# C A L C U L U S  I I

Bernd Sing

## Good luck in the exam!

All material is also available at MyCavehill eLearning.
Use the forum there to discus the material in this course!

## OVERVIEW

This page will be used to make announcements and provide copies of handouts, lecture notes, problem sheets and their solutions for this course. Files will be supplied in pdf format.

I welcome feedback in the form of constructive comments or criticism. Just send an email to or talk to me after the lectures. My office hours are directly after the lectures on Mondays and Tuesdays.

Information handout

### LECTURE NOTES

Lecture notes are available at MyCavehill eLearning.

Note: Lecture notes are not a textbook! There might be misprints as well as mathematical errors (please do notify me, preferrably by email, if you spot an error, even if it is only a minor misprint).

### EXERCISE SHEETS

Exercise sheet 10 with solutions (without solutions)

Exercise sheet 10 with solutions (without solutions)

Exercise sheet 9 with solutions (without solutions)

Exercise sheet 8 with solutions (without solutions)

Exercise sheet 7 with solutions (without solutions)

Exercise sheet 6 with solutions (without solutions)

Exercise sheet 5 with solutions (without solutions)

Exercise sheet 4 with solutions (without solutions)

Exercise sheet 3 with solutions (without solutions)

Exercise sheet 2 with solutions (without solutions)

Exercise sheet 1 with solutions (without solutions)

### SELF-ASSESSMENT SHEETS

Self-assessment sheet 4

Self-assessment sheet 3

Self-assessment sheet 2

Self-assessment sheet 1

### CLASS TESTS

Second class test (including sketch of solutions)

First class test (including sketch of solutions)

Applet "Spherical Coordinates": explore spherical coordinates.

Applet "Contour diagram Grapher/3D Grapher": plot graphs and level curves of scalar fields.

Applet "Motion in 3D": draw parametric curves in 3-space and see their velocity and acceleration vectors

Applet "Derivative at a Point": geometric interpretation of the derivative in single variable calculus

### DIARY

19.4.: line integrals of vector fields; Green's theorem

13.4.: chain rule for vector fields; the nabla-operator (curl, div, grad); line integrals of scalar fields

12.4.: continuity and differentiability of vector fields

6.4.: applications of changes of variables formula; Cauchy-Poisson integral

30.3.: change of variables in multiple integrals

23.3.: classification of stationary points; double integrals

22.3.: level surfaces; (local) maxima/minima/extrema; stationary points

16.3.: gradient & derivative; Clairaut's theorem; level curves & surfaces

15.3.: differentiable scalar fields; directional and partial derivatives; gradient

9.3.: velocity, speed and acceleration in polar coordinates; scalar fields, their graphs and continuity

8.3.: binormal and torsion; polar coordinates

2.3.: velocity, speed and acceleration; unit tangent vector, principal unit normal and curvature

1.3.: arc length

23.2.: continuity and differentiability of vector functions

16.2.: linear functions & matrices; affine functions

15.2.: distance point-plane; linear functions

9.2.: planes and hyperplanes

8.2.: scalar triple product; lines

2.2.: projections; angles; cross product

1.2.: distance; spheres and (open/closed) balls; perpendicular vectors

26.1.: vectors; standard basis vectors; scalar product; norm

25.1.: introduction & overview; the Euclidean space ℝn

© 2010 by Bernd Sing • • last update: 20.04.2010 (04/20/2010)