Homepage for Math 1A
Calculus -- [4 units]
Course Format: Three hours of lecture and two hours of discussion/workshop per week; at the discretion of the instructor, an additional hour of discussion/workshop or computer laboratory per week.
Prerequisites: Three and one-half years of high school math, including trigonometry and analytic geometry, plus a satisfactory grade in one of the following: CEEB MAT test, an AP test, the UC/CSU math diagnostic test, or 32. Consult the mathematics department for details. Students with AP credit should consider choosing a course more advanced than 1A.
Credit Option: Students will receive no credit for 1A after taking 16B and 2 units after taking 16A.
Description: This sequence is intended for majors in engineering and the physical sciences. An introduction to differential and integral calculus of functions of one variable, with applications and an introduction to transcendental functions. (F,SP)
Textbook: Stewart, Single Variable, Essential Calculus, Early Transcendentals, Student Edition, University of California, Berkeley (Index for Paperback Edition of Math 1A Textbook)
Outline of the Course:
Chapter 1: Functions and Limits
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6 hours
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Spend no more than one hour on pages 31-32 and spend no more than one hour on pages 64-65.
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Chapter 2: Derivatives
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9 hours
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Emphasize 2.2. Before 2.3 remind students about the properties of trigonometric functions (pages A1-A9 in Appendix A in Stewart, Essential Calculus, Instructors Edition).
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Chapter 3: Inverse Functions
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8 hours
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Before 3.1 remind the students about the rules for exponential functions. Before 3.2 remind the students about logarithms. Go slowly on all aspects of inverse functions.
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Chapter 4: Applications of Differentiation
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8 hours
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Chapter 5: Integrals
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6 hours
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If time permits discuss "logarithms defined as an integral" (see pages A31-A33 in Appendix D in Stewart, Essential Calculus, Instructors Edition).
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Chapter 7: Applications of Integrals
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3 hours
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Cover no more than sections 7.1, 7.2, and 7.3.
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Total
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40 hours
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Midterms
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2 hours
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Holidays & Reviews
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3 hours
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45 hours
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Warning: The student edition is missing the appendices with the detailed proofs, "the logarithm defined as an integral" and "general exponential functions". It has second order ODE (1B), but is missing linear equations (which however can be found on the website). Section 9.6 in the student edition contains the material from the solution manual for section 9.7 of Stewart: Calculus, Early Transcendentals, 5th edition, but the Lotka-Volterra theory is neither in the book, nor the website: stewartcalculus.com. Notice that population growth and Newtons law of cooling has moved from second semester to first.
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