An introduction to the calculus of functions of two variables, and vector valued functions. The topics include: Vectors; Multivariate Calculus; Optimization of elementary multivariate functions; Integration of elementary multivariate functions over polygons.
Learning Outcomes 1. Apply vectors to describe lines and planes in 3-d; 2. Solve 3-d geometric problems using vectors; 3. Compute partial derivatives of chains of elementary multivariate functions; 4. Interpret gradient and tangent planes graphically; 5. Classify extreme values of elementary multivariate functions; 6. Solve a range of optimization problems modelled by multivariate functions; 7. Compute iterated integrals of multivariate functions over polygons; 8. Solve problems related to computing volumes in 3-d.