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      <image:title>The Spivak Difference: Why His Texts Endure</image:title>
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    <loc>https://mathpop.com/blogs/news/a-triumphant-return-the-new-print-of-physics-for-mathematicians-is-a-milestone-for-publish-or-perish-inc-%C2%AE</loc>
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      <image:title>Pre-Orders LIVE: Securing Your Copy of Physics for Mathematicians and Informing the Current Print Run</image:title>
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      <image:title>Meeting Modern Academic Needs: Announcing the New Publish or Perish Digital Editions Collection</image:title>
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    <loc>https://mathpop.com/blogs/news/instant-access-to-rigor-physics-for-mathematicians-digital-edition-is-now-available</loc>
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      <image:title>Instant Access to Rigor: Physics for Mathematicians Digital Edition is Now Available</image:title>
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    <loc>https://mathpop.com/blogs/news/now-live-the-official-digital-edition-of-spivaks-calculus-4th-edition</loc>
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      <image:title>Physics for Mathematicians Now In Stock and Shipping</image:title>
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    <loc>https://mathpop.com/blogs/news/requesting-a-desk-or-examination-copy-now-easier-for-educators</loc>
    <lastmod>2026-08-14T16:55:07-05:00</lastmod>
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      <image:title>Requesting a Desk or Examination Copy: Now Easier for Educators</image:title>
      <image:caption>Desk &amp; Examination Copies, now live — MathPop for educators</image:caption>
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    <loc>https://mathpop.com/blogs/news/the-epsilon-delta-definition-of-a-limit-finally-made-intuitive</loc>
    <lastmod>2026-09-11T21:47:34-05:00</lastmod>
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      <image:title>The Epsilon-Delta Definition of a Limit, Finally Made Intuitive</image:title>
      <image:caption>Graph illustrating the epsilon-delta definition of a limit, showing the delta interval around a and the epsilon band around L</image:caption>
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    <loc>https://mathpop.com/blogs/news/proof-based-calculus-vs-computational-calculus-which-one-do-you-actually-need</loc>
    <lastmod>2026-09-11T21:47:34-05:00</lastmod>
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      <image:title>Proof-Based Calculus vs. Computational Calculus: Which One Do You Actually Need?</image:title>
      <image:caption>Split graphic comparing computational calculus (d/dx) and proof-based calculus (for-all epsilon, exists delta) notation</image:caption>
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    <loc>https://mathpop.com/blogs/news/what-is-a-manifold-a-rigorous-but-friendly-first-look</loc>
    <lastmod>2026-09-11T21:47:34-05:00</lastmod>
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      <image:title>What Is a Manifold? A Rigorous (But Friendly) First Look</image:title>
      <image:caption>Diagram of a sphere with a tangent plane touching one point and a flat coordinate chart, illustrating the idea of a manifold</image:caption>
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    <loc>https://mathpop.com/blogs/news/the-three-hard-theorems-hiding-in-every-calculus-course</loc>
    <lastmod>2026-09-11T21:47:34-05:00</lastmod>
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      <image:title>The Three &quot;Hard&quot; Theorems Hiding in Every Calculus Course</image:title>
      <image:caption>A wavy continuous function graph crossing the x-axis between points a and b, illustrating the Intermediate Value Theorem, with three circled numbers for Spivak&apos;s Three Hard Theorems</image:caption>
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    <loc>https://mathpop.com/blogs/news/the-chain-rule-proof-that-almost-works-but-doesnt</loc>
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      <image:title>The Chain Rule Proof That Almost Works (But Doesn&apos;t)</image:title>
      <image:caption>An oscillating function squeezed between the parabolas x-squared and negative x-squared near a point a, illustrating the function that breaks the naive chain rule proof</image:caption>
