Welcome to Calculus with a Computer’s documentation!

Contents:

• Problem Set I
  • Question 1: Addition
  • Question 2: Multiplication
  • Question 3: Descartes
  • Question 4: Babylonian Algorithm for Square Root
  • Question 5: Functions with Python
• Introduction to Infinite Processes
  • Computing Square Roots
  • Problem 1: Using Approximation Formula
• What is \(\pi\)?
  • Rough Approximations
  • Problem II
  • Extra: Recurrence Relationships from Antiquity
  • Zeno’s Paradox
  • The Quadrature of the Parabola
  • Problem III: Approximating the Area under Parabola
  • Tossing a Coin
• Day 3: Functions
  • Linear Functions: College Debt
  • Linear Functions: Experiment
  • Quadratic Growth
  • Experiment: Quadratic
  • Exponential Functions
  • Experiment: Exponential Function
  • Harmonic Functions
  • Experiment: Sine and Cosine Functions
  • Weather in Central Park
• Functions and Summations
  • Functions and Summations
  • Riemann Sums
  • Problem
  • Taking it to the limit
  • Example of \(f(x) = x^2\)
  • Example of \(f(x) = \sin(x)\)
• Warm Up
  • Riemann Review
  • Getting Formal \(\Sigma\)
  • An Algorithm
  • A Definition
  • Using the Definition
  • A General Rule
  • Some Examples
  • Net Change
• More with the Definite Integral
  • More Rules of Integrals
  • Computing Solutions
  • Pure Symbolic Computing
  • Application I: Area Between Curves
  • A Creative Exercise
  • Functions in Higher Dimensions
• Wealth Distribution
  • Quadratic Fit
  • Inequality through Time
  • Census Bureau Data and Pandas
  • Volumes of Revolution
  • Practice
• Rates of Change
  • Slope and Rate of Change
  • Definition of Derivative
• Derivatives
  • Other Functions
• Optimization Problems
  • PROBLEM 1: Economics and Profit
  • PROBLEM
  • PROBLEM
  • A Second Approach
  • Extending the work
  • Curves vs. Surfaces
  • A Picture of 3D
  • Function in 3D
  • Slicing Dimensions
  • Analytic Solutions
  • PROBLEMS
  • The Second Derivative in 3D
  • Example
  • The Nested Loop
• Calculus: LMTH 2040
  • Course Description
  • Course Policies
  • Course Structure and Learning Outcomes
  • Course Outline
• Homework 2
  • Problem I: Media Consumption
  • Problem 5: Iris Data
  • Problem 6: Cars
  • Problem 7: Textbook Problems
  • Problem 8: Twitter
  • Problem 9: The Triangle
• Homework 3
• Review
  • Problem: Summations
  • Problem 2: Mean, Variance, Standard Deviation
  • Problem: Root Mean Squared Error
  • Problem: Area under a curve.
  • Problem: Area between curves
  • Problem: Volumes and Revolution
  • Problem: Gini Index
• PROBLEMS: FAST
• Homework: Derivatives Intro
  • PROBLEM I: Definition
  • PROBLEM II: Tables
  • PROBLEM III: Equations of Tangent Lines
  • PROBLEM IV: Shapes of curves

Indices and tables

• Index
• Module Index
• Search Page