Integral Transforms and Their Applications - Mathematical Methods (Undergraduate Advanced)
Integral transforms (Laplace, Fourier, Mellin, Hankel and other transforms ), their inverses and applications to the solutions of ordinary differential equations.
Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
CHE 306: Engineering Analysis IIAdvanced engineering mathematics covering numerical and analytical methods of engineering analysis.
Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
CHE 306: Engineering Analysis II
Advanced engineering mathematics covering numerical and analytical methods of engineering analysis.
Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Advanced engineering mathematics covering numerical and analytical methods of engineering analysis. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
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Course Chapters
1. Introduction
1. Introduction
Welcome and course outline. Review of elementary integral concepts. Motivation for integral transforms.
2. Laplace Transforms (1)
2. Laplace Transforms (1)
Definition and existence of Laplace transforms of real-valued or complex-valued functions.
3. Laplace Transforms (2)
3. Laplace Transforms (2)
General properties of Laplace transforms, including Laplace transforms of derivatives, integrals and convolutions.
4. Laplace Transforms (3)
4. Laplace Transforms (3)
Some elementary Laplace transforms.
5. Inverse Laplace Transforms
5. Inverse Laplace Transforms
Definition and evaluation of inverse Laplace transforms.
6. Applications of Laplace Transforms
6. Applications of Laplace Transforms
Applications of Laplace transforms to the solutions of ordinary differential equations.
7. Mellin Transforms
7. Mellin Transforms
Definition and existence of Mellin transforms and their inverses.
8. Hankel Transforms
8. Hankel Transforms
Definition and existence of Hankel transforms and their inverses.
9. Fourier Transforms (1)
9. Fourier Transforms (1)
An introduction to Fourier series. Definition and existence of Fourier transforms and their inverses.
10. Fourier Transforms (2)
10. Fourier Transforms (2)
General properties of Fourier transforms.