Mathematics 10C Syllabus (December 2010) 1Lecture schedule based on Hughes-Hallet, et. al. Calculus, fifth edition[See next page for explanatory comments.]Section Lectures Topic8.7 1.5 Distribution Functions8.8 1.5 Probability, Mean, and Median9.2 1 Geometric Series10.1 1 Taylor Polynomials12.1 1 Functions of Two Variables12.2 1 Graphs of Functions of Two Variables12.3 1 Contour Diagrams12.4 1 Linear Functions13.1 1 Displacement Vectors13.2 1 Vectors in General13.3 1 The Dot Product13.4 1 The Cross Product114.1 1 The Partial Derivative14.2 1 Computing Partial Derivatives Algebraically14.3 1 Local Linearity and the Differential14.4 1.5 Gradients and Directional Derivatives in the Plane14.6 1 The Chain Rule14.7 1 Second-Order Partial Derivatives15.1 1.5 Local Extrema15.2 1.5 Optimization15.3 1.5 Constrained Optimization: Lagrange MultipliersNote: The following topics may be discussed at the discretion of the instructor as time p ermits;however, some may be more technical than is appr op riate for Math 10 and some care should beexercised when deciding which to includ e.Section Lectures Topic12.5 0.5 Functions of Three Variables12.6 1 Limits and Continu ity14.5 1 Gradients and Directional Derivatives in Space14.8 1 Differentiability1skip “Areas and Volumes Using the Cross Product and Determinants”, pg 713-714Mathematics 10C Syllabus (December 2010) 2Mathematics 10A and 10B are single-variable differential and integral calculus courses intendedfor majors in life and social sciences. The most common majors are biology and economics. Thesequence continues with multivariable calculus (10C) or elementary probability and statistics (11).The course meets three times a week in large sections conducted by the instructor. The s tudentsalso meet in smaller (about 30-35 students) recitation sections once each week; these sections areconducted by teaching assistants. A f ou rth hour is reserved for each class: It m ay be used atthe instructor’s discretion for various activities including quizzes, m idterm exams, review sessions,extended office hours, and make-up lectures. Throughout the year, the Mathematics Departmentmakes a Calculus Lab available to students every weekday with undergraduate tutors staffing theLab. Math 10A in the Fall, 10B in the Winter, and 10C in the Spring are coordinated and followa common calendar agreed upon by the instructors with common homework assignments, quizzes,midterms, and final examination.Students are encouraged to use graphing calculators at times throughout the sequence. Calculatorsare used to facilitate computation and graphing, but such uses are always to facilitate mathemat-ical understanding so that learning how to use the calculator should never be a primary focus ofthe course. Instructors, teaching assistants, and the staff of the Calculus Lab will expected tosupport the TI-83, which is the recommended calculator for the sequence. The use of calculatorson quizzes, midterms, and final examinations is at th e discretion of the instructor; in some ofthose situations calculators with Computer Algebra Systems may be forbidden. Students may usegraphing calculators other than the TI-83 at their own r isk since no assistance will be provided forthese.The principal goal of Math 10ABC is for students to develop a solid understanding of the fun-damental ideas of calculus. As a result, the emphasis is on developing a good understanding ofwhy the ideas and procedures of calculus make sense. While a certain level of tech nical proficiencyis essential for that und ers tanding, more attention should be given to presenting rationales forunderlying concepts and results and their applications than to proofs that may be too formal forthe stud ents or to intricate technical processes. Whenever possib le, applications should be chosenfrom areas that are likely to be of interest to the students, with special emphases on biology an deconomics. The text often retreats to a level of formality that is probably inappropriate for thisclass; this should be a caution to the faculty not to replicate th at error (from our point of view),but rather to try to complement it with greater attention to informal motivating arguments whenpossible. Similarly, some of the problems in the text appear to be more intricate and technical thanis suitable for the students in this course; consequently, some care sh ou ld be taken in assigninghomework to assure that students develop needed technical competency along the way to acquiringsolid understanding without being overwhelmed by inappropriate technical difficulties.The sequence of topics in the text may not be everyone’s first choice. The extent to which it shouldbe followed d epends upon the degree of coordination among instructors in addition to dependingupon each instructor’s taste. For simplicity, the cours e outlines presented here follow the order ofthe topics in the text. Similarly, the time allotted to each section represents our best estimate ofthe time that is need for the section in the context of a course with 30 or slightly fewer