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If you’re preparing for AP Calculus AB and want a book that teaches you calculus from the ground up, with clear explanations and a problem-solving focus, The Calculus by Louis Leithold has been a trusted resource for decades.
Many students feel intimidated when they first encounter calculus — the jump from algebra and trigonometry to limits, derivatives, and integrals can feel huge. For USAn and NRI students, there’s also the added challenge of balancing school curriculum with AP exam preparation, often across completely different education systems.
Here’s a chapter-wise breakdown of AP Calculus AB–relevant sections from The Calculus by Louis Leithold:
| Chapter | Topics Covered |
| 1. Functions, Graphs, and Models | Understanding functions, domains, ranges, transformations |
| 2. Limits and Continuity | Definition of limits, evaluating limits, continuity, one-sided limits |
| 3. The Derivative | Derivative as a limit, differentiation rules, implicit differentiation |
| 4. Applications of Derivatives | Tangent lines, extrema, related rates, optimization |
| 5. The Integral | Antiderivatives, area under curves, definite integrals, Fundamental Theorem of Calculus |
| 6. Applications of the Integral | Area between curves, volumes, average value of a function |
| 7. Transcendental Functions | Exponential and logarithmic differentiation, inverse trig functions |
| 8. Differential Equations | Separable equations, slope fields, modeling with differential equations |
| 9. Sequences and Series (BC-level, but helps with AP AB enrichment) | Infinite series, convergence tests, Taylor series basics |
| Appendix | Formula sheet, graphing tips, and practice sets |
Along with the main book, I’m also giving you a bonus TestprepKart eBook. This is not an academic textbook. It’s more of a helpful guide that answers many common questions students have about AP exams.
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