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Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Advanced Calculus
Verfügbare Sprachen: 
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Kursinhalt
Differentiëren, afgeleide functies en
Taylor benaderingen
Taylor approximations
ÃœBUNG
Ã
1.
Taylorontwikkeling *
1
THEORIE
T
2.
Taylor veeltermen *
THEORIE
T
3.
Taylorreeksbenaderingen in Scipy (Python opdracht) *
THEORIE
T
4.
Taylor veeltermen *
THEORIE
T
5.
Taylorbenadering van de sinus *
THEORIE
T
6.
Gelijkvormigheid van driehoeken *
Steven LinAlg
ÃœBUNG
Ã
1.
Steven LinAlgLinEqsAndMats
8
ÃœBUNG
Ã
2.
Steven LinAlgLinIndep
11
ÃœBUNG
Ã
3.
Steven LinAlgMats
2
ÃœBUNG
Ã
4.
Steven LinaAlgSubspaces
12
ÃœBUNG
Ã
5.
Steven LinAlgEigen
6
ÃœBUNG
Ã
6.
Steven LinAlgLeastSquares
8
DemoArjeh *
ÃœBUNG
Ã
1.
DemoArjehInstantFeedback *
5
ÃœBUNG
Ã
2.
DemoArjehGame *
3
ÃœBUNG
Ã
3.
Demo
22
ÃœBUNG
Ã
4.
DemoArjehTheorieOndersteuning *
5
Multivariate functions
Introduction
THEORIE
T
1.
About the contents
Basic concepts of multivariate functions
THEORIE
T
1.
Functions of two variables
ÃœBUNG
Ã
2.
Functions of two variables
8
THEORIE
T
3.
Functions and relations
ÃœBUNG
Ã
4.
Functions and relations
6
THEORIE
T
5.
Visualizing bivariate functions
ÃœBUNG
Ã
6.
Visualizing bivariate functions
5
THEORIE
T
7.
Multivariate functions
ÃœBUNG
Ã
8.
Multivariate functions
6
Partial derivatives
THEORIE
T
1.
Partial derivatives of the first order
ÃœBUNG
Ã
2.
Partial derivatives of the first order
6
THEORIE
T
3.
Chain rules for partial differentiation
ÃœBUNG
Ã
4.
Chain rules for partial differentiation
6
THEORIE
T
5.
Higher partial derivatives
ÃœBUNG
Ã
6.
Higher partial derivatives
10
Stationary points
THEORIE
T
1.
Stationary points
ÃœBUNG
Ã
2.
Stationary points
10
THEORIE
T
3.
Minimum, maximum, and saddle point
ÃœBUNG
Ã
4.
Minimum, maximum, and saddle point
10
THEORIE
T
5.
Criteria for extrema and saddle points
ÃœBUNG
Ã
6.
Criteria for extrema and saddle points
10
End
THEORIE
T
1.
Conclusion
Differential equations
Introduction to Differential equations
THEORIE
T
1.
The notion of differential equation
ÃœBUNG
Ã
2.
The notion of differential equation
6
THEORIE
T
3.
Notation for ODEs
ÃœBUNG
Ã
4.
Notation for ODEs
4
THEORIE
T
5.
Order and degree of an ODE
ÃœBUNG
Ã
6.
Order and degree of an ODE
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Solutions of differential equations
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Solutions of differential equations
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Linear ODEs
ÃœBUNG
Ã
10.
Linear ODEs
Kompletten Zugriff freischalten locked
Direction field
THEORIE
T
1.
Direction fields
ÃœBUNG
Ã
2.
Direction fields
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Euler's method
ÃœBUNG
Ã
4.
Euler's method
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Autonomous ODEs
ÃœBUNG
Ã
6.
Autonomous ODEs
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Existence and uniqueness of solutions of ODEs
ÃœBUNG
Ã
8.
Existence and uniqueness of solutions of ODEs
Kompletten Zugriff freischalten locked
THEORIE
T
9.
Solution strategy on the basis of the slope field
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
10.
Solution strategy on the basis of the slope field
Kompletten Zugriff freischalten locked
Separation of variables
THEORIE
T
1.
Differentials
ÃœBUNG
Ã
2.
Differentials
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Differential forms and separated variables
ÃœBUNG
Ã
4.
Differential forms and separated variables
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Solving ODEs by separation of variables
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Solving ODEs by separation of variables
Kompletten Zugriff freischalten locked
Linear first-order differential equations
THEORIE
T
1.
Uniqueness of solutions of linear first-order ODEs
ÃœBUNG
Ã
2.
Uniqueness of solutions of linear first-order ODEs
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Linear first-order ODE and integrating factor
ÃœBUNG
Ã
4.
Linear first-order ODE and integrating factor
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Solving linear first-order ODEs
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Solving linear first-order ODEs
Kompletten Zugriff freischalten locked
Linear second-order differential equations
THEORIE
T
1.
