I. Introduction
Calculus is the math of change and accumulation; derivatives describe how something changes in an instant, and integrals describe how quantities add up over an interval.
II. Outline
- Calculus I - Single-Variable Differentiation
- Limits, Continuity
- Derivative Rules
- Applications
- Calculus II - Single-Variable Integration
- Fundamental Theorem of Calculus
- Integration techniques
- Applications
- Sequences & Series
- Calculus III - Multivariable Calculus
- Vectors and 3D geometry
- Partial Derivatives
- Multiple Integrals
- Vector Fields & Line/Surface Integrals
- Divergence & Gradient, Related Theorems
- Calculus IV - Differential Equations
- First-order ODEs (separable, linear, exact)
- Second-order linear ODEs (homogeneous/forced, oscillations)
- Laplace transforms
- Systems of ODEs
- eigenvalues/eigenvectors connection
- Modeling Applications
III. Free Books
- Univ. of Minnesota Open Library - Calculus Textbooks
- I recommend Elementary Calculus by Corral or Multivariable Calculus by Shinamoto
- ActiveCalculus.org
- Paul’s Online Notes
- Scroll down to see the different classes, then click notes.
IV. Video Series
- MIT OpenCourseWare
- Visual intuition (great alongside a main course)
