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Calculus I

Přírodovědecká fakulta Jihočeské University v Českých Budějovicích
Course type

Content of lectures:

  1. Review (Functions, Inverse Functions, Trig Functions, Exponential Functions, Logarithm Functions, Common Graphs)
  2. Limits (One-sided limits, Tangent Lines and Rates of Change, Limit Properties, Computing Limits, Limits Involving Infinity)
  3. Continuity (Definition, One-sided limits, Upper and Lower Bound Theorem, Mean Value Theorem)
  4. Derivatives (Definition, Interpretation of the Derivative, Non-differentiable functions)
  5. Differentiation Formulas (Product and Quotient Rule, Derivatives of Trig Functions, Derivatives of Exponential and Logarithm Functions, Derivatives of Inverse Trig Functions Derivatives of Hyperbolic Trig Functions, Chain Rule, Implicit Differentiation, Higher Order Derivatives)
  6. Applications of Derivatives (Critical Points, Minimum and Maximum Values, Increasing and Decreasing Functions, Inflection points, Concavity, the Second Derivative Test)
  7. Mean Value Theorem, Optimization Problems, L'Hospital's Rule and Indeterminate Forms, Linear Approximations, Differentials, Newton's Method Content of practicals: Functions, limits and derivatives. Various applications.
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