Math 16A - Analytic Geometry and Calculus -- [3 units]
Course Format: Three hours of lecture, one and one-half hours of discussion per week.
Prerequisites: Three years of high school math, including trigonometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic exam, or 32. Consult the mathematics department for details.
Credit Restrictions: Students will receive no credit for 16A after taking 1A.
Description: Calculus of one variable; derivatives, definite integrals and applications, maxima and minima, and applications of the exponential and logarithmic functions. The sequence Math 16A, 16B is intended for students outside the physical sciences and engineering whose major requirements are satisfied by one or both courses, and who do not plan to take more advanced mathematics courses. (F,SP)
Textbook: Lial, Greenwell, Ritchey, Calculus with Applications, 11th Edition
| Outline of the Course: | |
| Chapter 1: Linear Functions Linear functions, straight lines, supply and demand, revenue, profit, cost. |
2 hours |
| Chapter 2: Nonlinear Functions Properties of functions, quadratic functions, exponential and logarithmic functions, compound interest. |
4 hours |
| Chapter 13: The Trigonometric Functions Definitions of the trigonometric functions. |
1 hours |
| Chapter 3: The Derivative Limits, continuity, rate of change, the derivative, graphical methods. |
6.5 hours |
| Chapter 4: Calculating the Derivative Techniques for finding the derivative, the product and quotient rules, the chain rule, derivatives of exponential and logarithmic functions. |
5 hours |
| Chapter 13: The Trigonometric Functions Derivatives of trigonometric functions. |
1 hours |
| Chapter 12: Sequences and Series L'Hospital's rule. (Optional) |
0.5 hours |
| Chapter 5: Graphs and Derivatives Increasing and decreasing functions, relative extrema, higher derivatives and concavity, curve sketching. |
5 hours |
| Chapter 6: Applications of the Derivative Absolute extrema, optimization applications, economics applications, implicit differentiation, related rates. |
6 hours |
| Chapter 7: Integration Antiderivatives, substitution, area and the definite integral, the fundamental theorem of calculus, areas between curves, consumer surplus. |
7 hours |
| Total | 38 hours |
| Midterms & Holidays | 4 hours |
| Reviews are appropriate during the RRR week. The total number of class hours may vary during the Fall and Spring semesters. |
42 hours |