How can we calculate planet transits mathematically for a particular planet like Jupiter or Saturn from date of birth
Transit (or Gochara) is the current position of planets. From the date of birth, we calculate the natal chart (or horoscope or D1 chart). If you go to an astrologer today, he will create a horoscope with today's date and time. All planets will be there except the current Lagna (ascendant). This is the transit chart. On that chart, he will superimpose your Lagna position or Moon position (depending on the astrologer, some astrologers prefer the one over other). Now that becomes your transit chart.
Modern astrology software will give you a transit chart. There you can see the transit planetary position of any date and time. Usually, you can do it dynamically, you can move forward or backwards in time.
For example, saravali maitreya is a software that gives you all the details. It is free also.