Calculus


Topic 1   Patterns to infinity

•  From limits of sequence to limits of functions
•  Squeeze theorem and algebra of limits of convergence sequences
•  Divergent sequences: indeterminate forms and evaluation of limits
•  From limits of sequences to limits of functions

 
 

Topic 2   Smoothness in Mathematics

•  Continuity and differentiability on an interval
•  Theorems about continuous functions
•  Differentiable functions: Rolle’s Theorem  and Mean Value Theorem
•  Limits at a point, indeterminate forms, and L’Hopital’s rule
•  Smooth graphs of functions
•  Limits of functions and limits of sequences

 



Topic 3   Modeling dynamic phenomena

•  Classifications of differential equations and their solutions
•  Differential Equations with separated variables
•  Separable variables, differential equations and graphs of their solutions
•  Modeling of growth and decay phenomena
•  First order exact equations and integrating factors
•  Homogeneous differential equations and substitution methods
•  Euler Method for first order differential equations

 
 

 
 
Topic 4   The finite in the infinite

•  Series and convergence
•  Introduction  convergence tests for series
•  Improper Integrals
•  Integral test for convergence
•  The p-series test
•  Comparison test for convergence
•  Limit comparison test for convergence
•  Ratio test for convergence
•  Absolute convergence of series
•  Conditional convergence of series

 




Topic 5   Everything polynomic

•  Representing functions by Power Series 1
•  Representing Power series as functions
•  Representing functions by Power Series 2
•  Taylor Polynomials
•  Taylor and Maclaurin Series
•  Using Taylor Series to approximate functions
•  Applications of power series