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