Calculus builds on itself, so the lessons learned in previous chapters will be required to solve problems in later chapters. You must master the earlier material to do well on the later material.
Important topics that you may not think are important but really are:
Algebra and algebraic manipulations/simplifications,
Exponential functions and exponential laws,
Logarithmic functions and logarithm laws, and
Trigonometric functions and trig identities.
Missing classes will result in gaps in your knowledge, and those gaps will make understanding calculus more difficult than it needs to be. If you miss class be sure to get the notes from a fellow student, or come and see me about what you have missed. But please make every effort not to miss class!
I try to structure lectures so that everyone can come out of them having learned something. However, attending lectures without doing the homework will not lead to a good understanding of calculus. To be honest, I doubt that it will lead to any understanding of calculus! Learning will come as you tackle problems yourself, using your mathematical skill and expertise to solve increasingly more complex problems.
Doing the homework is the single most important thing you can do to help yourself succeed in calculus! You will note that homework is not collected. This means that you are responsible to ensure that you are doing the homework, and you are responsible for seeking help when you have difficulties with the homework. You can seek help in a number of ways:
during office hours or by appointment with me,
in the math room in the library (Briggs 360), or
from your fellow classmates.
The notation of mathematics and presentation of solutions is an important component of problem solving in calculus. Without the proper notation, solutions become hard to decipher later, or the reasoning behind the solution can be difficult for the reader to see. Reaching the correct final answer to a problem without presenting a complete solution that is mathematically correct and easy for the reader to understand means the solution is incomplete (and sometimes, incorrect). As you construct solutions, you should write down what you are thinking, using English sentences where appropriate to help guide the reader (and usually, that reader will be you as you prepare for the final exam!).
Please talk to me as the course progresses--whether you are having difficulty or not! The journal entries should help facilitate discussions amongst us. There is more to calculus than can be covered in a single semester (or two); if you have questions about material we only cover briefly (or cover not at all!), I will be happy to discuss them with you at our leisure.
One of the goals I have when I teach calculus is that my students will be able to reflect at the end and see some connection between the topics we have covered. I am willing to work hard to help you reach this goal, but you must be willing to work equally hard. Do the homework, talk to me, talk to your peers, and take time periodically to reflect on what you are doing.
Calculus is like a mountain hike. The act of climbing the mountain may be difficult, but the view from the top is worth every challenge you met (and passed) on the climb up!