Spring 2006 Math 1b Calculus Series and Differential Equations About Math 1b The goal of Math 1b is to provide you with a deep understanding of topics calculus as well as a strong sense of how useful mathematics can be and how you can apply mathematics in your work and studies Our aim is to provide you with a solid set of mathematical skills and a high degree of mathematical confidence when you finish the course so that you will be well equipped for future studies in mathematics biology chemistry economics or other disciplines To help you achieve these goals we will use multiple approaches to problem solving and we will stress understanding the ideas behind the mathematical formulas and techniques that you will learn Course Head Thomas W Judson Ph D Preceptor in Mathematics Office 429 Science Center Tel 617 495 5735 Email judson math harvard edu Office Hours Tuesdays at 2 3 PM Wednesdays at 6 7 PM Thursdays at 4 5 PM Course Web Site http www courses fas harvard edu math1b Course Goals To gain an appreciation of the conceptual structure of functions and calculus and differential equations To acquire a foundation of mathematical concepts needed in the natural and social sciences and to see how mathematics is influential in other disciplines To gain an appreciation of the role of mathematics in the modern world To gain some measure of the mathematical way of approaching and viewing the modern world To develop skills in numerical and symbolic computation mathematical reasoning and mathematical modeling To gain skills in learning and communicating mathematics Learning Objectives Upon successfully completing Math 1b you should have acquired a solid foundation of the following topics and be able to move directly into Mathematical Modeling Math 19 Introduction to Linear Al Math 1b Calculus Series and Differential Equations Spring 2006 1 Spring 2006 Math 1b Calculus Series and Differential Equations gebra and Multivariable Calculus Math 20 or multivariable calculus Math 21a depending on your interests Integration and Applications of the Definite Integral Techniques of integration numerical integration areas volumes arc length applications to the natural sciences and economics Infinite Sequences and Series sequences series testing for convergence power series and Taylor series Differential Equations Modeling differential equations from a numerical an analytical and a geometrical approach systems of differential equations Textbooks The textbook for this course is James Stewart Single Variable Calculus Concepts Context third edition Brooks Cole Belmont CA 2005 ISBN 0 534 41022 7 If you are plan to take Math 21a at some future date you may want to consider purchasing the edition of the textbook that covers both single and multivariable calculus ISBN 0 534 40986 5 Calculators A graphing calculator will be a tremendous asset in this course We encourage you to bring your calculator to class with you everyday If you are purchasing a calculator we recommend a Texas Instruments TI 84 TI 86 or TI 89 calculator With the advent of graphing calculators and mathematical software programs it is now possible to do an amazing number of things almost instantaneously that would otherwise take hours or days to do by hand Calculators can help you with your math skills and instincts by reducing the time you spend doing burdensome computations However you should not rely on computers and calculators to such an extent that they keep you from developing your own skills Technology should be used as an aid but without a good understanding of the underlying mathematical concepts the calculator will quite happily mislead you without your even knowing it In general technology is a good thing but as with everything sometimes too much of a good thing can lead to problems For this reason we generally do not allow calculators to be used on exams Grading and Exams Your course grade will be determined as follows Math 1b Calculus Series and Differential Equations Spring 2006 2 Spring 2006 Math 1b Calculus Series and Differential Equations Component Date Percentage Homework 20 Techniques Exam Wednesday February 22 at 6 7 PM PM in Science B Tuesday February 28 at 8 9 PM in Science B Re Test 10 Midterm I Tuesday March 14 2006 at 7 9 PM in Science B 20 Midterm II Tuesday April 18 2006 at 7 9 PM in Science B 20 Final Exam Tuesday May 23 2006 30 You need only take the techniques of integration exam one time If you choose to take this exam a second time we will count the higher of your two scores Semester numerical scores will be converted into letter grades according to the following method Range of Numerical Values Corresponding Letter Grade 100 90 A 89 80 B 79 65 C 64 50 D 49 0 E When we calculate your final grade at the end of the course we will calculate a score on a 0 100 point Math 1b Calculus Series and Differential Equations Spring 2006 3 Spring 2006 Math 1b Calculus Series and Differential Equations scale using the scores that you have obtained during the course and using the grade breakdown given above Your course grade will then be obtained using this table In the event of a fractional score we will always round up to the nearest integer We may modify these letter grades with a or a if we believe that your performance in the course warrants this Exam Policy Midterm exams are scheduled far in advance and it is impossible to move the time or date However in rare cases where it is impossible for an individual to take the exam at the scheduled time we will work with you to make other arrangements Exceptions for taking the exam out of sequence are the following 1 2 3 4 5 A medical excuse Please have your senior tutor or freshman dean contact us A University sponsored event such as an athletic tournament a play or a musical performance Your coach or director must contact us in advance Athletic practices and rehearsals do not fall into this category A religious holiday Please send a short email explaining the situation Extreme hardship such as a family emergency Please have your senior tutor or freshman dean contact us A class conflict Please send us your complete schedule Labs or a sections that can be rescheduled do not fall into this category The above are the only allowable excuses for taking the exam before the scheduled time Under no circumstances do we give late exams Since we can only accommodate a limited number of students taking the exam at an earlier time please make sure that you fall into one of the above