M2231 Calculus I

Review Topics

2.1 Introduction to Calculus
2.2 Introduction to Limits
2.4 One-Sided Limits
2.3 The Formal Definition of the Limit
2.5 Introduction to Continuity
2.6 Infinite Limits and Limits at Infinity
Study Resources for Limits and Continuity

3.1/3.2 Introduction to the Derivative
3.3 Basic Derivative Rules
3.4 Position, Velocity, and Acceleration
3.5 Trigonometric Derivatives
3.6 The Chain Rule
3.7 Implicit Differentiation
3.8 Derivatives of General Exponential and General Logarithmic Functions
3.9 Derivatives of Inverse Trig Functions
3.10 Related Rates Problems
3.11 Linearization
Study Resources for Derivatives

4.1 Extreme Values on Closed Intervals and Critical Points
4.2 The Mean Value Theorem
4.3 The First Derivative Test for Extrema
4.4 Graphing
4.5 L'Hopital's Rule
4.6 Optimization
4.7 Newton's Method
4.8 Antiderivatives

5.1 Area Estimates and Riemann Sums
5.2 Sigma Notation and Riemann Sums as n->Infinity
5.3 Definite Integrals and Using Known Area Formulas to Calculate Definite Integrals
5.4 The Fundamental Theorem of Calculus
5.5 The Substitution Method with Indefinite Integrals
5.5 The Substitution Method with Indefinite Integrals

7.1 The Logarithm Defined as an Integral
7.2 Separable Differential Equations and Exponential Growth or Decay