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    <loc>https://mathpop.com/blogs/news/what-is-a-derivative-really-the-precise-meaning-behind-slope-of-the-tangent-line</loc>
    <lastmod>2026-09-14T09:00:02-05:00</lastmod>
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      <image:title>What Is a Derivative, Really? The Precise Meaning Behind &quot;Slope of the Tangent Line&quot;</image:title>
      <image:caption>Diagram of a curve with a tangent line touching at one point (instantaneous slope) contrasted with a dashed secant line spanning a wider interval to a second point (average slope), illustrating the definition of the derivative.</image:caption>
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    <loc>https://mathpop.com/blogs/news/the-mean-value-theorem-why-average-speed-guarantees-an-exact-speed</loc>
    <lastmod>2026-09-21T09:00:02-05:00</lastmod>
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      <image:loc>https://cdn.shopify.com/s/files/1/0829/3705/3486/articles/mvt-cover.png?v=1787712385</image:loc>
      <image:title>The Mean Value Theorem: Why Average Speed Guarantees an Exact Speed</image:title>
      <image:caption>Line-art diagram illustrating the Mean Value Theorem: a curve from point a to point b with a straight secant line connecting the endpoints and a dashed tangent line parallel to it touching the curve at an interior point x</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/how-do-you-know-a-function-has-an-inverse-the-calculus-answer</loc>
    <lastmod>2026-10-05T09:00:03-05:00</lastmod>
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      <image:title>How Do You Know a Function Has an Inverse? The Calculus Answer</image:title>
      <image:caption>Line art showing an increasing function f and its inverse f-inverse reflected across the diagonal line y=x, illustrating invertibility in calculus</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/convexity-concavity-precisely-what-makes-a-graph-curve-the-way-it-does</loc>
    <lastmod>2026-09-28T09:00:06-05:00</lastmod>
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      <image:loc>https://cdn.shopify.com/s/files/1/0829/3705/3486/articles/convexity-cover.png?v=1787712473</image:loc>
      <image:title>Convexity &amp; Concavity, Precisely: What Makes a Graph Curve the Way It Does</image:title>
      <image:caption>Diagram of a convex curve with a chord connecting two points on it lying above the graph between them, illustrating the definition of convexity from Spivak&apos;s Calculus</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/spivak-vs-apostol-vs-courant-which-calculus-book</loc>
    <lastmod>2026-09-11T21:55:19-05:00</lastmod>
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      <image:title>Spivak vs. Apostol vs. Courant: Which Rigorous Calculus Book Is Right for You?</image:title>
      <image:caption>Three book spines labeled Spivak, Apostol and Courant, illustrating a comparison of rigorous calculus textbooks</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/how-to-self-study-spivaks-calculus</loc>
    <lastmod>2026-09-11T21:43:50-05:00</lastmod>
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      <image:title>How to Self-Study Spivak&apos;s Calculus: Prerequisites, Pacing, and a Realistic Path</image:title>
      <image:caption>Timeline of Spivak&apos;s Calculus chapters from Numbers through Limits, Derivatives and Integrals, Series and Epilogue, illustrating a self-study path</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/spivak-calculus-3rd-edition-vs-4th-edition-what-changed</loc>
    <lastmod>2026-09-11T21:55:19-05:00</lastmod>
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      <image:title>Spivak&apos;s Calculus, 3rd Edition vs. 4th Edition: What Actually Changed</image:title>
      <image:caption>3rd edition (1994) arrow to 4th edition (2008), illustrating the changes between editions of Spivak&apos;s Calculus</image:caption>
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  <url>
    <loc>https://mathpop.com/blogs/news/physics-for-mathematicians-who-its-for-prerequisites-and-how-it-compares-to-arnold</loc>
    <lastmod>2026-09-14T02:41:15-05:00</lastmod>
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      <image:title>Physics for Mathematicians: Who It&apos;s For, What You Need First, and How It Compares to Arnold</image:title>
      <image:caption>Newton&apos;s F = ma with an arrow to Hamilton&apos;s symplectic form, illustrating the arc of Spivak&apos;s Physics for Mathematicians</image:caption>
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