Learning Outcomes:
Students are expected to achieve the following competence:
• Find limits,continuity, total differential of multi-variable functions
• 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;
• Computing double integrals in right coordinates, especially iterated integrals;
• Computing double integrals in polar coordinates;
• Computing triple integrals in right coordinates;
• Computing triple integrals in cylindrical and spherical coordinates.
Indicative Module Content:
week 9 Partial derivatives of composite functions and implicit functions.
week 10 Tangent lines of curves and tangent planes of surfaces in space.
week 11 Gradients and directional derivatives.
week 12 Lagrangian multiplier method, double integrals in Right coordinates.
week 13 Double integrals in polar coordinates, triple integrals in Right coordinates.
week 14 Triple integrals in Right, cylindrical and spherical coordinates.
week 15 Revision.