**Calculus**

Topic 1 Patterns to infinity

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