accurately

**PROGRAMMATIC
STUDENT LEARNING OBJECTIVES:**

GG student learning objectives emphasized:

2. Students can apply technical knowledge of relevant computer applications, laboratory methods, field methods, and the supporting disciplines (math, physics, chemistry, biology) to solve real-world problems in geology and geophysics.

3. Students use the scientific method to define, critically analyze, and solve a problem in earth science.

GES student learning outcomes emphasized:

1. Define and explain the basic principles and concepts of chemistry, physics, biology, calculus, geology, geophysics, meteorology, and oceanography.

2. Apply their understanding of the fundamentals of science and mathematics to the description and quantification of the interactions of the atmosphere, hydrosphere, lithosphere, and biosphere, including humans.

3. Employ the scientific approach to problem solving, and hypothesis formation and testing.

Engineering student learning outcomes emphasized:

**•**An
ability to apply knowledge of mathematics, science, and engineering

**•**An
ability to identify, formulate, and solve engineering problems

**•**An
ability to communicate effectively

**•**A
recognition of the need for and an ability to engage in life-long learning

**Class
format. **Course material
will be learned by a combination of reading assignments, YouTube 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

**ONLINE LECTURES: **Links to the lecture videos
for each data are provided on the syllabus below. Again the lectures must be viewed__ prior to
class__.

**WEEKLY PROBLEM SETS and READING Reading** will reinforce the lectures and will provide formal background to do
the problem sets. __Problem sets are
due on Fridays at 9:30 a.m.____ at the beginning of class__. Only under extraordinary,
incredible, unusually extenuating circumstance can a problem set be turned in
late; and you must obtain permission __prior to the due date__.

**Software: **Computer
programming literacy
is an important part of applied math.
Some of the class exercises will provide practice in this. For these, you will need Matlab,
or a free-ware version such as Freemat or Octave.
Click here for a tutorial on FreeMat and here for a full
list of commands and how to use them.

**grading**: 5% class participation, 45% problem sets, 15% midterm 1, 15% midterm 2, 20% final.

**HONOR
CODE: **Our class
culture will be built upon respectful and honest interaction. 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. Unless
specifically designated, there will be no collaborations during exams. Cheating will not be tolerated, and everyone
is responsible for upholding our honor code.

__ __

** ****WORKING SYLLABUS**

__ __**Links to videos
are blue underlined**

__ ____Reading assignments are red ____in square brackets____ __

Week 1 [*read p 1-6, Schaum’s Outlines*]

**•**M 8/21: Class Introduction

**•**W 8/23: Elementary functions: logarithms, exponentials, trigonometric__ __

**•**F 8/25: Calculus: Limits
and derivatives I PS0,
due 8/25:

Limits and derivatives II Copies
of class notes

for evaluation

See these tables
of functions, limits, derivatives, and integrals

Week 2

**•**M 8/28: Calculus: Integrals I

**•**W 8/30 Example of trig. substitution

**•**F 9/1: Taylor Series [*pp. 629-636*] (see example Matlab script for tips on
PS2) and…

** **Functions of Multiple Variables and Partial
derivatives [*pp. 620-624*]__ __

PS1 due 9/1

Week 3

**•**M 9/4: Happy Labor Day Holiday!

**•**W 9/6: Complex numbers I [*pp.1108-1113, 116-1121, 1125-1129*]__ __

Also, review cylindrical and
spherical coordinates (e.g., pages
from Simmons)

**•**F9/8 Introduction to Differential
Equations [*Ch1, pp. 1-16*] PS2 due 9/8

** **

Week
4

**•**M9/11 Linear 1st-order ODEs: [*Ch2.2
pp. 18-31 ]*

Non-homogeneous case I: Integrating factor
method

**•**W9/13:Non-homogeneous case II: Variation of
parameters

**•**F9/15 Linear first-order ODEs: Applications [*Ch2.3 pp. 33-43 ]* PS3 due
9/15

Week
5

**•**M9/18 Separable Equations [*§
2.4*]

**•**W9/20 Solving ODE’s as Exact Differentials [*§
2.5.1*]

** **Using Integrating Factors to make Exact
Differentials [*§ 2.5.2*]

**•**F9/22 Numerical Methods* *[*§
6.1 & 6.2*] PS4 due 9/22

** **Euler’s Method (20 min)

Euler’s Method: Errors and error analysis

Week
6

**•**M9/25 Mid-Point rule (*§
6.3.1*)

** **

**•**W9/27 Runge-Kutta
(*§ 6.3.2*)

**•**F9/29 Higher Order ODEs [*§ 3.1-3.2*]

** **Summary and Linear Dependence vs
Linear Independence (27 min).

** **Review for Exam PS 5 due 9/29

Week
7

**•M10/2 Midterm 1 on material for Problem Sets 1-4 (midterm 1 study problems)**

**•**W10/4 Higher Order ODEs [*§ 3.3*]

General solution to the initial value
problem (28 min.)

