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This accessible text covers key results in functional analysis that are essential for further study in the calculus of variations, analysis, dynamical systems, and the theory of partial differential equations. The treatment of Hilbert spaces covers the topics required to prove the Hilbert–Schmidt theorem, including orthonormal bases, the Riesz representation theorem, and the basics of spectral theory. The material on Banach spaces and their duals includes the Hahn–Banach theorem, the Krein–Milman theorem, and results based on the Baire category theorem, before culminating in a proof of...

Johann Gottlieb Fichte (1762-1814) was the founding figure of the philosophical movement known as German idealism, a branch of thought which grew out of Kant's critical philosophy. Fichte's work formed the crucial link between eighteenth-century Enlightenment thought and philosophical, as well as literary, Romanticism. Some of his ideas also foreshadow later nineteenth- and twentieth-century developments in philosophy and in political thought, including existentialism, nationalism and socialism. This volume offers essays on all the major aspects of Fichte's philosophy, ranging from the...