Help Videos & Practice Problems for MATH 2413
Calculus I
The following help materials contain practice problems, worked-out solutions, and video lessons for the topics below. Though not an exact match to every section of MATH 2413 content, they can serve as a helpful supplement to the course material.
The videos referenced in these help materials are from the Video Calculus series, created by Selwyn Hollis. A similar but larger set of help materials covering a wide array of Calculus I and II topics can be found at our AP Calculus Help by Topic page.
Note: MATH 2413 was formerly named MATH 1431.
Limits and Continuity (Chapter 1)
- Calculating limits intuitively
- The definition of a limit
- The arithmetic of limits; limits of sums, differences, products and quotients
- Continuity, including the Intermediate and Extreme Value Theorems
- Trigonometric limits
Differentiation (Chapter 2)
- Definition of the derivative; calculating derivatives using the definition; interpreting the derivative as the slope of the tangent line
- Differentiation formulas; the power, product, reciprocal, and quotient rules
- The chain rule
- Differentiating trigonometric functions
- Higher Order Derivatives
- Implicit differentiation
Applications of the Derivative (Chapters 3 & 5)
- Rates of change per unit time; related rates
- Velocity and Acceleration
- Rolle's Theorem and the Mean Value Theorem
- Critical numbers and the first derivative test
- Concavity and the second derivative test
- Curve sketching
- Extreme values on intervals
- Optimization problems
- L'Hospital's Rule
- Differentials and Newton's method
Integration (Chapter 6)
- The definite integral; Riemann sums, area, and properties of the definite integral
- The fundamental theorem of calculus
- Area; area under a curve, area between two curves
- Anti-differentiation and indefinite integrals
- Integration by substitution
- Mean Value Theorem for integrals; average value