Virgielcollege Mede mogelijk gemaakt door uw Eerstejaarsch Commissie.

Presentatie over: "Virgielcollege Mede mogelijk gemaakt door uw Eerstejaarsch Commissie."— Transcript van de presentatie:

1 Virgielcollege Mede mogelijk gemaakt door uw Eerstejaarsch Commissie

2 Hoe ziet vandaag eruit? Studeerkunde – 10 min Analyse – 35 min Pauze – 15 min Analyse – 20 min Tentamenvragen – 25 min

3 Studeerkunde Hoe studeer je? Studeerkunde Analyse Tentamen

4 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 Analyse Tentamen

5 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 Tentamen

6 Studeerkunde ? !!! Studeerkunde Analyse Tentamen

7 Analyse 1 CalculusDifferentiationIntegration - Trigonometry - Logarithms - Complexe Numbers - Vectors - Limits - Differentials - Productrule - Chain Rule - Impliciet Differentiëren - Differential Equations - Integrals - Substitution - Integration by Parts Studeerkunde Analyse Tentamen

8 Calculus Appendix D: Trigonometry Appendix H: Complex numbers H12: Vectors and the geometry of space H2: Limits and derivatives

9 APPENDIX D Trigonometry Calculus Differentiëren Integreren b a c What exactly is a cosine or sine?

10 APPENDIX D Trigonometry Calculus Differentiëren Integreren

11 APPENDIX D Trigonometry Calculus Differentiëren Integreren 1 1 45 o 60 o 30 o 2 1

12 APPENDIX H Complex numbers Calculus Differentiëren Integreren Complex numbers are ‘imaginary’, but very useful in engineering situations. Especially Euler’s formula.

13 CHAPTER 12 Vectors and the geometry of space Calculus Differentiëren Integreren A vector is a point in space, and can be used to visualize a mathematical problem.

14 CHAPTER 12 Vectors and the geometry of space Calculus Differentiëren Integreren Important formulas concerning vectors Length of a vector Angle between two vectors Volume determined by three vectors

15 CHAPTER 12 Vectors and the geometry of space Calculus Differentiëren Integreren Parametric equations of a line Parametric equations of a function

16 Differentiëren H3, H4, H9

17 Differentials Calculus Differentiëren Integreren Power Rule Constant Multiple Rule Sum Rule ‘Core Analysis Business’, very important for engineering purposes. Lot of different notations.

18 Product- & Quotiëntregel Calculus Differentiëren Integreren

19 Chain Rule Calculus Differentiëren Integreren 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:

20 Implicit Differentiation Calculus Differentiëren Integreren Occurs when functions are defined implicitly by a relation between x and y such as: For example, differentiate with respect to x,

21 Implicit Differentiation Calculus Differentiëren Integreren !!! Because y is a function of x, apply chain rule:

22 Integration H5, H7

23 Integrals Calculus Differentiëren Integreren The Fundamental Theorem of Calculus states that if:

24 Integrals Calculus Differentiëren Integreren There are two important techniques for integrals: - Integration by parts - Substitution Rule Mind the Chain Rule!

25 Tentamen WTB & MT, Januari 2008 Studeerkunde Analyse Tentamen

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