Introduction to Calculus and Analysis Volume II/2

- Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
- Vector Form of the Divergence Theorem. Stokes's Theorem
- Formula for Integration by Parts in Two Dimensions: Green's Theorem
- The Divergence Theorem Applied to the Transformation of Double Integrals
- Area Differentiation
- Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows
- Orientation of Surfaces
- Integrals of Differential Forms and of Scalars over Surfaces
- Gauss's and Green's Theorems in Space
- Appendix: General Theory of Surfaces and of Surface Integrals.- Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions
- The General Linear Differential Equation of the First Order
- Linear Differential Equations of Higher Order
- General Differential Equations of the First Order
- Systems of Differential Equations and Differential Equations of Higher Order
- Integration by the Method of Undermined Coefficients
- The Potential of Attracting Charges and Laplace's Equation
- Further Examples of Partial Differential Equations from Mathematical Physics .- Calculus of Variations: Functions and Their Extreme Values of a Functional
- Generalizations
- Problems Involving Subsidiary Conditions. Lagrange Multipliers.- Functions of a Complex Variable: Complex Functions Represented by Power Series
- Foundations of the General Theory of Functions of a Complex Variable
- The Integration of Analytic Functions
- Cauchy's Formula and Its Applications
- Applications to Complex Integration (Contour Integration)
- Many-Valued Functions and Analytic Extension.- List of Biographical Dates Index

Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called "a reservoir of talent" to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Biography of Fritz JohnFritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John's research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). Fritz John's work exemplifies the unity of mathematics as well as its elegance

From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students. Acta Scientiarum Mathematicarum, 1991