Differential and integral calculus

Limits and continuity

A:

  • Calculating limits – polynomials and rational functions
  • One-sided limits
  • Finding limits of functions from graphs

B:

  • Calculating limits – trigonometric functions
  • Calculating limits – functions with radicals
  • Continuity, discontinuity points

C:

  • Theoretical aspects related to limits calculations

Derivative

A:

  • Geometric interpretation of the derivative
  • Derivatives of elementary functions

B:

  • Derivative of a product of functions
  • Derivative of a quotient function
  • Derivative of a composite function

C:

  • Derivative of a composite function – complex problems
  • Applications of derivatives in physics

Analyzing function behavior

A:

  • Function’s monotonicity
  • Local extrema

B:

  • Second derivative and its geometric interpretation
  • Concavity and convexity of a function
  • Inflection points

C:

  • Asymptotes of a graph of a function

Applications of derivatives

A:

  • Calculating limits using L'Hospital's rule  

B:

  • Tangent line to graph of a function
  • Normal line to graph of a function

C:

  • Global extrema
  • Optimization problems (global extrema)

Primitive function

A:

  • Geometric interpretation of the antiderivative (primitive function)
  • Solving simple indefinite integrals (Finding a primitive function)

B:

  • Solving integrals requiring simplification of expressions
  • Solving integrals by substitution
  • Solving integrals by Parts

C:

  • Integrals solved by substitution – complex problems
  • Integrals solved by Parts – complex problems
  • Solving integrals requiring partial fraction decomposition

Definite integral

A:

  • Evaluation of simple definite integrals

B:

  • Evaluating integrals requiring simplification of expressions
  • Evaluating integrals using substitution
  • Evaluating integrals by Parts

C:

  • Evaluating integrals using substitution – complex problems
  • Evaluating integrals by Parts – complex problems
  • Evaluating integrals requiring partial fraction decomposition

Applications of definite integral

A:

  • The area of a plane region

B:

  • The volume of a solid

C:

  • The area of a plane region – complex problems
  • The volume of a solid – complex problems
  • Applications to physics