MATH 4B03

CALCULUS ON MANIFOLDS

Undergraduate

Review of multivariable calculus, basic properties of manifolds, differential forms, Stokes' theorem, de Rham cohomology and applications. Three lectures; one term

Fall 2025 · Calculus:Manifolds · C01

Readings

Etext An Introduction To Manifolds Permanent Access
Required
ISBN 9781441974006; 9781441973993

Fall 2025 · C01

Review of multivariable calculus, basic properties of manifolds, differential forms, Stokes' theorem, de Rham cohomology and applications. Three lectures; one term

Readings

An Introduction to Manifolds
Loring W Tu · 2010 · second · Required
Universitext, Springer-Verlag · ISBN 978-1-4419-7399-3; 978-1-4419-7400-6
Differential Forms with Applications to the Physical Sciences
H. Flanders · 1963 · Recommended / optional
Dover
Calculus on Manifolds
Michael Spivak · 1969 · Recommended / optional
Avalon Publishing · ISBN 978-081-334-6120
Differential Forms
V. Guillemin and P. Haine · 2019 · Recommended / optional
World Scientific · ISBN 978-981-327-2798

Sources