School of Mathematics
MA1131:
Advanced Calculus
Solutions to tutorial sheets
- Tutorial Sheet 1 [September 30 - October 1]
- The first tutorial sheet (on graphs
of functions)
is available here in with solutions (in PDF
format).
- Tutorial Sheet 2 [October 7 - 8]
-
Limits (of rational functions), differentiation practice, linear approximation.
- Tutorial Sheet 3 [October 14 - 15]
-
Implicit differentiation;
sign of the derivative; critical points.
- Tutorial Sheet 4 [October 21 - 22]
-
Exponential function; inverse functions; natural
log function; integrating factors (for linear differential equations
with constant coefficients).
- Tutorial Sheet 4 [October 28 - 29]
-
(Derivatives of) inverse trig functions, inverse hyperbolic functions,
arbitary powers. Tangent vectors and tangent lines to parametric curves.
- Tutorial/Exercise Sheet 6 [November 4 - 5]
-
Finding partial derivatives.
(Solutions here.)
- Tutorial Sheet 7 [November 18 - 19]
-
Directional derivatives, tangents to graphs of functions of two
variables, linear approximation, gradient vector.
- Tutorial Sheet 8 [November 25 - 26]
-
The gradient vector (in 3 dimensions).
- Tutorial Sheet 9 [December 9 - 10]
-
Chain rule in 3 variables. Fundfamental theorem. Substitution.
- Tutorial/Exercise Sheet 10 [due Tuesday
December 14]
-
Techniques of integration (in one variable).
(Outline solutions here.)
- Tutorial Sheet 11 [For
December 16-17]
-
Double integrals.
(Solutions here.)
- Assignment Sheet 12 [For
January 17]
-
Triple integrals. Double integrals using polar coordinates.
(Solutions here.)
