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5.2 Getting started with symbolics
==================================

1. Define symbolic expressions in sage(0.29 - 2.52)
   * Exercise 1: Define given expressions as symbolic expressions(3.03 - 3.44)

#. Use built-in constants and functions
   * built-in constants(3.46 - 4.59)
   * built-in functions(5.00 - 6.02)
   * Exercise 2: Combined problem of built-in constants and functions(6.06 - 7.00)

#. Define Symbolic functions
   * Define arbitary functions(7.03 - 8.09)
   * Define functions piecewise(8.10 - 9.19)
   * Define functions convergent series & other series(9.20 - 11.37)
   * Exercise 3:Define a piecewise function(11.43 - 12.57)

#. Perform calculus using sage
   * Differentiation(12.58 - 14.36)
   * Integration(14.37 - 15.16)
   * Find factors(15.17 - 15.45)
   * Simplify(15.46 - 16.31)
   * Find roots and substitute(16.32 - 18.02)
   * Exercise 4: Perform calculus on given expressions(18.07 - 19.51)

#. Matrices in Sage(19.52 - 20.56) 
   * Exercise 5: Find the determinant and inverse of the given expression(20.57 - 21.43)

#. Summary(21.46 - 22.27)

#. Evaluation Questions(22.28 - 23.2s1)