Calculus-I-PUC

This is a repository, that have all my TA and my personal textbook of Calculus/Analysis I at PUC .

content organization

The repository is organized in the following way:'

• generals contains textbook of excersis, the resume and the specification of the content covered in the course.
• Teacher-assistant contains the content of the teacher-assistant, that is the content that I have to teach to the students.

Then I have the following folders, that have the resume, the exercises, the solutions and my teachers assistans maded of the topics of the course:

• Limits contains the content of the limits topic.
• Derivatives contains the content of the derivatives topic.
• Integrals contains the content of the integrals topic.

Program of the course

• Limits:
  • Precise definition of a limit
  • Polynoms and Squares Limit
  • Trigonometrics Limit
  • Limit at Infinity
  • Sandwich Theorem
  • Asintotic Limit
  • Continuity
  • Intermediate Value Theorem
• Derivates
  • Definition
  • Derivation rules
  • The Chain rule
  • Implicit Differentiation
  • Inverse function
  • Rate of Change
• Aplication of Derivates
  • Rolle's Theorem
  • The Mean Value Theorem (TVM)
  • Maximun, Minimun and grafics functions
  • L'Hopital
  • Optimization Problems
  • Antiderivatives
• Integrals:
  • Rieman Sums
  • Fundamental Theorem of Calculus
  • The Substitution Rule
• Aplication of Integrals:
  • Areas Between Curves
  • Volumes
• Techniques of integration
  • Integration by Parts
  • Trigonometric Integrals
  • Trigronometric Substitution
  • Integration of Rational Funcions by Partial Fractions

Guide text:

• STEWART, J. (2007). Essential calculus: early transcendentals. Belmont, CA, Thomson Higher Education.