Mathematics for Engineers and Scientists 3 (178)

Online assessment: an introduction to math software which generates individualized assessments and feedback. First-Order Differential Equations: Terminology; First-Order DEs; Separation of Variables; Solution of DEs using Transformations; First-Order Linear DEs, Applications. Second-Order Differential Equations: Second-Order Homogeneous DEs with Constant Coefficients; Applications. Further Second-Order Differential Equations: Second-Order Inhomogeneous DEs with Constant Coefficients; Applications. Partial Differentiation: Review of Differentiation; Partial Differentiation; Higher-Order Partial Derivatives; Directional Derivatives; Chain Rule; Partial Differential Equations. Maxima and Minima: Stationary Points; Maxima, Minima and Saddle Points; Applications. Taylor Series: Taylor series in 1D; Maclaurin Series; Taylor Series in 2D; Error Analysis. Multiple Integrals: Double Integrals over Rectangular Domains and over More General Regions. Further Multiple Integrals: Double Integrals using Polar Coordinates; Length of Curves; Surface Area; Mass; Centre of Mass; Applications