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MATH 241 Calculus I
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1 Finding Limits
1.1 Introduction to Limits and One-sided Limits
1.2 Calculating Limits
1.3 Limits Involving Infinity
2 Applications of Limits
2.1 Continuity
2.2 Formal Treatment of Limits
2.3 Introduction to Finding Derivatives
3 Finding Derivatives
3.1 Basic Differentiation Rules
3.2 Derivatives of Trigonometric Functions
3.3 The Chain Rule
4 Applications of Differentiation
4.1 Derivatives as Rates of Change
4.2 Implicit Differentiation
4.3 Related Rates
4.4 Linear Approximation and Differentials
5 Curve Sketching
5.1 Maxima and Minima
5.2 Increasing and Decreasing Functions and First Derivatives
5.3 Concavity and Second Derivatives
5.4 Graphing Functions
5.5 The Mean Value Theorem
6 Optimization Problems
6.1 Optimization Problems
7 Integration
7.1 The Area Under a Curve
7.2 Definite Integrals and Properties of Integrals
7.3 Anti-Derivatives and The Fundamental Theorem of Calculus
7.4 Integrations by Basic (u) Substitutions
8 Applications of Integration
8.1 Velocity and Net Change
8.2 The Area Between Two Curves
8.3 Volumes by Slicing
8.4 Volumes of Solids Formed by Revolving Regions Around an Axis
8.5 Physical Applications (Density, Mass, Work)
MATH 241 Calculus I
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