Welcome

You can find instructional videos by clicking on: topics in the table of contents below, the categories to the right, the tags to the right and down, or by searching in the search bar to the right and up.

  •  Multivariable Calculus

◦ 1 – Functions of two variables, surfaces of revolution, level curves

◦ 2 – Partial derivatives, higher order derivatives

◦ 3 – Tangent planes, normals, differentials

◦ 4 – Directional derivatives, gradient vector

◦ 5 – Maxima, minima, extrema

6 – Chain rules, implicit differentiation

  • Sequences and Series

◦ 7 – Combinations, permutations, binomial theorem/expansions, sequences

◦ 8 – Bounded, monotone, convergence, limits, divergence, squeeze theorem, L’Hopital’s

◦ 9 – Series, divergence test, ratio test, absolute convergence, other tests

◦ 10 – Power series, interval/radius of convergence, manipulation of power series

◦ 11 – Taylor and Maclaurin series

◦ 12 – Taylor’s inequality, binomial series

  •  Differential Equations

◦ 1 – Introduction, direction fields, Euler’s method

◦ 2 – Review of single variable calculus, separable Des, autonomous DEs, steady state solutions

◦ 3 – Exact DEs, integrating factors for linear DEs, modelling

◦ 4 – Homogeneous second order linear DEs with constant coefficients

◦ 5/6 – Non-homogeneous/inhomogeneous second order linear DEs with constant coefficients, method of undetermined coefficients

  • Linear Algebra
 

Not the same ordering as in lectures

7/8/9 – Matrices, solving systems of equations, determinants, linear independence/dependence, transformations, eigenvalues, eigenvectors

◦ 10/11/12 – Coupled linear DEs

Learning and Practicing Mathematics via the Internet

The Khan Academy, available at http://www.khanacademy.org/, has over 2600 videos, many of which are mathematics. You can watch videos without logging in, but signing up only requires a Google account or a Facebook account and means your activity is recorded so that points and badges are earned by watching videos.

When each problem in the video is presented you should pause the video and attempt to solve the problem yourself. Once you have had an attempt or two, continue watching the video to see the approach taken by the presenter. At the end of the video you can often click the green ‘Practice this concept’ button above and to the right of the video.

Some of the videos start very basic and progress, some are just basic as an introduction for the next video, but if you can’t understand something in the video, there is help available. You could leave a comment on the post that sent you to the video, leave a comment on the video in the Khan Academy, search YouTube (http://patrickjmt.com/http://rootmath.org/AlRichards314  and Bullcleo1 are all good channels), the Khan Academy or this Maths Support Site for another explanation.

Another amazing collection of material designed to educate the public is MIT OpenCourseWare, go on have a browse. Possibly most useful to you is the

Multivariable calculus notes

Application of calculus java apps

Differential Equations

Linear Algebra

A group that call themselves the world wide centre of mathematics has a good series of long lectures on calculus, you can find their collections here.

There are also some decent textbooks available online

Sections 14-16 are infinite series, representations of functions through power series and differential equations

Multivariable and differential calculus (wikibooks)

Linear algebra (wikibooks)

Multivariable calculus notes (MIT)

Calculus with applications (MIT)

Differential equations (HK University)

Maths for Engineering (more likely to be useful in revising MATH1110)

GAIM 2 – Getting Ahead in Mathematics 2 – MATH1120 University of Newcastle, Australia

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