F18ZF - Mathematics for Data Scientists 6 Further Multivariable Calculus

Course leader(s):

Aims

To develop the mathematical skills and knowledge of science and engineering students and students in other numerate disciplines. The level of the material presented is appropriate for second year students and will be applied in the latter years of their courses.

Syllabus

1. Partial Differentiation (1.1 Review of Differentiation; Partial Differentiation; Higher-Order Partial Derivatives; Directional Derivatives; Chain Rule; Partial Differential Equations.)

2. Maxima and Minima (2.1 Stationary Points; Maxima, Minima and Saddle Points; Applications.)

3. Taylor Series (3.1 Taylor series in 1D; Maclaurin Series; Taylor Series in 2D; Error Analysis.)

4. Multiple Integrals (4.1 Multiple Integrals: Double Integrals over Rectangular Domains and over More General Regions.)

5. Further Multiple Integrals (5.1 Double Integrals using Polar Coordinates; Length of Curves; Surface Area; Mass; Centre of Mass; Applications.)

6. Computer Algebra System (6.1 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:

compute partial derivatives of functions of several variables
use partial derivatives to compute a linear approximation of a function of several variables
use partial derivatives to determine the extrema of functions of two variables
compute double integrals using standard techniques of integration
apply the mathematical concepts from this course to various disciplines in sciences and engineering
interact with computer algebra system by inputting mathematical data in an accurate and precise manner

Further details

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SCQF Level: 8

Credits: 7.5