Calculus

These notes organize Stewart's Essential Calculus: Early Transcendentals scope into a compact study path from single-variable foundations through vector calculus. The source PDF available in this workspace is the Appendix E odd-answer material, so the structure follows the chapter and exercise coverage reflected there: functions and limits, derivatives and their applications, integrals and integration techniques, infinite series, parametric and polar curves, vectors and space geometry, partial derivatives, multiple integrals, and the major theorems of vector calculus.

Each page is written as a self-contained reference: an intuition paragraph, formal definitions and theorems, derivations where useful, worked examples, and common pitfalls. Use the sequence below as the primary reading order. The first half builds the single-variable toolkit; the second half extends the same ideas to curves, surfaces, fields, and higher-dimensional accumulation.

1. Functions and Models
2. Limits and Continuity
3. Derivatives and Rates
4. Differentiation Rules
5. Implicit Differentiation and Linearization
6. Exponential Log and Inverse Functions
7. Applications of Derivatives
8. Optimization Newton and Antiderivatives
9. Definite Integrals and the Fundamental Theorem
10. Integration Techniques and Improper Integrals
11. Applications of Integrals
12. Sequences and Series
13. Power Series and Taylor Polynomials
14. Parametric Polar and Conic Curves
15. Vectors and Geometry of Space
16. Vector Functions and Motion
17. Partial Derivatives and the Gradient
18. Extrema and Lagrange Multipliers
19. Multiple Integrals
20. Vector Calculus