Chapter 10 — Further Reading

Every entry below says what to read and why, and maps our sections to the corresponding treatments in the two reference texts (Stewart and OpenStax, per the continuity tracker §8). Use these to see a second voice on the same ideas, to find more drill problems, or to push past the single-variable boundary of this chapter.

Textbook Section Mapping

The whole of Chapter 10 corresponds to a single, famous section in each reference text — applied optimization is traditionally taught as one big unit.

Full chapter-by-chapter cross-references for the whole book live in appendices/appendix-h-stewart-chapter-mapping.md and appendices/appendix-i-openstax-chapter-mapping.md.

Primary Reference Texts

• Stewart, Calculus: Early Transcendentals (9th ed.), §4.7 — Optimization Problems. The canonical treatment our chapter is benchmarked against. Stewart's six-step problem-solving strategy is essentially our §10.3, and his worked examples (the fence, the can, the closest point, the least-time swim) parallel ours closely. Read it for a second pass on the same archetypes and, above all, for its large and well-graded exercise set — the best source of additional drill. Pair §4.7 with §4.1 for the closed-interval method underpinning our §10.4.

• OpenStax, Calculus Volume 1 (Strang & Herman), §4.7 — Applied Optimization Problems. Free and open-licensed. Its "Problem-Solving Strategy: Solving Optimization Problems" mirrors our procedure step for step, and its solved examples include the open box and the inscribed-rectangle problems from our exercises. Read it for a slightly gentler pace, fully worked solutions, and an honest companion to this book. Its §4.3 (Maxima and Minima) covers the EVT and Fermat's theorem we lean on in §10.4.

• Spivak, Calculus (4th ed.), Chapter 11 (Significance of the Derivative). The rigorous, proof-first treatment. Read it for the careful statements and proofs behind why $f'(c) = 0$ at an interior extremum and exactly when the closed-interval method is valid — the "Formal" rigor level of our §10.4 taken further. For math majors who want the theorems airtight.

On the Economic Applications (§10.10–§10.11)

• Harris, F. W. (1913), "How Many Parts to Make at Once." The original EOQ derivation — short, concrete, and historically delightful (see the §10.11 Historical Note). Read it for the realization that the square-root inventory law predates its calculus dressing and came straight from the factory floor.

• Varian, Intermediate Microeconomics: A Modern Approach. The standard undergraduate micro text. Read it for the economic meaning of marginal revenue = marginal cost (§10.10) and average-cost minimization (Exercise E6) — calculus results that are the backbone of the theory of the firm.

• Nahmias & Olsen, Production and Operations Analysis (7th ed.). Read it for the EOQ extended to quantity discounts, backorders, and uncertain demand — exactly the "grow the objective function" exercises our Case Study 1 gestures toward. The bridge from clean derivative to messy supply chain.

On the Biological Applications (§10.12)

• Charnov, E. L. (1976), "Optimal foraging, the marginal value theorem," Theoretical Population Biology 9, 129–136. The founding paper for our §10.12. Read it for the elegant derivation of $g'(t^*) = g(t^*)/(\tau + t^*)$ and a vivid example of calculus reshaping a biological field. Short and accessible.

• Stephens & Krebs, Foraging Theory (Princeton, 1986). The standard graduate reference. Read it for the marginal value theorem developed rigorously with variants (predation risk, information, patch depletion) — the natural next step after Case Study 2's discussion questions.

• Kacelnik, A. (1984), "Central place foraging in starlings," J. Animal Ecology 53, 283–299. Read it for a model experiment that tested a calculus prediction against live birds and found them obeying the marginal value theorem — the empirical heart of Case Study 2.

On the Physics and Engineering Applications (§10.8, §10.14)

• Feynman, The Feynman Lectures on Physics, Vol. I, Ch. 26 (Optics: The Principle of Least Time). Read it for the deepest version of our §10.8 lifeguard/Snell's-law connection — Fermat's principle that light takes the least-time path, and why nature "optimizes" without computing. One of the finest pieces of physics exposition ever written.

• Any introductory circuits text (e.g., Sadiku, Fundamentals of Electric Circuits) on the maximum power transfer theorem for the impedance-matching result of §10.14 in its engineering home.

Looking Past Single-Variable Optimization (§10.16)

• Stewart, §14.7–14.8, or OpenStax Calculus Vol. 3, §4.7–4.8. Read these next to meet $\nabla f = \mathbf{0}$, the Hessian second-derivative test, and Lagrange multipliers — the multivariable machinery our §10.16 previews and our Chapter 31 develops in full. The geometric punchline there (gradients of objective and constraint becoming parallel at the optimum) is the multivariable echo of the perpendicularity in our §10.7.

• Boyd & Vandenberghe, Convex Optimization (free PDF, Cambridge). Read it for where this all leads in modern applied math: large-scale optimization, why convexity (our constant-concavity argument, §10.15) guarantees global optima, and the gradient-descent algorithms (our Ch. 6 / Ch. 30 anchor) that power machine learning. Ambitious but the gold-standard reference.