Virgielcollege Mede mogelijk gemaakt door uw Eerstejaarsch Commissie.

Virgielcollege

Mede mogelijk gemaakt door uw Eerstejaarsch Commissie

Hoe ziet vandaag eruit?

Studeerkunde – 10 min

Analyse – 35 min

Pauze – 15 min

Analyse – 20 min

Tentamenvragen – 25 min

Studeerkunde

Hoe studeer je?

Studeerkunde Analyse Tentamen

Studeerkunde

Discipline- Op tijd opstaan- ‘Combineer’ discipline, geen geheelonthouding- Gewoon doen!

Plannen- Stel haalbare doelen- Schets mogelijke scenario’s- Leg duidelijke prioriteiten wanneer dat nodig is- Plan in dagdelen (‘s morgens, ‘s middags, ‘s

avonds)- Plan resultaatgericht


Studeerkunde

Makkelijk punten scoren- Prioriteit bij projecten

- Beter 2 zessen dan 3 vijven

- Makkelijk vakken doen

- Let op vervolgvakken

Verder- Thuis of UB, wat werkt voor jou het beste?

- Regelmaat, afleiding (toko eten etc.)


Studeerkunde

?

!!!


Analyse 1

Calculus Differentiation Integration

- Trigonometry

- Logarithms

- Complexe Numbers

- Vectors

- Limits

- Differentials

- Productrule

- Chain Rule

- Impliciet Differentiëren

- Differential Equations

- Integrals

- Substitution

- Integration by Parts


Calculus

Appendix D: TrigonometryAppendix H: Complex numbers

H12: Vectors and the geometry of spaceH2: Limits and derivatives

APPENDIX DTrigonometry

Calculus Differentiëren Integreren

b

a

c

sin( )

cos( )

tan( )

b

ca

cb

a

What exactly is a cosine or sine?



1

1

2

45o

60o

30o

2

1

3

180o rad

APPENDIX HComplex numbers


2 1i

Complex numbers are ‘imaginary’, but very useful in engineering situations. Especially Euler’s formula.

( ) cos( ) sin( )ixe x i x

CHAPTER 12Vectors and the geometry of space


A vector is a point in space, and can be used to visualize a mathematical problem.



Important formulas concerning vectors

Length of a vector

Angle between two vectors

Volume determined by three vectors



Parametric equations of a line

Parametric equations of a function

Differentiëren

H3, H4, H9

Differentials


1

01

( )'n n

cdxxdxx nx

cos( )' sin( )sin( )' cos( )

x xe dx ex xx x

1( )'

( ( ))' ( ( ))'

( ) ( ) ' ( )' ( )'

n nx nx

c f x c f x

f x g x f x g x

Power Rule

Constant Multiple Rule

Sum Rule

‘Core Analysis Business’, very important for engineering purposes. Lot of different notations.

Product- & Quotiëntregel


Chain Rule


If g is differentiable at x and f is differentiable at g(x), then the composite function F= f o g defined by F(x) = f(g(x)) is differentiable at x and F’ is given by the product:

Implicit Differentiation


Occurs when functions are defined implicitly by a relation between x and y such as:

2 2

3 3

256

x yx y xy

For example, differentiate with respect to x,2 2 25x y

Implicit Differentiation


!!!

Because y is a function of x, apply chain rule:

Integration

H5, H7

Integrals


11

1n n ncx dx c x dx c x

n

( ) ( ) ( ) ( )bb

a a

f x dx F x F b F a

( ) ( ) ( ) ( )f x g x dx f x dx g x dx

1ln( )

x xe dx e

x dxx

The Fundamental Theorem of Calculus states that if:

( ) '( ) ( )f x dx means F x f x

Integrals


There are two important techniques for integrals:

- Integration by parts

- Substitution Rule

( ( )) '( ) ( )f g x g x dx f u du

( ) '( ) ( ) ( ) ( ) '( )f x g x dx f x g x g x f x dx

Mind the Chain Rule!

Tentamen

WTB & MT, Januari 2008


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Virgielcollege Mede mogelijk gemaakt door uw Eerstejaarsch Commissie.

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