Uniqueness of solutions of linear 2nd-order ODEs
ÃœBUNG
Ã
2.
Uniqueness of solutions of linear 2nd-order ODEs
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Homogeneous linear 2nd-order ODEs with constant coefficients
ÃœBUNG
Ã
4.
Homogeneous linear 2nd-order ODEs with constant coefficients
Kompletten Zugriff freischalten locked
THEORIE
T
5.
Solving homogeneous linear ODEs with constant coefficients
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
6.
Solving homogeneous linear ODEs with constant coefficients
Kompletten Zugriff freischalten locked
THEORIE
T
7.
The Ansatz
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
The Ansatz
Kompletten Zugriff freischalten locked
Solution methods for linear-second order ODEs
THEORIE
T
1.
The Wronskian of two differentiable functions
ÃœBUNG
Ã
2.
The Wronskian of two differentiable functions
Kompletten Zugriff freischalten locked
THEORIE
T
3.
Variation of constants
ÃœBUNG
Ã
4.
Variation of constants
Kompletten Zugriff freischalten locked
THEORIE
T
5.
From one to two solutions
ÃœBUNG
Ã
6.
From one to two solutions
Kompletten Zugriff freischalten locked
THEORIE
T
7.
Solving linear second-order ODEs
Kompletten Zugriff freischalten locked
ÃœBUNG
Ã
8.
Solving linear second-order ODEs
Kompletten Zugriff freischalten locked
Systems of differential equations
THEORIE
T
1.
Systems of coupled linear first-order ODEs
ÃœBUNG
Ã
2.
Systems of coupled linear first-order ODEs
Kompletten Zugriff freischalten locked
End of Differential equations
ÃœBUNG
Ã
1.
Applications of ODEs
Kompletten Zugriff freischalten locked
THEORIE
T
2.
End of Differential equations
Fourier series
Coefficients of Fourier series
THEORIE
T
1.
Periodic functions
ÃœBUNG
Ã
2.
Periodic Functions
6
THEORIE
T
3.
Piecewise continuous and smooth functions
ÃœBUNG
Ã
4.
Piecewise continuous and smooth functions
6
THEORIE
T
5.
Calculation of Fourier coefficients
ÃœBUNG
Ã
6.
Calculation of Fourier coefficients
17
THEORIE
T
7.
Fourier coefficients for arbitrary periods
ÃœBUNG
Ã
8.
Fourier coefficients for arbitrary periods
8
THEORIE
T
9.
Even and odd functions
ÃœBUNG
Ã
10.
Even and odd functions
9
THEORIE
T
11.
Fourier series for even and odd functions
ÃœBUNG
Ã
12.
Fourier series for even and odd functions
18
Convergence of Fourier series
THEORIE
T
1.
The Riemann-Lebesgue lemma
ÃœBUNG
Ã
2.
The Riemann-Lebesgue lemma
6
THEORIE
T
3.
Infimum and supremum
ÃœBUNG
Ã
4.
Infimum and supremum
6
THEORIE
T
5.
Convergence of Fourier series
ÃœBUNG
Ã
6.
Convergence of Fourier series
9
Differentiation and integration of Fourier series
THEORIE
T
1.
Differentiation of Fourier series
ÃœBUNG
Ã
2.
Differentiation of Fourier series
6
THEORIE
T
3.
Integration of Fourier series
ÃœBUNG
Ã
4.
Integration of Fourier series
10
Uniform Convergence of Fourier series
THEORIE
T
1.
Uniform convergence
ÃœBUNG
Ã
2.
Uniform convergence
9
THEORIE
T
3.
Applications of uniform convergence
ÃœBUNG
Ã
4.
Applications of uniform convergence
10
THEORIE
T
5.
Uniform convergence of Fourier series
ÃœBUNG
Ã
6.
Uniform convergence of Fourier series
6
utwente POC
Introduction to utwente POC
THEORIE
T
1.
On the content of POC utwente
Power and Taylor series
THEORIE
T
1.
Geometric series
THEORIE
T
2.
Power series
ÃœBUNG
Ã
3.
Power series - Homework
11
THEORIE
T
4.
Taylor series
ÃœBUNG
Ã
5.
Taylor series - Homework
14
ÃœBUNG
Ã
6.
Power and Taylor series - Diagnostic Test
14
First-order differential equations
THEORIE
T
1.
The notion of differential equation
ÃœBUNG
Ã
2.
The notion of differential equation - Homework
13
THEORIE
T
3.
Slope fields
ÃœBUNG
Ã
4.
Slope fields - Homework
6
THEORIE
T
5.
Solution methods for first-order ODEs
ÃœBUNG
Ã
6.
Solution methods for first-order ODEs - Homework
18
THEORIE
T
7.
Solving linear first-order ODEs
ÃœBUNG
Ã
8.
Solving linear first-order ODEs - Homework
19
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