When was vector calculus developed

As it turns out, this construction only works for dimension 1, 2, 4 and 8. Hamilton came up with the fundamental formulas for quaternions while he and his wife Helen Marie Bayly were strolling across Brougham Bridge.

He was so excited by his flash of inspiration that he used his pocketknife to carve the formulas into a stone of the bridge. Although his original carving has disappeared, the moment is commemorated by a plaque which people can still visit today. Carroll a. You can read her analysis here. III , 3. James Clerk Maxwell, A treatise on electricity and magnetism , vol.

Active 3 years, 5 months ago. Viewed 2k times. Improve this question. VicAche 1, 14 14 silver badges 31 31 bronze badges. The first one is closest. But it does completely answer my question. In fact it just leads me to more questions like: How influential was Heaviside's The Electrian to modern vector analysis?

Was vector calculus written in its entirely modern form in Gibb's Vector Analysis -- or was it just mostly complete? If the latter, what was missing? What did Hamilton use quaternions for? Is there such a thing as "quaternion calculus"? Show 1 more comment. Active Oldest Votes. These are: complex numbers and their geometrical interpretation Leibniz's work on the geometry of position the parallelogram representation of force and velocity The first one can be traced back to Cardan's Ars Magna published in as the guy was the first to introduce roots of negative numbers for themselves.

Now let's quote a genius "A body, acted on by two forces simultaneously, will describe the diagonal of a parallelogram in the same time as it would describe the sides by those forces separately. Going 3-D: the quaternion Hamilton we're getting closer to electromagnetism published a philosophical-ish paper in in which he expresses his hope to come up with a "theory of triplets" to describe 3-D geometry.

Maxwell, or answering the original question In , Maxwell published his Treatise on Electricity and Magnetism , a paper that had a huge impact on 19th century science. Improve this answer. VicAche VicAche 1, 14 14 silver badges 31 31 bronze badges. Add a comment. Elements in Space 1 1 silver badge 12 12 bronze badges. Edgar Mueller Edgar Mueller 31 2 2 bronze badges.

Rabi Rabi 5 1 1 bronze badge. Perhaps try to summarize what can be found in the books you linked? On Stack Exchange sites we strive to avoid link-only answers, and currently this answer is not very far away from being one.

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The Mean Value Theorem 7 Integration 1. Two examples 2. The Fundamental Theorem of Calculus 3. Some Properties of Integrals 8 Techniques of Integration 1. Substitution 2. Powers of sine and cosine 3. Trigonometric Substitutions 4. Integration by Parts 5.

Rational Functions 6. Numerical Integration 7. Additional exercises 9 Applications of Integration 1. Area between curves 2. Distance, Velocity, Acceleration 3.

Volume 4. Average value of a function 5. Work 6. Center of Mass 7. Kinetic energy; improper integrals 8. Probability 9. Arc Length Polar Coordinates 2.

Slopes in polar coordinates 3. Areas in polar coordinates 4. Parametric Equations 5. Calculus with Parametric Equations 11 Sequences and Series 1. Sequences 2. Series 3. The Integral Test 4. Alternating Series 5. Comparison Tests 6. Absolute Convergence 7. The Ratio and Root Tests 8. Power Series 9. Calculus with Power Series