# Differential and integral calculus

The topic is divided into the following subtopics:
• Limits and continuity
• Derivative
• Analyzing function behavior
• Applications of derivatives
• Primitive function
• Definite integral
• Applications of definite integral

### Limits and continuity

Part I:
• Calculating limits – polynomials and rational functions
• One-sided limits
• Finding limits of functions from graphs
Part II:
• Calculating limits – trigonometric functions
• Calculating limits – functions with radicals
• Continuity, discontinuity points
Part III:
• Theoretical aspects related to limits calculations

### Derivative

Part I:
• Geometric interpretation of the derivative
• Derivatives of elementary functions
Part II:
• Derivative of a product of functions
• Derivative of a quotient function
• Derivative of a composite function
Part III:
• Derivative of a composite function – complex problems
• Applications of derivatives in physics

### Analyzing function behavior

Part I:
• Function’s monotonicity
• Local extrema
Part II:
• Second derivative and its geometric interpretation
• Concavity and convexity of a function
• Inflection points
Part III:
• Asymptotes of a graph of a function

### Applications of derivatives

Part I:
• Calculating limits using L'Hospital's rule
Part II:
• Tangent line to graph of a function
• Normal line to graph of a function
Part III:
• Global extrema
• Optimization problems (global extrema)

### Primitive function

Part I:
• Geometric interpretation of the antiderivative (primitive function)
• Solving simple indefinite integrals (Finding a primitive function)
Part II:
• Solving integrals requiring simplification of expressions
• Solving integrals by substitution
• Solving integrals by Parts
Part III:
• Integrals solved by substitution – complex problems
• Integrals solved by Parts – complex problems
• Solving integrals requiring partial fraction decomposition

### Definite integral

Part I:
• Evaluation of simple definite integrals
Part II:
• Evaluating integrals requiring simplification of expressions
• Evaluating integrals using substitution
• Evaluating integrals by Parts
Part III:
• Evaluating integrals using substitution – complex problems
• Evaluating integrals by Parts – complex problems
• Evaluating integrals requiring partial fraction decomposition

### Applications of definite integral

Part I:
• The area of a plane region
Part II:
• The volume of a solid
Part III:
• The area of a plane region – complex problems
• The volume of a solid – complex problems
• Applications to physics