To develop the mathematical skills and knowledge of science and engineering students and students in other numerate disciplines in the area of vector calculus and differentiation equations. The level of the material presented is appropriate for second year students and will be applied in the latter years of their courses.
1. First-Order Differential Equations (1.1 Terminology; First-Order DEs; Separation of Variables; Solution of DEs using Transformations; First-Order Linear DEs, Applications.)
2. Second-Order Differential Equations (2.1 Second-Order Homogeneous DEs with Constant Coefficients; Applications.)
3. Further Second-Order Differential Equations (3.1 Second-Order Inhomogeneous DEs with Constant Coefficients; Applications.)
4. Partial Differentiation (4.1 Review of Differentiation; Partial Differentiation; Higher-Order Partial Derivatives; Directional Derivatives; Chain Rule; Partial Differential Equations.)
5. Maxima and Minima (5.1 Stationary Points; Maxima, Minima and Saddle Points; Applications.)
6. Taylor Series (6.1 Taylor series in 1D; Maclaurin Series; Taylor Series in 2D; Error Analysis.)
7. Multiple Integrals (7.1 Multiple Integrals: Double Integrals over Rectangular Domains and over More General Regions.)
8. Further Multiple Integrals (8.1 Double Integrals using Polar Coordinates; Length of Curves; Surface Area; Mass; Centre of Mass; Applications.)
By the end of the course, students should be able to do the following:
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SCQF Level: 8
Credits: 15