**The first rule of bootcamp is: You DO talk about bootcamp!**

I know that the start of the semester is busy, but now is the time to consolidate what you learnt last semester if you feel that you are struggling. It will take a good number of hours each week for a couple of weeks, but with effort you can do it. It’s really useful to go through these with other people, but it’s also important to spend some time going through exercises on your own. I suggest finding a balance between the two.

I’m going to list some links below, some of which have explanations, some of which have videos and many of which have exercises. Here’s your task if you choose to accept it:

- Put aside Whatsapp, Facebook, news feeds, anything distracting and make sure that you are in a quiet place – if possible take the material offline so you don’t have to have any internet connection when you are going through these.
- Make sure you have pen and paper ready. Actively writing is infinitely more useful than just thinking about whether you know how to solve a problem
- Choose which topic you are going to focus on and set your timer for an hour
- Read through the topic and take notes for yourself
- Go through as many exercises as you can in the time you’ve given yourself
- After the hour is up, go for a stretch, a walk, a breather for 15 minutes
- Come back and go through any of the questions which you got stuck on and go through another hour’s worth
- Stop
- Come back the next day and look at the questions you struggled with the day before
- Repeat

After you have been through as much of the material as is in the links, send an email to me and tell me how it’s going. Let me know:

- Do you now understand the topic?
- Do you need more questions?
- Do you need more explanation?
- What has been the biggest stumbling block?
- What has been the greatest insight so far?

Note that there will be some questions in here which we haven’t covered and so you will have to figure out if there is something that you are not expected to know. If you are not sure, send me a message and I’ll tell you whether you should be able to do it.

Here are some useful links which I’ve found for the topics which you have asked about:

**Related rates:**

http://tutorial.math.lamar.edu/Classes/CalcI/RelatedRates.aspx

http://fireflylectures.com/Related-Rates-Intro-and-Theory/

http://fireflylectures.com/Related-Rates-Example-Falling-Ladder/

http://fireflylectures.com/Related-Rates-Example-Water-In-Trough/

http://fireflylectures.com/Related-Rates-Example-Fill-Balloon-With-Air/

https://www.khanacademy.org/math/differential-calculus/derivative_applications/rates_of_change/v/rates-of-change-between-radius-and-area-of-circle

**Optimization:**

https://www.coursera.org/learn/calculus1 – check out the section on optimization.

http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx

**Graph sketching:**

fireflylectures.com/Curve-Sketching-Introduction

http://fireflylectures.com/Curve-Sketching-Polynomial-Example/

http://calculus.nipissingu.ca/tutorials/curves.html

https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/graphingdirectory/Graphing.html

**Integration by substitution**

http://tutorial.math.lamar.edu/Classes/CalcI/SubstitutionRuleIndefinite.aspx

http://archives.math.utk.edu/visual.calculus/4/substitutions.1/

http://www.teaching.martahidegkuti.com/shared/lnotes/6_calculus/integral/substitution/substitutionb.pdf

http://17calculus.com/integrals/substitution/

http://www2.bc.cc.ca.us/resperic/math6a/lectures/ch5/4/HW5.4/HW5.4sols.htm

**Integration by parts**

http://archives.math.utk.edu/visual.calculus/4/int_by_parts.1/

http://www.teaching.martahidegkuti.com/shared/lnotes/6_calculus/integral/parts/parts.pdf

http://math.arizona.edu/~calc/Text/Section7.2.pdfhttp://www.math.ucsb.edu/~vtkala/2014/Math3B/Math3B-IntegrationByParts-Solutions.pdf

http://17calculus.com/integrals/integration-by-parts/

**Limits**

http://tutorial.math.lamar.edu/Classes/CalcI/LimitsIntro.aspx

https://www.math.ucdavis.edu/~kouba/ProblemsList.html

http://www.math.ucla.edu/~ronmiech/Actuarial_Review/Limits/Master/Master.html

https://www3.nd.edu/~apilking/Math10560/Calc1Lectures/Lecture%204%20Limit%20Laws.pdf

**Inverse functions**

http://tutorial.math.lamar.edu/Classes/CalcI/InverseFunctions.aspx

**Applications of derivatives**

http://tutorial.math.lamar.edu/Classes/CalcI/DerivAppsIntro.aspx

**Newtonâ€™s method**

http://tutorial.math.lamar.edu/Classes/CalcI/NewtonsMethod.aspx

http://www.millersville.edu/~bikenaga/calculus/newton/newton.html

If there are any other topics which I’ve not listed here which you would like to have more questions on, let me know and I’ll find some suitable ones for you.

