Learning Outcomes:
Students are expected to achieve the following competence:
• Computing dot and cross products of vectors;
• Finding equations of tangent lines of curves and tangent planes of surfaces;
• Understanding the geometric meaning of partial derivatives;
• Computing (higher) partial derivatives;
• Computing total differentials;
• Finding gradients of multi-variable functions;
• Using gradients to find greatest increasing and decreasing directions of multi-variable function.
• Optimizing a function under constraints in terms of the method of Lagrangian multiplier.
Indicative Module Content:
Teaching Plan
Week 1 Review of vectors and geometry in space.
Week 2 Tangent lines and normal planes of curves, tangent planes and normal lines of surfaces.
Week 3 Multi-variable functions, limits and continuity.
Week 4 Partial derivatives, higher order partial derivatives.
Week 5 Total differentials, with applications in approximate computations; partial derivatives of composite functions and implicit functions.
Week 6 Tangent lines of curves and tangent planes of surfaces in space.
Week 7 Gradients and directional derivatives, and the Lagrangian multiplier method.
Week 8 Revision and final exam.
* Tutorials will be held every week from Week 2.