Course Description

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

Course Documents

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: The Mean Value Theorem (§3.2)
• Exam 2
• Lecture 22: How Derivatives Affect the Shape of a Graph-The First Derivative Test (§3.3)
• Lecture 23: How Derivatives Affect the Shape of a Graph-The Second Derivative Test (§3.3)
• Lecture 24: Optimization Problems (§3.7)
• Lecture 25: Antiderivatives (§3.9)
• Lecture 26: Definite Integrals: The Definition (§4.1-4.2)
• Lecture 27: Definite Integrals: Approximating with Riemann Sums (§4.1-4.2)
• Lecture 28: The Fundamental Theorem of Calculus-Part 1 (§4.3)
• Lecture 29: The Fundamental Theorem of Calculus-Part 2 and Indefinite Integrals (§4.3-4.4)
• Lecture 30: The Substitution Rule-Part 1 (§4.5)
• Lecture 31: The Substitution Rule-Part 2 (§4.5)
• Exam 3
• Lecture 32: Areas Between Curves (§5.1)
• Lecture 33: Volumes (§5.2)
• Lecture 34: Work (§5.4)
• Lecture 35: Average Values (§5.5)
• Final Exam