Here everyone doing a Physics/Maths/Engineering degree will have A Level Mathematics qualification and a Physics A Level qualification. In the pure Maths part, it covers integration and differentiation (inc. of trigonometric functions, log, exp and by parts), vectors, and 1st order ODEs as a minimum. There is also mechanics though depending on the school you study at, this did not used to be compulsory (you could choose to do Statistics instead).
In Physics A Level, it covers general physics topics - using SUVAT equations for e.g., electric circuits, radiation, some very basic QM like photoelectric effect. Knowing calculus is not a requirement for that qualification as it's designed to be independent from Mathematics A Level (at one point you had to take it as well to study Physics, but declinining numbers of students caused them to stop that), but to study most STEM subjects at University you do need both qualifications.
Around 50% going on to study for one of these degree courses will go beyond this and will have studied for an A Level in Further Maths. In this you do second order ODEs, complex numbers, matrices, conic sections, and more mechanics. In the Universities I've taught/studied at, the entirety of these Further Maths topics is usually covered in a 1st year + 1st semester course before going on to do harder stuff beyond that.
So from that mathematical background, everything numerical methods-like assumes you already have that knowledge almost from the beginning at University.
I actually studied things like Newton's method and even Runge-Kutta ODE solution in a numerical methods A-level module (i.e. at school). There are other bits of the curriculum that are quite different too -- like decision maths, which basically was lots of algorithms (routefinding! critical path analysis!). As a result, my university-level courses were very much based on efficient numerical implementations of stable algorithms, and looked a lot at something like how to solve chaotic ODEs, or integrating rather unpleasant functions. (I was actually taught by this person and how to solve his problems! https://mathworld.wolfram.com/Hundred-DollarHundred-DigitCha...)
Here everyone doing a Physics/Maths/Engineering degree will have A Level Mathematics qualification and a Physics A Level qualification. In the pure Maths part, it covers integration and differentiation (inc. of trigonometric functions, log, exp and by parts), vectors, and 1st order ODEs as a minimum. There is also mechanics though depending on the school you study at, this did not used to be compulsory (you could choose to do Statistics instead).
In Physics A Level, it covers general physics topics - using SUVAT equations for e.g., electric circuits, radiation, some very basic QM like photoelectric effect. Knowing calculus is not a requirement for that qualification as it's designed to be independent from Mathematics A Level (at one point you had to take it as well to study Physics, but declinining numbers of students caused them to stop that), but to study most STEM subjects at University you do need both qualifications.
Around 50% going on to study for one of these degree courses will go beyond this and will have studied for an A Level in Further Maths. In this you do second order ODEs, complex numbers, matrices, conic sections, and more mechanics. In the Universities I've taught/studied at, the entirety of these Further Maths topics is usually covered in a 1st year + 1st semester course before going on to do harder stuff beyond that.
So from that mathematical background, everything numerical methods-like assumes you already have that knowledge almost from the beginning at University.