Chapters in Volume I:
Part I. Introduction. Part II. Understanding Smoothness. 2. Proving Propositions. 3. Sequences of Real Numbers. 4. Bolzano – Weierstrass Results. 5. Topological Compactness. 6. Function Limits. 7. Continuity. 8. Consequences of continuity of intervals. 9. Lower Semicontinuous and Convex Functions. 10. Basic Differentiability. 11. The Properties of Derivatives. 12. Consequences of Derivatives. 13. Exponential and Logarithm Functions. 14. Extremal Theory for One Variable. 15. Differentiation in R2 and R3.16. Multivariable Extremal Theory. Part III. Integration and Sequences of Functions. 17. Uniform Continuity. 18. Cauchy Sequences of Real Numbers. 19. Series of Real Numbers. 20. Series in Gerenal. 21. Integration Theiry. 22. Existence of Reimann Integral Theories. 23. The Fundamental Theorem of Calculus (FTOC). 24. Convergence of sequences of functions. 25. Series of Functions and Power Series. 26. Riemann Integration: Discontinuities and Compositions. 27. Fourier Series. 28. Application. Part IV. Summing it all Up. 29. Summary. Part V. References. Index.
Chapters in Volume II:
Part I. Introduction. 1. Beginning Remarks. Part II. Linear Mappings. 2. Preliminaries. 3. Vector Spaces. 4. Linear Transformations. 5. Symmetric Matrices. 6. Continuity and Topology. 7. Abstract Symmetric Matrices. 8. Rotations and Orbital Mechanics. 9. Determinants and Matrix Manipulations. Part III. Calculus of Many Variables. 10. Differentiability. 11. Multivariable Extremal Theory. 12. The Inverse and Implicit Function Theorems. 13. Linear Approximation Applications. Part IV. Integration. 14. Integration in Multiple Dimensions. 15. Change of Variables and Fubini’s Theorem. 16. Line Integrals. 17. Differential Forms. Part V. Applications. 18. The Exponential Matrix. 19. Nonlinear Parametric Optimization Theory. Part VI. Summing it all up. 20. Summing It all Up. Part VII. References. Index
Chapters in Volume III:
Part I. Introduction. Part II. Metric Spaces. 2. Metric Spaces. 3. Completing a Metric Space. Part III. Normed Linear Spaces. 4. Vector Spaces. 5. Normed Linear Spaces. 6. Linear Operators on Normed Spaces. Part IV. Inner Product Spaces. 7. Inner Product Spaces. 8. Hilbert Spaces. 9. Dual Spaces. 10. Hahn - Banach Results. 11. More About Dual Spaces. 12. Some Classical Results. Part V. Operators. 13. Sturm–Liouville Operators. 14. Self Adjoint Operators. Part VI. Topics in Applied Modeling. 15. Fields and Charges on a Set. 16. Games. Part VII. Summing It All Up. Part VIII. References. Index.
Chapters in Volume IV:
Part I. Introductory Matter. 1. Introduction. Part II. Classical Riemann Integration. 2. An Overview of Riemann Integration. 3. Functions of Bounded Variation. 4. The Theory of Riemann Integration. 5. Further Riemann Integration Results. Part III. Riemann–Stieltjes Integration. 6. The Riemann–Stieltjes Integral. 7. Further Riemann–Stieljes Results. Part IV. Abstract Measure Theory One. 8. Measurable Functions and Spaces. 9. Measure and Integration. 10. The Lp Spaces. Part V. Constructing Measures. 11. Constructing Measures. 12. Lebesgue Measure. 13. Cantor Set Experiments. 14. Lebesgue Stieljes Measure. Part VI. Abstract Measure Theory Two. 15. Modes of Convergence. 16. Decomposition of Measures. 17. Connections to Riemann Integration. 18. Fubini Type Results. 19. Differentiation. Part VII. Summing it all Up. 20. Summing It all Up. Part VIII. References. Index.
Chapters in Volume V:
Part I. Introduction. 1. Introduction. Part II. Some Algebraic Topology. 2. Basic Metric Space Topology. 3. Forms and Curves. 4. The Jordan Curve Theorem. Part III. Deeper Topological Ideas. 5. Vector Spaces and Topology. 6. Locally Convex Spaces and Seminorms. 7. A New Look at Linear Functionals. 8. Deeper Results on Linear Functionals. 9. Stone–Weierstrass Results. Part IV. Topological Degree Theory. 10. Brouwer Degree Theory. 11 Leray–Schauder Degree. 12. Coincidence Degree. Part V. Manifolds. 13. Manifolds. 14. Smooth Functions on Manifolds. 15. The Global Structure of Manifolds. Part VI. Emerging Topologies. 16. Asynchronous Computation. 17. Signal Models and Autoimmune Disease. 18. Bar Code Computations in Consciousness Models. Part VII. Summing It All Up. 19. Summing It All Up. Part VIII. References. Index.
Biography
James K. Peterson is an Emeritus Professor at the School of Mathematical and Statistical Sciences, Clemson University.
He tries hard to build interesting models of complex phenomena using a blend of mathematics, computation and science. To this end, he has written four books on how to teach such things to biologists and cognitive scientists. These books grew out of his Calculus for Biologists courses offered to the biology majors from 2007 to 2015.
He has taught the analysis courses since he started teaching both at Clemson and at his previous post at Michigan Technological University.
In between, he spent time as a senior engineer in various aerospace firms and even did a short stint in a software development company. The problems he was exposed to were very hard and not amenable to solution using just one approach. Using tools from many branches of mathematics, from many types of computational languages and from first principles analysis of natural phenomena was absolutely essential to make progress.
In both mathematical and applied areas, students often need to use advanced mathematics tools they have not learned properly. So, he has recently written a series of five books on mathematical analysis to help researchers with the problem of learning new things after they have earned their degrees and are practicing scientists. Along the way, he has also written papers in immunology, cognitive science and neural network technology in addition to having grants from NSF, NASA and the Army.
He also likes to paint, build furniture and write stories.
