⚠️ DRAFT HANDOUT - NOT FINALIZED BY INSTRUCTOR - DO NOT PRINT YET

MATH-182 (Calculus II) Curriculum

Session 03 - Approximating Area

Handout Worksheet
Fall Semester 2026
Session Objectives & Overview

By the end of this session, you will be able to:

  • Asymptotic Thinking (Connecting Approximations to the Definite Integral)
  • Interval Partitioning and Sample Point Selection
  • Summation Mechanics and Function Evaluation

Micro-Lecture

Engineering Context: Engineering Calculus II Application

In real-world engineering, Riemann sums and definite integrals are vital for calculating the total accumulation of a quantity when its rate of change is constantly fluctuating. Aerospace engineers integrate variable thrust and atmospheric drag to determine a rocket's work and trajectory, while civil engineers integrate varying fluid pressure to calculate the total hydrostatic force acting against a dam. Similarly, electrical engineers integrate fluctuating power consumption over time to monitor grid energy usage, and modern simulation software (like MATLAB or ANSYS) utilizes computerized, high-speed Riemann sums to break complex fluid dynamics or structural stresses into millions of microscopic pieces for precise numerical analysis.

Skill Block 1

Regroup 1

  • Review common misconceptions and clarify key notations.

Skill Block 2

Regroup 2

  • Reflect on the physical modeling applications and mathematical setups.

Skill Block 3

Regroup 3

  • Verify calculations and mathematical reasoning.

Synthesis Wrap-up

  • Core takeaways from Session 03 and overview of homework homework assignment.