Mathematics for Scientists: An Introduction is intended for someone who wants to understand the use of mathematical models in the natural sciences but whose knowledge of mathematics may be rusty. It begins at the beginning with numbers, geometry and trigonometry. An introduction to analysis (series, limits, functions and continuity) leads on to differential and integral calculus and differential equations, followed by a chapter on vector and matrix algebra. Newton’s laws of motion and his theory of gravity are used to derive Kepler’s three laws of planetary motion and the equilibrium theory of the tides. The theory of mechanical waves (vibrating strings and sound and ocean waves) introduces the use of partial differential equations. The last two chapters discuss probability theory and statistical inference. The book is written for the scientist who wants to understand the underlying mathematical principles and how to apply them rather than for the pure mathematician who needs to dot all the i’s and cross all the t’s. Applications to biology and physics are emphasized. There are some fairly straightforward exercises at the end of the book.

The table of contents can be downloaded as a pdf.

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