GG/OCN 312: Advanced Mathematics for Scientists and Engineers I
Instructor: Garrett Apuzen-Ito (firstname.lastname@example.org, POST 810), Office hours: Thu 1-3:30pm POST 810
TA: Eric Tong (email@example.com), Office hrs: Mon. 10:30am-1:00 pm, Wed. noon-3pm, MSB 305
SOEST Math Tutor: Alma Trujillo-Costello (firstname.lastname@example.org), 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 outcomesemphasized:
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 homework will be done in class.
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.
Links to videos are blue underlined & should 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]
•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
•M 8/28: Calculus: Integrals I
•W 8/30 Example of trig. substitution
Functions of Multiple Variables and Partial derivatives [pp. 620-624]
PS1 due 9/1
•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)
•M9/11 Linear 1st-order ODEs: [Ch2.2 pp. 18-31 ]
•F9/15 Linear first-order ODEs: Applications [Ch2.3 pp. 33-43 ] PS3 due 9/15
•M9/18 Separable Equations [§ 2.4]
•W9/20 Solving ODE’s as Exact Differentials [§ 2.5.1]
•F9/22 Numerical Methods [§ 6.1 & 6.2] PS4 due 9/22
Euler’s Method (20 min)
•M9/25 Mid-Point rule (§ 6.3.1)
•W9/27 Runge-Kutta (§ 6.3.2)
•F9/29 Higher Order ODEs [§ 3.1-3.2]
Review for Exam PS 5 due 9/29
•M10/2 Midterm 1 on material for Problem Sets 1-4 (midterm 1 study problems)
•W10/4 Higher Order ODEs [§ 3.3]
Solution to Homogeneous Equation: Constant coefficients (36 min) [§ 3.4]
•F 10/6 Harmonic Oscillator, Free Oscillation;
•M10/9 Higher Order Homogeneous Equations with Non-Constant Coeffs (31 min) [§ 3.6]
•W10/11 Higher Order Nonhomogeneous Equations (43 min): [§ 3.7]
•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
•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) [§10.5.2]
•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]
•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]
•M11/6 Midterm 2 on material for Problem Sets 6-9
•W11/8 Diagonalization [§11.4]
•F11/10 No Class: Veteran’s Day Holiday
•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]
•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
•M11/27 Non-Cartesian Coordinates [§16.7]
•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)
•M12/4 Stokes theorem: Definition and derivation (21 min) [§ 16.9.1-16.9.2]
•W12/6 Final Exam Prep PS 13 due Wed 12/6