Math 2413 Calculus I
These notes are based on Larson’s Calculus, 10th Edition.
1.2: Finding limits graphically and numerically
1.3: Evaluating limits analytically
1.4: Continuity and one-sided limits
1.5: Infinite limits
3.5: Limits at infinity
2.1: The derivative and the tangent line problem
2.2: Basic differentiation rules and rates of change
2.3: Product and quotient rules and higher order derivatives
2.4: The chain rule
2.5: Implicit differentiation
2.6: Related rates
3.1: Extrema on an interval
3.2: Rolle’s Theorem and the Mean Value Theorem
3.3: Increasing and decreasing functions and the First Derivative Test
3.4: Concavity and the Second Derivative Test
3.6: A summary of curve sketching
3.7: Optimization problems
3.9: Differentials
4.1: Antiderivatives and indefinite integration
4.2: Area
4.3: Riemann sums and definite integrals
4.4: The Fundamental Theorem of Calculus
4.5: Integration by substitution
5.1: The natural logarithmic function – differentiation
5.2: The natural logarithmic function – integration
5.4: Natural exponential functions – differentiation and integration
5.5: Bases other than e and applications
5.7: Inverse trigonometric functions – differentiation
5.8: Inverse trigonometric functions – integration
5.9: Hyperbolic functions
7.1: Area of a region between two curves