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I believe our Numerics course was very interesting. Basically we had the reverse order of the structure in your example.

Numerics (1-Year-Course)

1. Motivational example, heat transfer between two Points. We discretized the Problem and derived a way to solve it (1-dimensional FDM). From this, we then moved on to multiple dimensions and time dependency (FTCS, etc..), introducing error estimates along the way.

2. As obviously each problem boils down to linear equations, we looked at a few of the different iterative algorithms (Gradient, CG, Multigrid...) and of course error estimates and Matrix conditions.

3. We then went on to Interpolation methods, Splines and Co., to replace our linear Ansatz from before.

4. Next, we looked at Quadrature. Even without motivation, it was clear to us that this was usefull

5. At this point, we were able to take short detours and look at different other fields of Numerics briefly, for example, Finite Volume Method. We also took a look at things we had left out, like Newton Method (alot of which were introduced in other lectures).

6. We finalized the course with the Finite Element Method (as this is a core research field at our University), starting with Ritz-Galerkin and ending at a-priori a-posteriori error estimates. (Althoug this would need some basic knowledge in Functional Analysis)

I'm the kind of student that will follow a lecture with alot of interest if there is a strong/reasonable motivation behind it. Or at least some sort of "big-picture".

Perhaps to your liking, we had a heavy emphasize on Error estimates. We had alot of real life/hands on examples in between highlighting how important this is. (http://www.ima.umn.edu/~arnold/disasters/sleipner.html)

Further, I have to point out (as briefly mentioned in point 5), that alot of things were already introduced in some other lectures. Mainly our physics lectures required some basic Numerics, so this was not a complete introduction to Numerics.

2 deleted 32 characters in body

I believe our Numerics course was very interesting. Basically we had the reverse order of the structure in your example. (Sadly, the notes are in german)

Numerics (1-Year-Course)

1. Motivational example, heat transfer between two Points. We discretized the Problem and derived a way to solve it (1-dimensional FDM). From this, we then moved on to multiple dimensions and time dependency (FTCS, etc..), introducing error estimates along the way.

2. As obviously each problem boils down to linear equations, we looked at a few of the different iterative algorithms (Gradient, CG, Multigrid...) and of course error estimates and Matrix conditions.

3. We then went on to Interpolation methods, Splines and Co., to replace our linear Ansatz from before.

4. Next, we looked at Quadrature. Even without motivation, it was clear to us that this was usefull

5. At this point, we were able to take short detours and look at different other fields of Numerics briefly, for example, Finite Volume Method. We also took a look at things we had left out, like Newton Method (alot of which were introduced in other lectures).

6. We finalized the course with the Finite Element Method (as this is a core research field at our University), starting with Ritz-Galerkin and ending at a-priori error estimates. (Althoug this would need some basic knowledge in Functional Analysis)

I'm the kind of student that will follow a lecture with alot of interest if there is a strong/reasonable motivation behind it. Or at least some sort of "big-picture".

Perhaps to your liking, we had a heavy emphasize on Error estimates. We had alot of real life/hands on examples in between highlighting how important this is. (http://www.ima.umn.edu/~arnold/disasters/sleipner.html)

Further, I have to point out (as briefly mentioned in point 5), that alot of things were already introduced in some other lectures. Mainly our physics lectures required some basic Numerics, so this was not a complete introduction to Numerics.

I believe our Numerics course was very interesting. Basically we had the reverse order of the structure in your example. (Sadly, the notes are in german)

Numerics (1-Year-Course)

1. Motivational example, heat transfer between two Points. We discretized the Problem and derived a way to solve it (1-dimensional FDM). From this, we then moved on to multiple dimensions and time dependency (FTCS, etc..), introducing error estimates along the way.

2. As obviously each problem boils down to linear equations, we looked at a few of the different iterative algorithms (Gradient, CG, Multigrid...) and of course error estimates and Matrix conditions.

3. We then went on to Interpolation methods, Splines and Co., to replace our linear Ansatz from before.

4. Next, we looked at Quadrature. Even without motivation, it was clear to us that this was usefull

5. At this point, we were able to take short detours and look at different other fields of Numerics briefly, for example, Finite Volume Method. We also took a look at things we had left out, like Newton Method (alot of which were introduced in other lectures).

6. We finalized the course with the Finite Element Method (as this is a core research field at our University), starting with Ritz-Galerkin and ending at a-priori error estimates. (Althoug this would need some basic knowledge in Functional Analysis)

I'm the kind of student that will follow a lecture with alot of interest if there is a strong/reasonable motivation behind it. Or at least some sort of "big-picture".

Perhaps to your liking, we had a heavy emphasize on Error estimates. We had alot of real life/hands on examples in between highlighting how important this is. (http://www.ima.umn.edu/~arnold/disasters/sleipner.html)

Further, I have to point out (as briefly mentioned in point 5), that alot of things were already introduced in some other lectures. Mainly our physics lectures required some basic Numerics, so this was not a complete introduction to Numerics.