Jan von Delft Alexander AltlandCambridge University Press, 2/14/2019EAN 9781108471220, ISBN10: 1108471226Hardcover, 600 pages, 25.3 x 19.3 x 3.7 cmLanguage: EnglishThis textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.PrefacePart I. Linear Algebra1. Mathematics before numbers2. Vector spaces3. Euclidean geometry4. Vector product5. Linear maps6. Determinants7. Matrix diagonalization8. Unitarity and hermiticity9. Linear algebra in function spaces10. Multilinear algebraProblemslinear algebraPart II. Calculus1. Differentiation of one-dimensional functions2. Integration of one-dimensional functions3. Partial differentiation4. Multi-dimensional integration5. Taylor series6. Fourier calculus7. Differential equations8. Functional calculus9. Calculus of complex functionsProblemscalculusPart III. Vector Calculus1. Curves2. Curvilinear coordinates3. Fields4. Introductory concepts of differential geometry5. Alternating differential forms6. Riemannian differential geometry7. Case studydifferential forms and electrodynamicsProblemsvector calculusSolutionslinear algebraSolutionscalculusSolutionsvector calculusIndex.
