This course covers the mathematical basis necessary for understanding the physical phenomena in Earth and planetary sciences. Especially, the mathematical skills learned in this course is fundamentally required in all geophysics courses in the Department of Earth and Planetary Sciences. Students are expected to understand the basic concepts of fundamental mathematics including vector operations, differential equations, and the Fourier transform, and to learn the mathematical skill necessary for studying Earth and planetary science. After the systematic explanation from the lecturer, students learn mathematical knowledge and skills by solving problems proactively throughout exercises.
By the end of this course, students will learn the mathematical basis required for understanding Earth and planetary sciences including:
1) Vector operations
2) Ordinary and partial differential equations
3) Fourier transform, delta function, and Green’s function
Scalar
Vector
Matrix
Differential equation
Fourier transform
✔ Specialist skills | ✔ Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
In each class, students are given a systematic explanation about the topic of the day during the first half of the class and do exercises during the last half of the class. Although there are no specific assignments, students are required to answer a quiz every class, so please carefully review what you learned in each class.
Course schedule | Required learning | |
---|---|---|
Class 1 | Vector calculus 1 | Vector analysis |
Class 2 | Vector calculus 2 | Vector derivative |
Class 3 | Vector calculus 3 | Integrals of a vector field |
Class 4 | Vector calculus 4 | Integral theorems |
Class 5 | Vector calculus 5 | Curvilinear coordinates and scale factors |
Class 6 | Vector calculus 6 | Vector calculus in curvilinear coordinates |
Class 7 | Vector calculus 7 | Matrices |
Class 8 | Differential equation 1 | 1st order differential equations |
Class 9 | Differential equation 2 | 2nd order differential equations |
Class 10 | Differential equation 3 | Higher order differential equations |
Class 11 | Fourier transform 1 | Fourier series and Fourier transform |
Class 12 | Fourier transform 2 | Delta function, power spectrum, and discrete Fourier transform |
Class 13 | Fourier transform 3 | Differential equation and Fourier transform |
Class 14 | Final exam | Comprehension check |
As the topic of each class bases on those of the previous classes, please review it after each class to prepare for the next class.
This course does not base on any specific textbook.
A summary note is provided at each class.
Students' scores bases on quizzes in every class and the final exam.
No prerequisites.
Junichi Nakajima （nakajima[at]geo.titech.ac.jp)
Walk-in visits might be OK, but it is preferred to make an appointment by e-mail in advance.