**Trig integrals**

http://tutorial.math.lamar.edu/Problems/CalcII/IntegralsWithTrig.aspx

http://tutorial.math.lamar.edu/ProblemsNS/CalcII/IntegralsWithTrig.aspx

http://www.zweigmedia.com/RealWorld/trig/trig4.html

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-27-trig-integrals/

https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/trigintdirectory/TrigInt.html

**Integration by trig substitution**

http://tutorial.math.lamar.edu/Problems/CalcII/TrigSubstitutions.aspx

http://tutorial.math.lamar.edu/ProblemsNS/CalcII/TrigSubstitutions.aspx

http://www.emathhelp.net/notes/calculus-2/integration-techniques/trigonometric-substitutions/

**Integration by partial fractions**

https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/partialfracdirectory/PartialFrac.html

http://tutorial.math.lamar.edu/Problems/CalcII/PartialFractions.aspx

http://tutorial.math.lamar.edu/ProblemsNS/CalcII/PartialFractions.aspx

http://www.dawsoncollege.qc.ca/public/72b18975-8251-444e-8af8-224b7df11fb7/programs/disciplines/math/coursesupplements/supplementary_notes_-_partial_fractions.pdf

http://www.ck12.org/book/CK-12-Calculus/section/7.3/

**Improper integrals**

http://tutorial.math.lamar.edu/Problems/CalcII/ImproperIntegrals.aspx

http://tutorial.math.lamar.edu/ProblemsNS/CalcII/ImproperIntegrals.aspx

http://www.sosmath.com/calculus/improper/convdiv/convdiv.html

http://ocw.mit.edu/courses/mathematics/18-01-single-variable-calculus-fall-2006/video-lectures/lecture-36-improper-integrals/

**The comparison theorem**

http://www.sosmath.com/calculus/improper/testconv/testconv.html

http://modular.math.washington.edu/20b/notes/html/node40.html

http://tutorial.math.lamar.edu/Problems/CalcII/ImproperIntegralsCompTest.aspx

https://en.wikibooks.org/wiki/Calculus/Improper_Integrals

**Proof by Induction**

http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-042j-mathematics-for-computer-science-fall-2010/video-lectures/lecture-2-induction/

http://www.analyzemath.com/math_induction/mathematical_induction.html

http://www.millersville.edu/~bikenaga/math-proof/induction/induction.html

http://people.math.sc.edu/sumner/numbertheory/induction/Induction.html

http://www.math.tamu.edu/~joel.zinn/433sum11/additional-material/induction-practice.pdf

**Proof by Contradiction** – these are somewhat harder to find good examples of

http://www.people.vcu.edu/~rhammack/BookOfProof/Contradict.pdf

http://zimmer.csufresno.edu/~larryc/proofs/proofs.contradict.html

**The Binomial Theorem**

http://www.desertacademy.org/Math/Alei/SLBinomialPractice.pdf

http://web.eecs.utk.edu/~booth/311-04/notes/combinatorics.html

http://www.mathwarehouse.com/algebra/polynomial/binomial-theorem.php

I’ve been told that this is a rather useful video to help understand the binomial theorem if you’ve struggled with the class material. With thanks to Sasha T!

**Complex Numbers**

https://brilliant.org/math/algebra/complex-numbers/

http://www.examsolutions.net/maths-revision/further-maths/complex-numbers/exam-questions/questions.php

http://tutorial.math.lamar.edu/ProblemsNS/Alg/ComplexNumbers.aspx

https://www.examsolutions.net/tutorials/exam-questions-complex-numbers/

http://www.maths.usyd.edu.au/u/UG/JM/MATH1901/Quizzes/quiz2.html

http://home.scarlet.be/math/Pcomplex.htm

**Differential equations**

Separable:

http://tutorial.math.lamar.edu/Classes/DE/Separable.aspx

https://math.dartmouth.edu/~klbooksite/3.03/303.html

First order linear:

http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx

http://mathinsight.org/ordinary_differential_equation_linear_integrating_factor_examples

https://www.khanacademy.org/math/differential-equations/first-order-differential-equations

Second order linear homogeneous with constant coefficients:

http://www.math.psu.edu/tseng/class/Math251/Notes-2nd%20order%20ODE%20pt1.pdf

http://www.intmath.com/differential-equations/7-2nd-order-de-homogeneous.php

**Vectors and Matrices**

https://math.dartmouth.edu/~doyle/docs/finite/fm3/scan/4.pdf

http://tutorial.math.lamar.edu/Classes/DE/LA_Matrix.aspx

https://www.wiziq.com/tutorial/167576-Matrices-And-determinants

https://mathsmartinthomas.files.wordpress.com/2014/12/fp3-matrices-vectors-examwizard.pdf

http://www.cimt.plymouth.ac.uk/projects/mepres/alevel/fpure_ch9.pdf

http://www.explainingmaths.com/vectors-matrices-and-transformations.html

**More video links from Vula announcements**

http://www.centerofmath.org/videos/index.html#subject1

http://tutorial.math.lamar.edu/ProblemsNS/CalcII/TaylorSeries.aspx

https://www.youtube.com/watch?

https://www.youtube.com/watch?

https://www.youtube.com/watch?

Partitions and Ramanujan’s amazing role in understanding them.

Here’s a Khan Academy video on Related Rates.

the limit of x->0 of sin(x)/x is in isiXhosa

Here’s a Khan academy video about the **Mean Value theorem**. I couldn’t find the same video in Xhosa, but I did find a **proof by induction video in Xhosa.**

https://www.youtube.com/user/blackpenredpen/videos

Graham’s Number – an unimaginably large number which is talked about in the Numberphile video here.

Mathemafrica - UCT MAM1000 lecture notes subject linksOctober 4, 2015 at 10:35 am[…] MAM1000 Bootcamp […]