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Trig Review

If you have The Mathematics Companion, this relevant material is in sections 1.1.6, and 1.6. The material is covered more comprehensively there then in the videos below at present.

Here is a selection of videos mostly from Kahn Academy that are most appropriate for reviewing key concepts in trigonometry applicable to physics:

The basics: cos, sin and tan. (intro)

The basics: examples

What are radians and why?

Sin and Cos relations

What are hyperbolic functions and why?

 

Need to add double-angle,  various addition rules and more on hyperbolic functions.

 

 

 

 

Integral Calculus Review

If you have The Mathematics Companion, the relevant sections are 1.4, 1.5.4, 1.6.2, and 1.7.

Here is a selection of videos mostly from Kahn Academy that are most appropriate for reviewing key concepts in integral calculus applicable to physics:

The antiderivative and the fundamental theorem of calculus (part 1)

The antiderivative and the fundamental theorem of calculus (part 2)

Integrals of elementary functions: sin, cos and e.

Integration via u-substitution (intro)

Integration via u-substitution (example)

Integration via u-substitution ( example, twice in one problem; really common)

Integration via trig-double angle identities (example)

Integration via trig-sub (intro)

Integration via trig-sub (example)

Integration with trig and hyperbolic functions (examples; mathsaurs)

Integration via trig and u-sub part 1 (also really common)

Integration via trig and u-sub part 2 (also really common)

Integration by parts (intro)

Integration by parts (example)

Differential Calculus Review

If you have The Mathematics Companion, the relevant material is in sections 1.3, 1.5,4. 1.6.2, 1.6.4, and 1.6.7.

Here is a selection of videos from Kahn Academy that are most appropriate for reviewing key concepts in differential calculus applicable to physics:

What are derivatives?

Intuition behind derivatives

Taking Derivatives I

Taking Derivatives II

Chain Rule

Example of the Chain Rule

Even more examples of the Chain Rule

Product Rule

Using derivatives: Minima, and maxima.

Concavity

The antiderivative and the fundamental theorem of calculus (part 1)

The antiderivative and the fundamental theorem of calculus (part 2)