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I. System of symbolic logicA. The simple language AB. The language BC. The extended language CII. Application of symbolic logicD. Forms and methods of the construction of languagesE. Axiom systems (ASs) for set theory and arithmeticF. Axiom systems (ASs) for geometryG. ASs of pysicsH. ASs of biology

Translated from the German by E.J. McShane I. IntroductionII. The fundamental ideas of the integral and differential calculusIII. Differentiation and integration of the elementary functionsIV. Further development of the integral calculusV. ApplicationsVI. Taylor's theorem and the approximate expression of functions by polynomialsVII. Numerical methodsVIII. Infinite series and other limiting processesIX. Fourier seriesX. A sketch of the theory of functions of several variablesXI. The differential...

Translated from the German by E.J. McShaneI. Preliminary remarks on analytical geometry and vector analysisII. Functions of several variables and their derivativesIII. Developments and applications of the differential calculusIV. Multiple integralsV. Integration over regions in several dimensionsVI. Differential equationsVII. Calculus of variationsVIII. Functions of a complex variable

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1. Fundamental Principles of Counting2. Fundamentals of Logic3. Set Theory4. Properties of the Integers: Mathematical Induction5. Relations and Functions6. Languages: Finite State Machines7. Relations: The Second Time Around8. The Principle of Inclusion and Exclusion9. Generating Functions10. Recurrence Relations11. An Introduction to Graph Theory12. Trees13. Optimization and Matching14. Rings and Modular Arithmetic15. Boolean Algebra and Switching Functions16. Groups Coding Theory and Polya's M...

Modules in Undergraduate Mathematics and Its Applications