This course is designed to achieve the overall objectives in
the form of learning outcomes that students are expected to acquire after
completing the course, as follows:
Studying the mathematical foundations and concepts of
geophysics and strengthening knowledge of basic mathematical methods and
understanding their application in the field of geophysics.
Studying the foundations and concepts for vector analysis and
algebraic operations of vectors.
Studying partial differential equations; equations in
geophysics: Laplace's equation, wave field equations.
Studying the Fourier series for odd and even functions, the
complex Fourier series, and advanced and inverse Fourier transforms.
Studying the forward and inverse Z-transform.
Intended learning outcomes
By completing this course, it is expected that the student
will be proficient in the following practical and professional skills:
Understanding the concept of analyzing vectors and the
concepts of operations and differential processes, and dealing with them in
different coordinate systems.
Being able to classify and solve a variety of differential
operations.
Familiarize the student with partial differential equations
in geophysics and the foundations and methods of solving them.
Familiarize the student with the Fourier series for
functions and advanced and inverse Fourier transforms.
The ability to use the Fourier series to transition between
time or distance domains and frequency domains.
Teaching and learning methods
The course is taught using the following methods and
techniques:
Lectures
Laboratory activities
Information gathering
Discussion groups
Methods of assessments
First midterm exam: 25% (written).
Second
midterm exam: 25% (written).
Final exam:
50% (written).
Passing grade: 50% or
above.
Overall course grade: 100%
Course
Contents.
The first week covers vector
analysis, algebraic operations for vectors, vector components, and coordinate
systems: rectangular, cylindrical, and spherical coordinates.
The second week uses the theories of
gradient, divergence and winding, delta applications, Laplace’s equation -
Poisson’s equation, and the definition of the potential field.
Week three Ordinary Differential
Equations (ODE); Define, arrange, solve
The fourth week: partial
differential equations; Equations in geophysics: Laplace equation, seismic wave
field equations.
Week 5: Complex functions, polar
form for complex functions, amplitude and phase for complex functions
The sixth week: Fourier series for
odd and even functions, cosine series
The seventh week: forward and
reverse Fourier integrals and transforms, amplitude and phase in the time
domain
The eighth week is the midterm exam
The ninth and tenth weeks: Fourier
transforms of some functions; Dirac delta function, step function, rectangular
function, cosine function, and sine function.
The eleventh and twelfth weeks:
Fourier properties (time interval or distance to the frequency domain) in
calculating deconvolution and aspects between functions
The thirteenth and fourteenth weeks
apply Fourier transforms to the general solution of partial differential
equations; Laplace equations - seismic wave field equations. Non-continuous
Fourier transforms (DFT).
Week 15: Z transform of a discrete-time function (time series), derivation of Z transform, forward and reverse Z
transform, properties of Z transform.