** **Solution to Homogeneous Equation: Constant coefficients (36 min) [*§
3.4*]

**•**F 10/6 Harmonic Oscillator, Free Oscillation;

** **Application to Harmonic Oscillator (26
min.) [*§ 3.5*] PS 6 due 10/6

2-minute video of a harmonic
oscillator in the lab

** **

Week
8

**•**M10/9 Higher Order Homogeneous Equations with Non-Constant Coeffs (31 min) [*§ 3.6*]

**•**W10/11 Higher Order Nonhomogeneous Equations
(43 min): [*§ 3.7*]__ __

**•**F10/13** **Non-damped, Forced Oscillator (33 min)
[*§ 3.8*] PS7 due 10/13

** **

Week
9

**•**M10/16 System of Linear
Equations [*Ch. 8*]__ __

** **Gauss Elimination (36 min)

Matrices & Gauss-Jordan Reduction
(42 min)

**•**W10/18 Matrices & Matrix Arithmetic (42
min) [*§ 10.1-10.3*]

•F10/20 Determinants (30 min) [*§
10.4*]

**No Class: ***Please volunteer
for SOEST Open House** PS8 due 10/20

** **

Week
10

**•**M10/23 Vector Space of a Matrix
(17 min) [*§9.9.2,
§10.5.1*]

** **Rank of a Matrix
(16 min) [*§10.5.1*]

Rank: Application to Stoichiometry (11 min) [*§10.5.1*]

** **Rank, Linear Dependence, and
Solution to *Ax**= c* (30 min) [

**•**W10/25 Inverse Matrix (31 min) [*§10.6.1*] and

** **Cramer’s Rule (9 min) [*§10.6.2*]

**•**F10/27 Basis of a vector (15 min) [*§9.9*]

** **Vector Transformations and Change of Basis (39
min) [*§10.7*] PS9 due 10/27

Week
11:

•M10/30 Eigenvalue
Problem [*§11.1-11.2*]

Solving the Eigenvalue problem (34
min.)

**•**W11/1 Applications
to solving systems of ODEs and Marcov Processes (21
min)

Eigenvectors of Symmetric Matrices (7 min.) [*§11.3*]

**•**F11/3 Midterm 2 Study Questions PS10 due 11/3

** **

Week
12

**•M11/6 Midterm 2 on material for Problem Sets 6-9**

**•**W11/8 Diagonalization [*§11.4*]

**•**F11/10 *No Class:
Veteran’s Day Holiday*

** **

Week
13

**•**M11/13 Vectors in
3D space (36 min) [*§ 14.1-14.5*]

**•**W11/15 Scalar and
Vector Fields (10 min) [*§ 16.1-16.2*]

** **Divergence (40 min) [*§16.3*]

**•**F11/17 Gradient (27 min) [*§16.4*] PS11 due 11/17

** **

Week
14

**•**M11/20 Curl (29 min) [*§16.5*]

**•**W11/22 Combinations of and with the “del” operator
(31 min) [*§16.6*]

**•**F11/24 *No Class: Happy Thanksgiving*

Week
15

**•**M11/27 Non-Cartesian
Coordinates [*§16.7*]

Cylindrical Coordinates I: Definition (9 min)

Cylindrical Coordinates II: Div, grad, curl,
and Laplacian (28 min)

•W11/29 Non-Cartesian Coordinates [*§16.7*]

Spherical Coordinates Definition (7
min)

Divergence theorem [*§ 16.8.1-16.8.2*]: derivation (20 min)

**•**F12/1 Divergence theorem [*§
16.8.1-16.8.2*]: PS12 due 12/1

Application to fluid continuity (17
min)

Application to conservation of heat (18
min)

Week
16:

**•**M12/4 Stokes theorem: Definition
and derivation (21 min) [*§ 16.9.1-16.9.2*]

** **Application to Ampere’s law and
Maxwell’s Equations (14 min)

**•**W12/6 Final Exam Prep PS 13 due Wed 12/6

Study Questions for PS10-11
and 12-13