You all know from previous math classes how one course will build upon the next, and calculus is no exception. Math 124 will introduce only one genuinely new idea, the concept of a "limit". The course then combines precalculus and algebra tools with "limits" to solve new types of problems. We will soon see that some calculations are very unforgiving, as far as algebra or precalculus mistakes are concerned.
Very few of you will go on to major in mathematics or computer science, but most of you will eventually see how calculus is applied in your chosen field of study. For this reason, we aim for ability to solve application problems using calculus. Some of the homework problems are quite lengthy and building up your "mathematical problem solving stamina" is just one of the aims of this course. If you have taken the Math 120 course at UW, you know what this all means. If you have not, it means that a large number of "word problems" ("story problems") or "multi-step problems" are encountered in the course. This is one key place Math 124 will differ from a typical high school course. In addition, it is important to note that the ability to apply calculus requires more than computational skill; it requires conceptual understanding.As you work through the homework, you will find two general types of problems: calculation/skill problems and multi-step/word problems. A good rule of thumb is to work enough of the skill problems to become proficient, then spend the bulk of your time working on the longer multi-step problems.
Misconception #1: Theory is irrelevant and the lectures should be aimed just at showing you how to do the problems.
The issue here is that we want you to be able to do ALL problems--not just particular kinds of problems--to which the methods of the course apply. For that level of command, the student must attain some conceptual understanding and develop judgment. Thus, a certain amount of theory is very relevant, indeed essential. A student who has been trained only to do certain kinds of problems has acquired very limited expertise.
Misconception #2: The purpose of the classes and assignments is to prepare the student for the exams.
The real purpose of the classes and homework is to guide you in achieving the aspiration of the course: command of the material. If you have command of the material, you should do well on the exams.
Misconception #3: It is the teacher's job to cover the material.
As covering the material is the role of the textbook, and the textbook is to be read by the student, the instructor should be doing something else, something that helps the student grasp the material. The instructor's role is to guide the students in their learning: to reinforce the essential conceptual points of the subject, and to show their relation to the solving of problems.
Misconception #4: Since you are supposed to be learning from the book, there's no need to go to the lectures.
The lectures, the reading, and the homework should combine to produce true comprehension of the material. For most students, reading a math text won't be easy. The lectures should serve to orient the student in learning the material.
Misconception #5: Since I did well in math, even calculus, in a good high school, I'll have no trouble with math at UW.
There is a different standard at the college level. Students will have to put in more effort in order to get a good grade than in high school (or equivalently, to learn the material sufficiently well by college standards).