Incidentally, staple the pages of your homework together before handing them in.Īlways do as much of the homework assignment as you can first by yourself. It's better to include too much than too little. Frequently, you'll need whole sentences to explain what you're doing. Pepper your answers with words so that the reader knows why what you claim is the answer actually is the answer. There are loads of logical connectivessince, therefore, but, thus we have, substituting (some expression for a variable) we findin the examples, and you should include them in your answers, too. Look at the exercises and you see that almost every equation is preceded by a few words explaining what the equation is doing there. But many of the problems require more than simple computation. It's true that some of the problems are simple computation, and for those it's enough to present the computation. There should be as much detail in your written answers as you see in the exposition of the problems in the section. Then, without cramming in the answer, write it clearly. When you do write your answer sheet, copy the statement of the problem and any given diagram. Except for the easiest problems, you should work out the problem on scratch paper before writing it on your answer sheet. After you've worked out your solution to thequestion on paper (or in your head if it's particularly easy), enter your final answer.For practice exercises, if you don't have the right final answer, then you may get some helpin finding the right answer.įor some of the homework exercises you'll write written answers rather than using thesoftware to check your final answer.
#Calculus math question software
(More about that below.) The course software for on-lineexercises checks your answer and does more. These are not complete answers, but just the final line of the answer so you can check to see if you got it right. You'll find "answers" to the odd problems at the end of the book. Most of the problems on the homework assignment for the section are similar to the examples in the section. Only a couple of examples will be presented, and probably different ones, but the proofs will be presented in detail and discussed in class. You'll see the concepts explained again, but probably in different words. That's the end of step one: read the section, work out the examples and understand the meaning of the theorems. Out textbook does not include proofs we'll do those in class. In other words, you'll know what it means even if you don't know why it's true. You'll nearly always be able to understand the statement of the theorem without understanding the proof. When you come to a theorem, you'll see first the statement of the theorem. Remember, the proofs answer the question "why" the theorem is true. Sometimes an abbreviated proof is easier to comprehend, then the details fall into place. Some of the proofs in our course are "formal", that is, fairly complete, self-contained, logical justifications of the statements, but many ofour proofs are only outlines. You don't just accept a statement on faith, or on the authority of a book or instructor, but because you can prove it yourself. College mathematics is differenta logical justification is required before any mathematics can be accepted. Probably most of the mathematics you've seen before coming to college was presented to you as fact with little or no justification. A theorem is a mathematical statement that can be justified with a logical proof. A typical section has a dozen or half a dozen examples, starting with easier examples and working up to complicated examples. But for others you'll want to use your notepad to write down algebraic equations and do missing intermediate steps in order to understand the example better. For easier examples it's probably just enoughto read and understand them. Then follow through the exposition of the example. An example often has a question or two at the beginning to be answered. When you get to an example, read and understand the statement at the beginning of the example. Have a notepad with you so you can follow through the examples and proofs. Each section introduces concepts, often through formal definitions, has theorems with proofs, and has worked out examples illustrating the definitions and theorems. On your own, read through one section of a chapter. So how should you study calculus? It doesn't work the same way for everyone, but here's a suggested pattern. Math 120 Calculus I Math 121 Calculus II About studying mathematics in general,