| MATHEMATICS 53: ELEMENTARY ANALYSIS I |
Lecture Notes Lecture 0: Exercises on Derivative Lecture 1: Higher-Order Derivatives Lecture 2: Rectilinear Motion and Instantaneous Rates of Change Lecture 3: The Cost/Revenue Function and the Marginal Cost/Revenue Lecture 4: Related Rates Lecture 5: Linear Approximations and Differentials Lecture 6: Relative Extrema and Absolute Extrema Lecture 7: Applications Involving Absolute Extrema on a Closed Interval Lecture 8: The Rolle's Theorem and the Mean Value Theorem Lecture 9: The First Derivative Test (Increasing and Decreasing Functions) Lecture 10: The Second Derivatie Test (Concavity and Points of Inflection) Lecture 11: Additional Exercises on Optimization and Sketching of Graphs Lecture 12: Antidifferenatiation Lecture 13: Techniques of Antidifferentiation Lecture 14: Differential Equations (will not be included in the exams) Lecture 15: The Area Under the Curve Lecture 16: Definite Integral Lecture 17: Theorems for Definite Integrals Lecture 18: Exercises on Areas of a Plane Region Lecture 19: Volume of Solids Using the Disk / Washer Method Lecture 20: Volume of Solids Using the Cylindrical Shell Method Lecture 21: The Length of an Smooth Arc |
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| Prepared by: Jose Maria L. Escaner IV, Ph.D. |