F18ZG - Mathematics for Data Scientists 7 Vector Geometry, Calculus and Integral Transforms

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Syllabus

1. Analytic Geometry (1.1 Vector Algebra, Scalar and Vector Products, Lines and Planes, Derivatives of Scalar and Vector Functions, Directional Derivatives, Linear Approximation of Curves, Tangent Planes, Grad, Div, Curl.)

2. Laplace Transforms (2.1 Laplace Transforms, Inverse Laplace Transforms, Solving Differential Equations DEs and Systems of DEs with Laplace Transforms.)

3. Fourier series and Fourier transforms (3.1 Fourier Series, Fourier Transforms, Inverse Fourier Transforms, Properties.)

4. Computer Algebra System (4.1 Accurately and precisely input mathematical syntax into a computer algebra system)

Learning outcomes

By the end of the course, students should be able to do the following:

• describe lines and planes in three-dimensional space using basic tools from vector geometry
• apply vector calculus techniques to calculate quantities related to scalar and vector functions of one or more variables
• calculate Fourier series, Fourier transforms, Laplace and inverse Laplace transforms and use them to solve systems of ordinary differential equation
• employ a suitable computer algebra system to illustrate some of the mathematical concepts and results in this course

Further details

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SCQF Level: 8

Credits: 7.5