Amy DeCelles' Calculus Notes

Math 1271, Outlines and Worked Examples

Review (outline)
Warm-up Exercises (problems and answers)
The Basics of Exponentials and Logarithms
Section 2.1: The Tangent and Velocity Problems
Section 2.2: The Limit of a Function
Section 2.3: The Limit Laws
Section 2.4: The Precise Definition of the Limit
Graph examples for 2.4
Section 2.5: Continuity
Section 2.6: Limits at Infinity
Section 2.7: Derivatives and Rates of Change
Section 2.8: The Derivative as a Function
Section 3.1: Derivatives of Polynomials and Exponential Functions
Section 3.2: The Product Rule and the Quotient Rule
Section 3.3: Derivatives of Trigonometric Functions
Section 3.4: The Chain Rule
Section 3.5: Implicit Differentiation
Section 3.6: Derivatives of Logarithmic Functions
Section 3.8: Exponential Growth and Decay
Section 3.9: Related Rates
Section 3.10: Linear Approximation and Differentials
Section 4.1: Maximum and Minimum Values
Section 4.2: The Mean Value Theorem
Section 4.3: How Derivatives Effect the Shape of a Graph
Section 4.4: Indeterminate Forms and L'Hospital's Rule
Section 4.5: Curve Sketching
Section 4.7: Optimization
Section 4.9: Antiderivatives
Section 5.1: Areas and Distances
Section 5.2: The Definite Integral
Handout on Volumes

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decel004@math.umn.edu