MA1132: Advanced Calculus
Solutions to tutorial sheets
These solutions need a PDF reader to view them.
- Tutorial Sheet 1 [January 18-19]
- $\varepsilon$-$N$ definition of a limit of a sequence, use of theorem on limits of sumps, products and quotients.
- Tutorial Sheet 2 [January 25-26]
- Limits of sequence related to limits of functions and continuity. Introduction to series.
- Tutorial Sheet 3 [February 1-2]
- Series - convergence tests.
- Tutorial Sheet 4 [February 8-9]
- Power series (radius of convergence and differentiation term-by-term). Integrating factor method for solving first order linear differential equations (constant coefficients case).
- Tutorial Sheet 5 [February 15-16]
- Tangents to curves in space. Partial derivatives (for functions of 2 variabes).
- Tutorial Sheet 6 [February 22-23]
- Directional derivatives; tangent lines and planes to graphs of functions of two variables; linear approximation formula (2 variables version).
- Tutorial Sheet 7 [March 7-8]
- Gradient vector; chain rule.
- Tutorial Sheet 8 [March 14-15]
- Partial derivatives, gradients in 3 dimensions. Tangent planes to level surfaces.
- Tutorial Sheet 9 [March 21-22]
- Double integrals.
- Tutorial Sheet 10 [March 28-29]
- Triple integrals.
- Tutorial Sheet 11 [April 4-5]
- Change of variables in double and triple integrals.