Calculus 1 Class Notes
Copies of the classnotes are on the internet in PDF and Postscript
formats as given below.
Chapter 2: Limits and Continuity.
- Section 2.1: Rates of Change and Limits.
PDF.
PS.
- Section 2.2: Calculating Limits Using the Limit Laws.
PDF.
PS.
- Section 2.3: The Precise Definition of Limit.
PDF.
PS.
- Section 2.4: One-Sided Limits and Limits at Infinity.
PDF.
PS.
- Section 2.5: Infinite Limits and Vertical Asymptotes.
PDF.
PS.
- Section 2.6: Continuity.
PDF.
PS.
- Section 2.7: Tangents and Derivatives.
PDF.
PS.
- Study Guide.
PDF.
PS.
Chapter 3: Differentiation.
- Section 3.1: The Derivative as a Function.
PDF.
PS.
- Section 3.2: Differentiation Rules for Polynomials, Exponentials, Products and Quotients.
PDF.
PS.
- Section 3.3: The Derivative as a Rate of Change.
PDF.
PS.
- Section 3.4: Derivatives of Trigonometric Functions.
PDF.
PS.
- Section 3.5: The Chain Rule and Parametric Equations.
PDF.
PS.
- Section 3.6: Implicit Differentiation.
PDF.
PS.
- Section 3.7: Derivatives of Inverse Functions and Logarithms.
PDF.
PS.
- Section 3.8: Inverse Trigonometric Functions.
PDF.
PS.
- Section 3.9: Related Rates.
PDF.
PS.
- Section 3.10: Linearization and Differentials.
PDF.
PS.
- Study Guide.
PDF.
PS.
Chapter 4: Applications of Derivatives.
- Section 4.1: Extreme Values of Functions.
PDF.
PS.
- Section 4.2: The Mean Value Theorem.
PDF.
PS.
- Section 4.3: Monotone Functions and the First Derivative Test.
PDF.
PS.
- Section 4.4: Concavity and Curve Sketching.
PDF.
PS.
- Section 4.5: Applied Optimization Problems.
PDF.
PS.
- Section 4.6: Indeterminate Forms and L'Hopital's Rule.
PDF.
PS.
- Section 4.7: Newton's Method.
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PS.
- Section 4.8: Antiderviatives.
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PS.
- Study Guide.
PDF.
PS.
Chapter 5: Integration.
- Section 5.1: Estimating with Finite Sums.
PDF.
PS.
- Section 5.2: Sigma Notation and Limits of Finite Sums.
PDF.
PS.
- Section 5.3: The Definite Integral.
PDF.
PS.
- Section 5.4: The Fundamental Theorem of Calculus.
PDF.
PS.
- Section 5.5: Indefinite Integrals and the Substitution Rule.
PDF.
PS.
- Section 5.6: Substitution and Area Between Curves.
PDF.
PS.
- Study Guide.
PDF.
PS.
Chapter 6: Applications of Definite Integrals.
- Section 6.1: Volumes by Slicing and Rotation About an Axis.
PDF.
PS.
- Section 6.2: Volumes of Cylindrical Shells.
PDF.
PS.
- Section 6.3: Lengths of Plane Curves.
PDF.
PS.
- Section 6.4: Moments and Centers of Mass.
PDF.
PS.
- Study Guide.
PDF.
PS.
Additional notes presented in class are also available:
- A "Quick Guide" to the use of the TI-89 in Calculus 1.
PDF.
PS.
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