Math 1500: Analytic Geometry & Calculus I

Course Description

This course is devoted to the study of elementary analytic geometry, functions, limits, continuity, derivatives, antiderivatives, and definite integrals.

Prerequisites

Course Documents

Sections covered and Practice Problems
Tentative Course Calendar

Course Outline

(Sections listing are from Stewart's Calculus, 9th Edition)

  • Lecture 01: Introduction to Calculus
  • Lecture 02: Limits-Part 1 (§1.4-1.5)
  • Lecture 03: Limits-Part 2 (§1.4-1.5)
  • Lecture 04: Calculating Limits Using Limits Laws and Continuity (§1.6)
  • Lecture 05: Calculating Limits-0/0 Scenarios (§1.6)
  • Lecture 06: Calculating Limits-Piecewise Defined Functions, The Squeeze Theorem (§1.6)
  • Lecture 07: Limits at Infinity (§3.4)
  • Lecture 08: Continuity (§1.8)
  • Lecture 09: The Derivative (§2.1)
  • Lecture 10: The Derivative as a Function (§2.2)
  • Lecture 11: Rules for Differentiation-The Power Rule and Polynomials (§2.3)
  • Exam 1
  • Lecture 12: Rules for Differentiation-Product and Quotient Rules (§2.3)
  • Lecture 13: Derivatives of Trigonometric Functions (§ 2.4)
  • Lecture 14: The Chain Rule (§ 2.5)
  • Lecture 15: Strategies for Differentiation (§2.5)
  • Lecture 16: Linear Approximation (§2.9)
  • Lecture 17: Implicit Differentiation (§2.6)
  • Lecture 18: Related Rates (§2.8)
  • Lecture 19: Maximum and Minimum Values-Critical Numbers (§3.1)
  • Lecture 20: Maximum and Minimum Values-The Closed Interval Method (§3.1)
  • Lecture 21: How Derivatives Affect the Shape of a Graph-The First Derivative Test (§3.3)
  • Lecture 22: How Derivatives Affect the Shape of a Graph-The Second Derivative Test (§3.3)
  • Lecture 23: How Derivatives Affect the Shape of a Graph-Points of Inflection (§3.3)
  • Exam 2
  • Lecture 24: Optimization Problems (§3.7)
  • Lecture 25: The Mean Value Theorem (§3.2)
  • Lecture 26: Antiderivatives (§3.9)
  • Lecture 27: Definite Integrals: The Definition (§4.1-4.2)
  • Lecture 28: Definite Integrals: Approximating with Riemann Sums (§4.1-4.2)
  • Lecture 29: The Fundamental Theorem of Calculus-Part 1 (§4.3)
  • Lecture 30: The Fundamental Theorem of Calculus-Part 2 and Indefinite Integrals (§4.3-4.4)
  • Lecture 31: The Substitution Rule-Part 1 (§4.5)
  • Lecture 32: The Substitution Rule-Part 2 (§4.5)
  • Lecture 33: Areas Between Curves (§5.1)
  • Lecture 34: Volumes (§5.2)
  • Lecture 35: Work (§5.4)
  • Lecture 36: Average Values (§5.5)
  • Exam 3