🎓 Differential and Integral Calculus Course

calculus
mathematics
derivatives
integrals
functions
limits
courses
differential equations
Taylor series
Introduction to Calculus with elegant theory (LaTeX), Quarto visuals, and examples in R/Python — with Advanced Path (AP) tracks.
Author

Blog do Marcellini

Published

August 23, 2025

← Mathematics Courses · ← Mathematics Section

Portrait of Isaac Newton, one of the founders of Calculus
Isaac Newton
Portrait of Gottfried Wilhelm Leibniz, one of the founders of Calculus
Gottfried Wilhelm Leibniz

1 🧮 Welcome to the Course

Note

This course was designed to master Limits, Derivatives, and Integrals with rigor, visualizations, and solved exercises, integrating LaTeX, Quarto, R, and Python.

Tip

AP Tracks (Advanced Path). Each module includes an AP track with more advanced topics that can be read later, without breaking the main flow.

1.1 📘 Objectives

  • Develop mathematical reasoning in limits, derivatives, and integrals;
  • Present applications (Physics, Engineering, Economics, Computer Science);
  • Explore problem solving with graphs and computational tools.

🧩 Quick Prerequisites

  • Basic algebra: algebraic manipulation, inequalities, factorization;
  • Notions of functions and Cartesian graphs;
  • Comfort with mathematical notation (∑, ε–δ will appear in AP).

📚 Course Outline

  • Definition of derivative (in progress)
  • Differentiation rules (in progress)
  • Applications: maxima, minima, and optimization (in progress)
  • Implicit and logarithmic derivatives (in progress)
  • Definite and indefinite integral (in progress)
  • Integration techniques (in progress)
  • Areas and volumes (in progress)
  • Physical applications (in progress)
  • Differential equations (in progress)
  • Taylor series (in progress)
  • Modeling with calculus (in progress)
  • Computational tools (in progress)

1.2 🚀 How to Study

  • Follow the suggested order. Read the central idea before the formal proof.
  • Solve the proposed exercises and then check the annotated solutions.
  • Run the R/Python scripts (folder code/) to explore the examples.
  • Use the AP topics to deepen concepts without losing pace.

Code: R and Python scripts are located in posts/courses/mathematics/calculus/code/ and are included in the lessons.

Project standard: graphs are generated by dedicated .py/.R scripts (outside the .qmd) to facilitate reuse and traceability.

2 📚 References

  • Anton, Howard; Bivens, Irl; Davis, Stephen. Calculus - Volume I, 10th ed. Bookman, 2014.
  • Courant, Richard; John, Fritz. Introduction to Calculus and Analysis - Volume I. Wiley, 1965.
  • Guidorizzi, Hamilton Luiz. Um Curso de Cálculo - Volume 1, 5th ed. LTC, 2001.
  • Leithold, Louis. The Calculus with Analytic Geometry - Volume 1, 3rd ed. Harbra, 1994.
  • Lima, Elon Lages. Curso de Análise - Volume 1, 11th ed. IMPA, 2004.
  • Simmons, George F. Calculus With Analytic Geometry, 2nd ed. McGraw-Hill, 1985.