Differential and integral calculus: limits; continuity; the derivative and applications; extrema; the definite integral; fundamental theorem of calculus; L'Hopital's rule.
Prerequisite:
None
Course Outline:
Section 1.1 and 1.2: Ways to Represent a Function/Mathematical Models
Section 1.3: New Functions from Old
Section Appendix D: Trigonometry
Section 1.4: Exponential Functions
Section 1.5: Inverse Functions and Logarithms
Sections 2.1 and 2.2: Tangent and Velocity Problems/Limit of a Function
Section 2.3A: Calculating Limits, Part 1
Section 2.3B: Calculating Limits, Part 2
Section 2.4: Precise Definition of a Limit
Section 2.5A: Continuity, Part 1
Section 2.5B: Continuity, Part 2
Section 2.6: Limits at Infinity, Horizontal Asymptotes
Section 2.7: Derivatives and Rates of Change
Section 2.8: The Derivative as a Function
Section 3.1: Derivatives of Polynomials and Exponentials
Section 3.2: Product and Quotient Rules
Section 3.3: Derivatives of Trig Functions
Section 3.4: Chain Rule
Section 3.5: Implicit Differentiation
Section 3.6: Derivatives of Log Functions
Section 3.7: Rates of Change in the Natural and Social Sciences
Section 3.9: Related Rates
Section 4.1: Maximum and Minimum Values
Section 4.2: Mean Value Theorem
Section 4.3: Shape of a Graph
Section 4.4: L'Hospital's Rule
Section 4.5: Curve Sketching
Section 4.7A: Optimization, Part 1
Section 4.7B: Optimization, Part 2
Sections 4.8 and 3.10: Newton's Method/Linear Approximation
Section 4.9: Antiderivatives
Appendix E: Sigma Notation
Section 5.1/5.2A: Areas and Distances/Definition of Definite Integral
Section 5.2B: The Definite Integral
Section 5.3A: The Fundamental Theorem of Calculus, Part 1
Section 5.3B: The Fundamental Theorem of Calculus, Part 2
Section 5.4: Indefinite Integrals and Net Change
Section 5.5: Substitution