Math 410 Description and Prerequisites

UM Undergraduate Catalog Course Description

More detailed outlines of some of the topics to covered can be found below and at
http://www.math.umd.edu/undergraduate/courses/syllabi/syllabusMATH410.shtml .

Course Prerequisites

• Math 240 and Math 241 or equivalents;
• Math 310 is recommended.

A More Detailed Outline

Real Numbers
     Natural, Integer, Rational, and Real Numbers
     Order, Positivity, Absolute Value, Bounds
     Least Upper Bound Axiom
     Sequences, Subsequences, Convergence
     Monotone Sequences, Limits Superior and Inferior
     Bolzano-Weierstrass Theorem, Nested Interval Theorem
     Cauchy Criterion, Completeness
Continuous Functions and Limits
     Continuity, Limits
     Extreme-Value Theorem, Intermediate-Value Theorem
     Uniform Continuity
Differentiation
     Algebra of Derivatives, Chain Rule
     Mean-Value Theorem, Taylor Approximation
     Cauchy Mean-Value Theorem, l'Hopital's Rule
Intergration
     Darboux and Riemann Sums, Integrability
     Linearity, Monotonicity, and Additivity over Intervals
     First Fundamental Theorem of Calculus
     Second Fundamental Theorem of Calculus
     Indefinite Integrals, Differential Equations
     Numerical Approximation of Integrals
Elementary Functions
     Natural Logarithm and Exponential Functions
     Trigonometric and Inverse Trigonometric Functions
Sequences and Series of Functions
     Sequences and Series of Numbers
     Pointwise Convergences and Uniform Convergence
     Uniform Limits of Continuous, Integrable, and Differentiable Functions
     Power Series