Textbook in PDF format

The series of textbooks "Mathematics that Works" presents mathematical methods with a sharp focus on applicability. There is an ample supply of worded-out examples and instructive exercises. The techniques are illustrated in applications from various branches of science; here, the connection between the mathematical method and the application is equally important as the mathematics itself. Thus the way the students digest the matter is aimed at practical usability within their own field, and skills take priority over the mathematical abstraction level. By connecting mathematics to its applications, the usage of mathematics in the applied sciences is facilitated.
Building on the introduction to calculus in volume 1, this second volume of Mathematics that Works presents a more in-depth treatment of elements of calculus: integration techniques, and differentiation and integration of functions of two variables. Besides, it introduces iterative processes and differential equations. These latter topics are especially rich in applications. In the discussion of these applications and the interpretation of their results, the first steps in mathematical modelling are made.
Functions and their Derivatives
Sequences, Series, and Iteration Processes
Change and Growth
Integrals
Integration Techniques
Differential Equations
Functions of Two Variables: Differentiation and Integration
Functions of Two Variables: Extreme Values
Complex Numbers
Answers
The Greek Alphabet
Formulas
Index of Mathematical Terms
Index of Applications