- Lectures: Mon and Wed from 8:15 to 9:30am in 202.
- Recitations: Fri from 9:45 to 11:00am in 202.

A. Differentiation

- Essential Notions and Concepts
- Inverse and Implicit Functions Theorems
- Around Exchanges of limits
- Higher order derivatives
- Derivatives of parametric integrals

- Integration of functions on $\mathbb R^k$
- Differential Forms
- Definitions
- Computation rules
- Differentiation
- Change of variables
- Simplices and Chains
- Stokes Theorem, closed and exact forms

- J. Munkres.
*Analysis on Manifolds*. Addison-Wesley, Reading, 1991. - W. Rudin.
*Principles of Mathematical Analysis*. 3rd Edition, McGraw-Hill, 1974. - M. Spivak.
*Calculus on Manifolds.*Addison-Wesley, Readin, 1995. - W. Wade.
*Introduction to Analysis*. 4th Edition, Pearson, 2009.

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