I'm not sure this is relevant to computer science, but as a mechanical engineer, I've used differential equations and topology quite a bit in my coding.

Topology has its important role in CAD and CAE softwares (particularly when dealing with manifold/non manifold objects) where it's important to understand the relation that various geometric entites have with one another (whether you're coding a tool or using one). There is also a good amount of research currently being done on automatic CAD model simplification for analysis (FEM/CFD) based on geometric simplification (various methods exist ranging from topology to fourier analysis [1]). Meshing theory also relies quite a bit on topology. [2] (but I don't think anyone denies the importance of topology in CS though)

As for differential equations and calculus, they are heavily used in FEM [3] and CFD [4] and there is therefore a need to numerically evaluate these equations in a efficient manner. They are also heavily used in controls (for instance, in a quadcopter PID controller [5]). So I'm guessing in that case, differential equations are used to describe something you're then modelling in your code through numerical integration. Numerical methods however rely both on understanding calculus and differential equations as a given numerical scheme may be more adapted to a particular type of DE than others [6][7][8][9] (sorry, couldn't find a comparaison of these schemes on a single link so I'm citing a few).

Signals processing and statistical analysis may also be used in conjunction with differential equations such as in turbulence modeling in CFD. RANS (Reynolds Averaged Navier-Stokes) equations essentially average the NS equations over time in order to locate areas of various turbulence strength [10]. LES (Large Eddy Simulation) filter small eddies out of the NS equations in order to be left with only the large eddies thus requiring less computational power [11] (the filtered eddies are modeled separately for the sake of energy balance).

Finally, I would argue that calculus is also used in optimization codes and neural networks with gradient based descents [12][13]

I hope I didn't go off topic with this post, all I was trying to say is that in some fields of computer science, you do have to come up with algorithms evaluating differential equations using numerical methods, and an understanding of calculus and DE is a definitely plus. I'm sure finance has its share of DE to model requiring their understanding.

[1] http://citeseerx.ist.psu.edu/viewdoc/download;jsessionid=7D3...
or
http://www.sciencedirect.com/science/article/pii/S0010448508...

[2] http://www.ann.jussieu.fr/frey/papers/meshing/Le%20K.H.,%20F...

[3] http://fenicsproject.org/documentation/tutorial/fundamentals...

[4] http://en.wikipedia.org/wiki/Finite_volume_method

[5] https://ghowen.me/build-your-own-quadcopter-autopilot/#toc4

[6] http://en.wikipedia.org/wiki/Lax%E2%80%93Friedrichs_method

[7] http://en.wikipedia.org/wiki/MUSCL_scheme

[8] http://en.wikipedia.org/wiki/Upwind_scheme

[9] http://en.wikipedia.org/wiki/QUICK_scheme

[10] http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%...

[11] http://en.wikipedia.org/wiki/Large_eddy_simulation

[12] http://en.wikipedia.org/wiki/Gradient_descent

[13] http://karpathy.github.io/neuralnets/

EDIT: added a paragraph on turbulence modeling

EDIT 2:
Optimization methods can be used to find optimal solutions to differential equations [A]. I talked about gradient descent earlier, but there's also the simplex method [B] that makes heavy use of linear algebra and topology to navigate in a solution space in order to optimize a solution.

[A] http://en.wikipedia.org/wiki/Mathematical_optimization#Appli...

[B] http://en.wikipedia.org/wiki/Simplex_algorithm