All lecture content sans the assignment(s) and important announcmenets will be hosted on the lectures Github Page which you can find it here.
Welcome to the lecture materials for use in M.Sc - Higher Mathematics I where our focus will be on the topics of:
- An overview on the types of ordinary differential equations and how to solve them.
- A significant refreshment on the topic of linear algebra and its applications in engineering.
- A look into defining what vector calculus is, its theorems and applications
NOTE: As the lecture is splitted into the tutorial and lectures, for the sake of smooth continuation it is decided to make the lectures in one continuous stream irregardless of whether it is a tutorial or teaching session.
The details of the lecture are given below.
| DESCRIPTION | VALUE |
|---|---|
| Program Name | M.Sc "Automation, Robotics & AI" |
| Module Name | Higher Mathematics I + Tutorials |
| Semester | 1 |
| Room | Lecture Room |
| Assessment(s) | Final Examination (100 %) |
| Lecturer | Daniel McGuiness |
| Software | Python, SageMath |
| Hardware | - |
| SWS Total | 3 |
| Total Units | 45 |
| ECTS | 5 |
| Lecture Type | ILV |
There will be one (1) assignments for this course.
The grade breakdown is as follows:
| DEFINITION | GRADE (%) |
|---|---|
| Final Examination | 100 |
| Sum | 100 |
NOTE: For the exam you will be allowed a calculator without any computational means (i.e., no TI-84, Hp 50g, …). You are also not allowed a personal cheat sheet as all important equations and information will be given to you with the exam.
As it currently is, the lecture covers topic from ordinary differential equations, linear algebra and vector calculis. The structure of the lecture is shown below.
| ORDER | TOPIC | DESCRIPTION | SESSION |
|---|---|---|---|
| 1 | Introduction | Discussion of the lecture structure and what will be covered | 1 |
| 2 | First-Order ODEs | Separable ODEs, Exact ODEs, Linear ODEs | 1-2 |
| 3 | Second-Order Linear ODEs | Homogeneous Linear ODEs, Euler-Cauchy Equations | 3-4 |
| 4 | Higher-Order Linear ODEs | Homogeneous and non-homogeneous Linear ODEs | 5-6 |
| 5 | Systems of ODEs. Phase Plane. Qualitative Methods | Constant-Coefficient Systems, Phase Plane Method | 7-8 |
| 6 | Series Solutions of ODEs & Special Functions | Legendre’s Equation, Legendre Polynomials | 8 |
| 7 | Laplace Transforms | Laplace Transform, Linearity, First Shifting Theorem | 9-10 |
| 8 | Linear Algebra I: Matrices and Vectors | Linear Systems of Equations, Gauss Elimination | 11-12 |
| 9 | Linear Algebra II: Eigenvalue Problems | Determining Eigenvalues and Eigenvectors | 13-14 |
| 10 | Vector Calculus I: Grad, Div, Curl | Vector and Scalar Functions and Their Fields | 14-15 |
| 11 | Vector Calculus II: Curvilinear Coordinates | Spherical and Cylindrical Coordinate Systems | 16-17 |
| 12 | Vector Calculus III: Integral Theorems | Stokes Theorem, Divergence and Green's Theorem | 17-18 |
The Code supplement is a Github webpage dedicated to hosting all the relevant code used in the lecture as it is not feasible to fit all the content of the code to the slides and it is easier to share this way.
Visit the Code Supplement Website
The following materials are recommend reading for the coure but by no means are they mandatory.
| TITLE | AUTHOR | PUBLISHER |
|---|---|---|
| Thomas Calculus (12th Edition) | George B. Thomas, | Pearson (2009) |
| Div, Grad, Curl, and All That: An Informal Text on Vector Calculus (4th Edition) | H. M. Schey | W. W. Norton & Company 2004 |
| Advanced Engineering Mathematics (10th Edition) | E. Kreyszig | Wiley (2011) |
| Linear Algebra and Its Applications (5th Edition) | D. Lay, et. al | Pearson (2015) |
| Mathematical Methods for Physics and Engineering: A Comprehensive Guide (3rd Edition) | K. F. Riley, et. al | Cambridge (2006) |
| Calculus: A Complete Course (5th Edition) | R. A. Adams | Wesley (2003) |
–DTMc