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Fundamentos da cálculo diferencial

Track :

Mathematics

Course Presenter :

matematica pt

Lessons no : 148

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What will you learn in this course?
  • Understand the concept of functions, limits, and continuity in differential calculus for mathematical analysis
  • Calculate derivatives of polynomial, rational, exponential, logarithmic, and trigonometric functions accurately
  • Apply differentiation rules such as sum, product, quotient, and chain rule to various functions
  • Interpret the geometric meaning of derivatives as slopes of tangent lines to curves in real-world contexts
  • Analyze rates of change and instantaneous variation in physics, economics, and engineering applications
  • Utilize derivatives to solve optimization problems and determine maximum or minimum values in practical scenarios
  • Develop skills to model real phenomena using differential calculus concepts and techniques
  • Enhance problem-solving abilities through practical exercises involving derivatives and their applications
  • Identify the relationship between derivatives and the shape or behavior of functions graphically
  • Apply limits and derivatives to understand the behavior of functions near specific points or asymptotes
  • Use derivatives to analyze motion, growth, and decay processes in scientific and economic models
  • Implement differentiation techniques to evaluate the sensitivity of functions to changes in variables
  • Interpret the significance of derivatives in analyzing the stability and dynamics of systems
  • Integrate geometric and algebraic methods to solve differential calculus problems effectively
  • Develop a foundational understanding necessary for progressing to integral calculus and advanced mathematical topics
  • Strengthen analytical thinking and mathematical reasoning skills through applied differential calculus exercises

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Lessons | 148
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Fundamentos da cálculo diferencial, apresenta os conceitos essenciais que formam a base do cálculo diferencial, ramo da matemática responsável por estudar taxas de variação e derivadas. Você aprenderá o que é uma função contínua, o limite de uma função e o conceito de derivada como medida da variação instantânea. O curso explica de forma intuitiva e prática como calcular derivadas de funções polinomiais, racionais, exponenciais, logarítmicas e trigonométricas, aplicando regras de derivação como soma, produto, quociente e cadeia. Também aborda interpretação geométrica, mostrando como a derivada representa a inclinação da reta tangente a uma curva. Com exemplos aplicados em física, economia e engenharia, o aluno compreenderá a importância do cálculo diferencial para analisar fenômenos de crescimento, movimento e otimização. Ao final, estará preparado para avançar no estudo do cálculo integral e aplicações matemáticas mais complexas. matematica pt