GG/OCN 312: Geomathematics
Instructor: Garrett Apuzen-Ito (gito@hawaii.edu, POST
810)
T.A.:
Elise Rumf (rumpf@higp.hawaii.edu)
Prerequisites: MATH 242 or consent
Required Textbook: Advanced Engineering
Mathematics by Michael. D. Greenberg
Overview
and Objectives:
The
main objective of this class is to familiarize students with a number of
mathematical concepts that are used heavily in science and engineering. Through a combination of lectures and lots of
practice during homework assignments you will develop the knowledge and
proficiency in using a variety of mathematical tools needed for future
coursework and careers in Earth Sciences, Ocean Sciences, and Engineering.
Class
format
The class meets
9:30 am – 10:20 pm, MWF, POST 703. The
lectures will introduce concepts and present methods needed to do the homework
sets.
RECITATION SESSIONS Recitation sessions are 1 hr on Wed. 11:30, 1:30, & 4:30 and
Thu 4:30 to answer questions
about lecture and/or homework. These
sessions are not required but highly recommended as most of you will find them
very helpful in for doing the homework.
grading
40% homework, 15% midterm 1, 15% midterm 2, 30% final.
READING
You will have
reading and homework assignments each week.
Reading will be reinforced by lectures and will provide formal
background to do the problem sets.
“In high school mathematics courses most students are accustomed to
tackling their homework problems first, out of impatience to have the whole
burdensome task over and done with as soon as possible. These students read the explanations in the
text only as a last resort, if at all.
This is a grotesque reversal of reasonable procedure, and makes about as
much sense as trying to put on one’s shoes before one’s socks. I suggest that students should read the text
first, and when this has been thoroughly assimilated, then and only then
turn to the homework problems. After
all, the purpose of these problems is to nail down the ideas and methods
described and illustrated in text” – George F. Simmons, Calculus with Analytic Geometry
HOMEWORK
Homework
is due on Fridays at 3:30 p.m. at the instructor’s office (POST 810). If it’s not in by 3:30 it doesn’t count. Only under extenuating circumstances can homework
be turned in late and only if permission is obtained from Prof. Ito prior to
the due date.
WORKING SYLLABUS
Reading assignments are in brackets
Week 1: Aug. 20-24 [read
p 1-6, Schaum’s Outlines]
·
Class
Introduction
·
Elementary
functions: logarithms, exponentials,
trigonometric
·
Calculus: derivatives
Week 2: Aug 27-Aug 31
·
Calculus:
integrals
·
Taylor Series [pp. 629-636]
·
Functions of
Multiple Variables and Partial derivatives [pp.
613-624]
·
Complex numbers
and complex plain [pp.1108-1113,
116-1121, 1125-1129 ]
HW1
due 8/31
Week 3:
Sept. 5-7 (no class Sept 3)
·
Coordinate
Systems [read Hass
et al Handout: focus on definition of cylindrical & spherical coords]
·
Introduction
to ODEs and First-order ODEs [Ch 1, § 2.1-2.2]
HW2 due 9/7
Week 4:
Sept 10-14
·
Linear
first-order ODEs [§ 2.2-2.3]
·
Separable
Equations [§ 2.4]
·
Exact
Equations and Integrating Factors [§ 2.5]
HW3 due
9/14
Week 5:
Sept 17-21
·
Numerical
Methods [Ch. 6] (Euler’s method)
·
Numerical
Methods [Ch. 6] (Mid-Point rule, Runge-Kutta) HW4 due 9/21
Week 6:
Sept 24-28
·
Second-order
ODEs [§ 3.1-3.3]
Wed Sept 26: Midterm 1 on material for weeks 1-4 HW
5 due 9/28
Week 7:
Oct 1-5
·
Solution
to Homogeneous Equation: Constant
coefficients [§ 3.4]
·
Application
to Harmonic Oscillator [§ 3.5]
·
Solution
to Homogeneous Equation: Nonconstant coeffs [§ 3.6]; HW
6 due 10/5
Week 8: Oct 8-12
·
Solution
to Nonhomogeneous Equation: [§ 3.7]
·
Harmonic
Oscillator: Forced Oscillation [§ 3.8]
·
System
of Linear Equations [Ch. 8] HW7
due 10/12
Week 9:
Oct 15-19
·
Matrices,
Matrix Algebra, and Determinants [§.
10.1-10.4]
·
Rank,
Linear Dependence, and Solution to Ax=c [§10.5]
·
Inverse
Matrix and Cramer’s Rule [§10.6] HW8
due 10/19
Week
10: Oct 22-26
·
Linear
Transformations, Change of Basis, Orthogonal Matrices [§10.7]
·
Eigenvalue
Problem [§11.1-11.2]
·
Prep
for Exam HW9
due 10/26
Week 11:
Oct 29-2
·
Eigenvalue
Problem [§11.1-11.2]
Wed Oct
31: Midterm 2 on material for HW6-9
·
Symmetric
Matrices [§11.3] No
HW due this week
Week 12:
Nov 5-9
·
Diagonalization [§11.4]
·
Vectors
in 3D space [§ 14.1-14.5]
·
Divergence
[§ 16.1-16.3] HW10
due 11/9
Week 13:
Nov 12-16
·
Gradient
and Curl [§16.4-16.5]
·
Combinations
of Grad operator [§16.6]
·
Non-Cartesian
Coordinates [§16.7] HW11
due 11/16
Week
14: Nov. 19-21 (no class Fri Nov 23)
·
Double
and triple integrals [§ 15.3] No
HW due this week
·
Divergence
theorem [§ 16.8.1-16.8.2]
Week
15: Nov 26-30
·
Stokes
theorem [§ 16.9.1-16.9.2]
·
Fourier
Series of a periodic function [§17.1-17.2] HW12 due 11/30
Week
16: Dec 3-5
·
Fourier
Series of a periodic function [§17.3]
·
Final
Exam Prep HW
13 due 12/5