Part III: Calculus

The third part of the course consists of a sequence of seven lectures. We call it calculus as we work with functions, used for differentiation, integration, and approximation. Giving a dictionary with as default value an empty dictionary as last argument of a recursive functions works great for memoization.

• Lecture 18: Defining Mathematical Functions
  • Functions in SageMath and in Python
  • Step Functions
  • Piecewise Functions
  • Combining Functions
  • Assignments
• Lecture 19: Recursive Functions
  • Memoization in Python
  • Memoization in SageMath
  • Assignments
• Lecture 20: Computing with Functions
  • List Comprehensions
  • Composing Functions
  • Functions Returning Functions
  • Assignments
• Lecture 21: Symbolic and Numeric Differentiation
  • Symbolic Differentiation
  • Numerical Differentiation
  • Implicit Differentiation
  • Plotting the Tangent Line
  • Assignments
• Lecture 22: Integration and Summation
  • Indefinite and Definite Integrals
  • Assisting the Integrator
  • Symbolic Summation
  • Assignments
• Lecture 23: Series, Approximations, and Limits
  • Taylor Series
  • Taylor Series in SymPy
  • Power Series
  • Approximations
  • Limits
  • Assignments
• Lecture 24: Symbolic-Numeric Computation
  • Interval arithmetic
  • Symbolic-Numeric Factorization
  • Constrained Optimization
  • Assignments