Explore the historical appendices

Read the Euler and equation-history appendices

This unit is historical reading and enrichment. Read the credits as the source’s simplified chronology; the equation catalog is not a list of additional assessed techniques.

Appendices A and B are on PDF/printed 37 in both copies; the earlier Appendix A pointer to page 36 is stale.

Appendix A describes Leonhard Euler (1707–1783), born 15 April 1707 in Basel, as an academy scholar whose work influenced geometry, trigonometry, calculus and physics.

It notes his hundreds of publications and continued productivity after losing his sight, before his death on 18 September 1783.

The original adaptation credits Biography.com; ETH Library’s account confirms the dates and continuing work after blindness.

The source QR links to further understanding.

Appendix B recommends Ian Stewart’s Seventeen Equations that Changed the World.

Its 2013 date fits the paperback edition; the publisher’s copyright page identifies the first British publication as 2012.

The source highlights the square-root-of-minus-one and polyhedron rows associated with Euler.

These are reading prompts about mathematical history, rather than additional assessed complex-number tasks.

Explore the seventeen equation topics

The embedded source chart is not searchable text in the original PDF. The table below retains all seventeen topics and its listed credits/years.

Those labels are a simplified source chronology, not claims of first discovery.

The equations are illustrative forms, with physical assumptions and units needed in their respective subjects.

Two mathematical corrections are explicit: the calculus limit has one equals sign before the limit expression, and the normal density has a negative quadratic exponent and positive scale σ.

The original graphic’s extra equals sign, positive exponent and ambiguous scale glyph remain in the retained source image/transcription.

Topic 1: Pythagoras’s Theorem

Equation, with reviewed notation:

$$a^2+b^2=c^2$$

Credit/year listed by the source: Pythagoras,530 BC

Topic 2: Logarithms

Equation, with reviewed notation:

$$\log xy=\log x+\log y$$

Credit/year listed by the source: John Napier,1610

Topic 3: Calculus

Equation, with reviewed notation:

$$\frac{df}{dt}=\lim_{h\to0}\frac{f(t+h)-f(t)}h$$

Credit/year listed by the source: Newton,1668

Topic 4: Law of Gravity

Equation, with reviewed notation:

$$F=G\frac{m_1m_2}{r^2}$$

Credit/year listed by the source: Newton,1687

Topic 5: The Square Root of Minus One

Equation, with reviewed notation:

$$i^2=-1$$

Credit/year listed by the source: Euler,1750

Topic 6: Euler’s Formula for Polyhedra

Equation, with reviewed notation:

$$V-E+F=2$$

Credit/year listed by the source: Euler,1751

Topic 7: Normal Distribution

Equation, with reviewed notation:

$$\phi(x)=\frac1{\sigma\sqrt{2\pi}}e^{-\frac{(x-\mu)^2}{2\sigma^2}}$$

Credit/year listed by the source: C.F.Gauss,1810

Topic 8: Wave Equation

Equation, with reviewed notation:

$$\frac{\partial^2u}{\partial t^2}=c^2\frac{\partial^2u}{\partial x^2}$$

Credit/year listed by the source: J.d’Alembert,1746

Topic 9: Fourier Transform

Equation, with reviewed notation:

$$\widehat f(\omega)=\int_{-\infty}^{\infty}f(x)e^{-2\pi i x\omega}\,dx$$

Credit/year listed by the source: J.Fourier,1822

Topic 10: Navier-Stokes Equation

Equation, with reviewed notation:

$$\rho\left(\frac{\partial\mathbf v}{\partial t}+\mathbf v\cdot\nabla\mathbf v\right)=-\nabla p+\nabla\cdot\mathbf T+\mathbf f$$

Credit/year listed by the source: C.Navier,G.Stokes,1845

Topic 11: Maxwell’s Equations

Equation, with reviewed notation:

$$\nabla\cdot\mathbf E=0;\quad\nabla\cdot\mathbf H=0;\quad\nabla\times\mathbf E=-\frac1c\frac{\partial\mathbf H}{\partial t};\quad\nabla\times\mathbf H=\frac1c\frac{\partial\mathbf E}{\partial t}$$

Credit/year listed by the source: J.C.Maxwell,1865

Topic 12: Second Law of Thermodynamics

Equation, with reviewed notation:

$$dS\ge0$$

Credit/year listed by the source: L.Boltzmann,1874

Topic 13: Relativity

Equation, with reviewed notation:

$$E=mc^2$$

Credit/year listed by the source: Einstein,1905

Topic 14: Schrodinger’s Equation

Equation, with reviewed notation:

$$i\hbar\frac\partial{\partial t}\Psi=H\Psi$$

Credit/year listed by the source: E.Schrodinger,1927

Topic 15: Information Theory

Equation, with reviewed notation:

$$H=-\sum p(x)\log p(x)$$

Credit/year listed by the source: C.Shannon,1949

Topic 16: Chaos Theory

Equation, with reviewed notation:

$$x_{t+1}=kx_t(1-x_t)$$

Credit/year listed by the source: Robert May,1975

Topic 17: Black-Scholes Equation

Equation, with reviewed notation:

$$\frac12\sigma^2S^2\frac{\partial^2V}{\partial S^2}+rS\frac{\partial V}{\partial S}+\frac{\partial V}{\partial t}-rV=0$$

Credit/year listed by the source: F.Black,M.Scholes,1990