Please capitalize where necessary: the difference between the s-models and the other models is the connection of the draw bar to the mower frame. the s-models have a longer draw bar which is connected to the middle of the mower frame.
A: The difference between the S-models and the other models is the connection of the draw bar to the mower frame. The S-models have a longer draw bar which is connected to the middle of the mower frame.

Q: after heel dec pick up 10-11-12 sts each side of heel and slip the 26-26-30 sts from stitch holder back on needle = 56-58-66 sts.

A: After heel dec pick up 10-11-12 sts each side of heel and slip the 26-26-30 sts from stitch holder back on needle = 56-58-66 sts.

Q: definition identifies the status of the referenced line with respect to its original state
A: Definition Identifies the status of the referenced Line with respect to its original state

Problem: any teacher of mathematics today can identify with what yang is trying to do here.
Can you repeat this sentence, but capitalize it?
Answer: Any teacher of mathematics today can identify with what Yang is trying to do here.

Text: we'll try to establish a manned "scanning-station" - so if you have any old photo's of family members that you'd like to share with other family members, then please don't hesitate to bring them with you.

Correct capitalization: We'll try to establish a manned "Scanning-station" - so if you have any old photo's of family members that you'd like to share with other family members, then please don't hesitate to bring them with you.

Problem: it gives a much fuller treatment of the material in his 1943 book, and also contains results obtained since 1943.
Can you repeat this sentence, but capitalize it?
Answer:
It gives a much fuller treatment of the material in his 1943 book, and also contains results obtained since 1943.