Syllabus
Calculus
Sequences and Series
Introduction to sequences and series
Absolute convergence
Power series and representation of functions
Taylor and Maclaurin series

Functions of several variables
Limits and continuity
Polar coordinates and their properties
Partial derivatives, directional derivatives and the gradient vector
The chain rule
Maximum and minimum values
Lagrange multipliers

Integrals
Iterated integrals
Double integrals
Change of variables in multiple integrals
Stieltjes integral

Differential Equations
First order differential equations
Separable equations
Linear equations
Second order linear equations
Nonhomogeneous linear equations

Linear Algebra
Spaces and Subspaces
Bases and dimensions
Maximal sets
Abstract spaces and axiomatic approach
Eigenvectors and Eigenvalues
Diagonalization

Linear Operators
Linear transformations and matrix representations
Quadratic forms
Orthogonal operators
Inner product space

Convexity
Convex structures
Separation of convex sets

Textbooks
Lawrence E. Spence, Arnold J. Insel, Stephen H. Friedberg
Elementary Linear Algebra (Paperback)
Pearson Education; 2 edition (2007)
ISBN-10: 0131580345
ISBN-13: 978-0131580343

James Stewart
Calculus (International Metric Edition) (Paperback)
Brooks/Cole; International Edition (2008)
ISBN-10: 0495383627
ISBN-13: 978-0495383628

Teaching assistant
Mikhail Maslennikov