Calculus 120

Unit 1: Calculus

Differential and integral calculus: rates of change, the derivative and its rules, applications of the derivative (curve sketching, optimization, related rates), and the definite integral and its applications.

• Average and instantaneous rate of change
• The derivative from the definition

• Constant, power, sum, and difference rules
• Product and quotient rules
• Derivatives of trigonometric functions
• The chain rule
• Inverse trigonometric functions
• Limits and derivatives of exponential and logarithmic functions

• Analyzing a function for curve sketching
• Sketching the graph from the analysis
• Optimization problems
• Applied optimization in context
• Linearization and Newton's Method
• Related rates

• The definite integral
• Antiderivatives
• Integration to find area and accumulation
• Integral applications in science, economics, and business