Author Oliver Knill About This Book Math 22b, Harvard College, Spring 2022 Table of Contents 1. Pythagorean Theorem 2. Gauss-Jordan Elimination 3. Definitions, Theorems, and Proofs 4. Cross Product 5. Surfaces 6. Visual Proofs 7. Curves 8. Arc Length 9. Intuition 10. Coordinates 11. Parametrization 12. Creativity 13. Partial Differential Equations 14. First Hourly 15. Contradiction and Deformation 16. Chain Rule 17. Taylor Approximation 18. Number Magic 19. Extrema 20. Constraints 21. Island Mathematics 22. Double Integrals 23. Substitution 24. How to Solve: Literature Samples 25. Solids 26. Surface Area 27. A Visit by Archimedes 28. Second Hourly 29. Line Integrals 30. Perpetual Motion Machines 31. Green's Theorem 32. Stokes' Theorem 33. Discrete Vector Calculus 34. Gauss' Theorem 35. Generalized Stokes Theorem 36. A Discrete World 37. Review: Geometries and Fields 38. Review: Calculus in Hyperspace 39. Final Exam