### 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.

#### 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