References: calculus

The calculus modules cite the entries below by bracketed tags such as [O1FTC]; each tag in the text links here. The explanations, worked examples, exercises, and solutions in this book are original: they are not copied from the books cited in this chapter. Brief theorem statements express established mathematics. The hypotheses stated in this book are sometimes deliberately stronger, and easier to check, than the most general versions of the theorems.

Learning design#

[L1] Pashler et al. (2007). Organizing Instruction and Study to Improve Student Learning. Institute of Education Sciences practice guide. Supports the general learning design; it does not establish the particular review intervals used here as an optimum.

ies.ed.gov/ncee/wwc/practiceguide/1

[L2] Roediger and Karpicke (2006). Test-enhanced learning: taking memory tests improves long-term retention. Psychological Science, 17, 249–255. DOI: 10.1111/j.1467-9280.2006.01693.x. A retrieval-practice study, not a calculus-grade prediction.

pubmed.ncbi.nlm.nih.gov/16507066/

Open mathematical references#

Gilbert Strang and Edwin Herman, Calculus, Volumes 1–3, OpenStax / Rice University. Each linked entry names the official section it supports. The explanations and exercises in this book are not copied solutions from these books. The same sections are good places to continue on your own.

Volume 1#

[O1F] Function review. OpenStax Volume 1, section 1.1.

[O1L] Limits and precise limit definitions. OpenStax Volume 1, section 2.5.

[O1D] Derivative definitions and differentiability. OpenStax Volume 1, section 3.2.

[O1Ch] Chain rule. OpenStax Volume 1, section 3.6.

[O1Inv] Inverse-function derivatives. OpenStax Volume 1, section 3.7.

[O1Rates] Related rates. OpenStax Volume 1, section 4.1.

[O1MVT] Mean Value Theorem. OpenStax Volume 1, section 4.4.

[O1Apps] Applied optimization. OpenStax Volume 1, section 4.7.

[O1LH] L’Hopital’s rule. OpenStax Volume 1, section 4.8.

[O1Int] Definite integral. OpenStax Volume 1, section 5.2.

[O1FTC] Fundamental Theorem of Calculus. OpenStax Volume 1, section 5.3.

Volume 2#

[O2Vol] Volumes by slicing. OpenStax Volume 2, section 2.2.

[O2Apps] Physical applications. OpenStax Volume 2, section 2.5.

[O2Parts] Integration by parts. OpenStax Volume 2, section 3.1.

[O2Trig] Trigonometric integration and substitution. OpenStax Volume 2, section 3.3.

[O2PF] Partial fractions. OpenStax Volume 2, section 3.4.

[O2Num] Numerical integration and error bounds. OpenStax Volume 2, section 3.6.

[O2Improper] Improper integrals. OpenStax Volume 2, section 3.7.

[O2ODE] First-order linear differential equations. OpenStax Volume 2, section 4.5.

[O2Seq] Sequences. OpenStax Volume 2, section 5.1.

[O2Tests] Series divergence and integral tests. OpenStax Volume 2, section 5.3.

[O2Alt] Alternating series. OpenStax Volume 2, section 5.5.

[O2Power] Power series and their properties. OpenStax Volume 2, section 6.2.

[O2Taylor] Taylor polynomials and series. OpenStax Volume 2, section 6.3.

[O2Param] Calculus of parametric curves. OpenStax Volume 2, section 7.2.

[O2Polar] Polar area and arc length. OpenStax Volume 2, section 7.4.

Volume 3#

[O3Vectors] Lines and planes in space. OpenStax Volume 3, section 2.5.

[O3Curves] Arc length and curvature. OpenStax Volume 3, section 3.3.

[O3Limits] Multivariable limits and continuity. OpenStax Volume 3, section 4.2.

[O3Diff] Tangent planes and differentiability. OpenStax Volume 3, section 4.4.

[O3Chain] Multivariable chain rules. OpenStax Volume 3, section 4.5.

[O3Grad] Directional derivatives and gradient. OpenStax Volume 3, section 4.6.

[O3Opt] Lagrange multipliers. OpenStax Volume 3, section 4.8.

[O3Double] Double integrals over general regions. OpenStax Volume 3, section 5.2.

[O3Triple] Triple integrals and bounds. OpenStax Volume 3, section 5.4.

[O3Jac] Change of variables. OpenStax Volume 3, section 5.7.

[O3Line] Line integrals. OpenStax Volume 3, section 6.2.

[O3Conservative] Conservative vector fields. OpenStax Volume 3, section 6.3.

[O3Green] Green’s theorem. OpenStax Volume 3, section 6.4.

[O3Surface] Surface integrals. OpenStax Volume 3, section 6.6.

[O3Stokes] Stokes’ theorem. OpenStax Volume 3, section 6.7.

[O3Div] Divergence theorem. OpenStax Volume 3, section 6.8.

Selected OpenStax pages, including the derivative definition, the divergence and integral tests for series, and the Divergence theorem, were rechecked on 5 September 2026; not every link above was reopened on that date. Confirm that a section still matches its tag before you rely on the link.