Schaum 39s Outline Differential Geometry Pdf New ❲480p❳
Unlocking Curves and Surfaces: The Ultimate Guide to the New Schaum's Outline of Differential Geometry (PDF)
Week 4: Geodesics & Gauss-Bonnet
- Read: Chapter 5 (geodesic equations) and 6 (Gauss-Bonnet).
- Do: Show that lines of longitude on a sphere are geodesics; latitude lines are not (except equator).
- Apply: Compute total curvature of a triangle on a sphere.
Pro tip: Use the PDF’s search function for terms like "Christoffel symbols of the second kind"—the new PDF has them hyperlinked in the index.
The Specific Book: "Schaum's Outline of Differential Geometry" by Martin M. Lipschutz
The definitive text in this space is authored by Martin M. Lipschutz (affiliated with Temple University). The full citation is:
Schaum's Outline of Differential Geometry (Schaum's Outlines) by Martin Lipschutz. Originally published 1969; Revised and updated editions available. schaum 39s outline differential geometry pdf new
Key identifiers:
- ISBN-10: 0070379858 (older paperback)
- ISBN-13: 978-0070379855
- Pages: Approximately 288–320, depending on printing.
Q4: Is this enough to pass a PhD qualifying exam in geometry?
No. This is a remedial/undergraduate outline. For qualifying exams (differential topology, Riemannian geometry), you need Spivak’s 5-volume set or Lee’s Riemannian Manifolds. However, Lipschutz is excellent for the calculus-based portion of the exam (curves, surfaces, classical curvature). Unlocking Curves and Surfaces: The Ultimate Guide to
Chapter 3: Introductory Surface Theory
- Theory: Coordinate patches, tangent planes, and the First Fundamental Form (metric coefficients ( E, F, G )).
- Solved Problems: Calculating arc length, angle between curves, and area on a surface (e.g., sphere, torus, helicoid).
- New addition: More detailed comparison between intrinsic and extrinsic geometry.
Chapter-by-Chapter: What’s Inside the "New" PDF?
If you are about to download or purchase this PDF, here is exactly what you will find. The outline is structured for a one-semester undergraduate or beginning graduate course.
Q1: Is the "new" edition vastly different from the old one?
No—the mathematics is identical (differential geometry hasn’t changed in 50 years). The improvements are in readability, clarity of figures, and error correction. If you only have the 1969 PDF, you can still learn. But the "new" PDF saves you headaches. Read: Chapter 5 (geodesic equations) and 6 (Gauss-Bonnet)
Why the "New" PDF is Superior for Self-Study
Let’s say you find a legitimate digital copy of the most recent printing. Here is why it beats the older version:
| Feature | Old Edition (1969/80s scan) | New PDF (2000s+ printing) | | :--- | :--- | :--- | | Notation | Uses older ( r_u, r_v ) for partials, occasionally inconsistent. | Modern ( \mathbfr_u, \mathbfrv ) consistent with Do Carmo. | | Diagrams | Hand-drawn, some are faint. | Digital vector diagrams; clear labeling of tangent planes. | | Typography | Typewriter-style math; ( \Gammaij^k ) hard to read. | Professional LaTeX; subscripts/superscripts crisp. | | Index | Short, often missing terms like "Christoffel." | Expanded; includes modern keywords (e.g., "minimal surface," "Gaussian curvature"). | | Errata | Several unsolved typos in problem answers. | Corrected 3rd/4th printing; verified solutions. |